univariate probability distribution: Topics by WorldWideScience.org

Sample records for univariate probability distribution

Evaluation of droplet size distributions using univariate and multivariate approaches.

Science.gov (United States)

Gaunø, Mette Høg; Larsen, Crilles Casper; Vilhelmsen, Thomas; Møller-Sonnergaard, Jørn; Wittendorff, Jørgen; Rantanen, Jukka

2013-01-01

Pharmaceutically relevant material characteristics are often analyzed based on univariate descriptors instead of utilizing the whole information available in the full distribution. One example is droplet size distribution, which is often described by the median droplet size and the width of the distribution. The current study was aiming to compare univariate and multivariate approach in evaluating droplet size distributions. As a model system, the atomization of a coating solution from a two-fluid nozzle was investigated. The effect of three process parameters (concentration of ethyl cellulose in ethanol, atomizing air pressure, and flow rate of coating solution) on the droplet size and droplet size distribution using a full mixed factorial design was used. The droplet size produced by a two-fluid nozzle was measured by laser diffraction and reported as volume based size distribution. Investigation of loading and score plots from principal component analysis (PCA) revealed additional information on the droplet size distributions and it was possible to identify univariate statistics (volume median droplet size), which were similar, however, originating from varying droplet size distributions. The multivariate data analysis was proven to be an efficient tool for evaluating the full information contained in a distribution.
Evaluation of droplet size distributions using univariate and multivariate approaches

DEFF Research Database (Denmark)

Gauno, M.H.; Larsen, C.C.; Vilhelmsen, T.

2013-01-01

of the distribution. The current study was aiming to compare univariate and multivariate approach in evaluating droplet size distributions. As a model system, the atomization of a coating solution from a two-fluid nozzle was investigated. The effect of three process parameters (concentration of ethyl cellulose...... in ethanol, atomizing air pressure, and flow rate of coating solution) on the droplet size and droplet size distribution using a full mixed factorial design was used. The droplet size produced by a two-fluid nozzle was measured by laser diffraction and reported as volume based size distribution....... Investigation of loading and score plots from principal component analysis (PCA) revealed additional information on the droplet size distributions and it was possible to identify univariate statistics (volume median droplet size), which were similar, however, originating from varying droplet size distributions...
Log-concave Probability Distributions: Theory and Statistical Testing

DEFF Research Database (Denmark)

An, Mark Yuing

1996-01-01

This paper studies the broad class of log-concave probability distributions that arise in economics of uncertainty and information. For univariate, continuous, and log-concave random variables we prove useful properties without imposing the differentiability of density functions. Discrete...... and multivariate distributions are also discussed. We propose simple non-parametric testing procedures for log-concavity. The test statistics are constructed to test one of the two implicati ons of log-concavity: increasing hazard rates and new-is-better-than-used (NBU) property. The test for increasing hazard...... rates are based on normalized spacing of the sample order statistics. The tests for NBU property fall into the category of Hoeffding's U-statistics...
COVAL, Compound Probability Distribution for Function of Probability Distribution

International Nuclear Information System (INIS)

Astolfi, M.; Elbaz, J.

1979-01-01

1 - Nature of the physical problem solved: Computation of the probability distribution of a function of variables, given the probability distribution of the variables themselves. 'COVAL' has been applied to reliability analysis of a structure subject to random loads. 2 - Method of solution: Numerical transformation of probability distributions
Probability theory for 3-layer remote sensing radiative transfer model: univariate case.

Science.gov (United States)

Ben-David, Avishai; Davidson, Charles E

2012-04-23

A probability model for a 3-layer radiative transfer model (foreground layer, cloud layer, background layer, and an external source at the end of line of sight) has been developed. The 3-layer model is fundamentally important as the primary physical model in passive infrared remote sensing. The probability model is described by the Johnson family of distributions that are used as a fit for theoretically computed moments of the radiative transfer model. From the Johnson family we use the SU distribution that can address a wide range of skewness and kurtosis values (in addition to addressing the first two moments, mean and variance). In the limit, SU can also describe lognormal and normal distributions. With the probability model one can evaluate the potential for detecting a target (vapor cloud layer), the probability of observing thermal contrast, and evaluate performance (receiver operating characteristics curves) in clutter-noise limited scenarios. This is (to our knowledge) the first probability model for the 3-layer remote sensing geometry that treats all parameters as random variables and includes higher-order statistics. © 2012 Optical Society of America
Universal Probability Distribution Function for Bursty Transport in Plasma Turbulence

International Nuclear Information System (INIS)

Sandberg, I.; Benkadda, S.; Garbet, X.; Ropokis, G.; Hizanidis, K.; Castillo-Negrete, D. del

2009-01-01

Bursty transport phenomena associated with convective motion present universal statistical characteristics among different physical systems. In this Letter, a stochastic univariate model and the associated probability distribution function for the description of bursty transport in plasma turbulence is presented. The proposed stochastic process recovers the universal distribution of density fluctuations observed in plasma edge of several magnetic confinement devices and the remarkable scaling between their skewness S and kurtosis K. Similar statistical characteristics of variabilities have been also observed in other physical systems that are characterized by convection such as the x-ray fluctuations emitted by the Cygnus X-1 accretion disc plasmas and the sea surface temperature fluctuations.
Uncertainty of Hydrological Drought Characteristics with Copula Functions and Probability Distributions: A Case Study of Weihe River, China

Directory of Open Access Journals (Sweden)

Panpan Zhao

2017-05-01

Full Text Available This study investigates the sensitivity and uncertainty of hydrological droughts frequencies and severity in the Weihe Basin, China during 1960–2012, by using six commonly used univariate probability distributions and three Archimedean copulas to fit the marginal and joint distributions of drought characteristics. The Anderson-Darling method is used for testing the goodness-of-fit of the univariate model, and the Akaike information criterion (AIC is applied to select the best distribution and copula functions. The results demonstrate that there is a very strong correlation between drought duration and drought severity in three stations. The drought return period varies depending on the selected marginal distributions and copula functions and, with an increase of the return period, the differences become larger. In addition, the estimated return periods (both co-occurrence and joint from the best-fitted copulas are the closet to those from empirical distribution. Therefore, it is critical to select the appropriate marginal distribution and copula function to model the hydrological drought frequency and severity. The results of this study can not only help drought investigation to select a suitable probability distribution and copulas function, but are also useful for regional water resource management. However, a few limitations remain in this study, such as the assumption of stationary of runoff series.
New Riemannian Priors on the Univariate Normal Model

Directory of Open Access Journals (Sweden)

Salem Said

2014-07-01

Full Text Available The current paper introduces new prior distributions on the univariate normal model, with the aim of applying them to the classification of univariate normal populations. These new prior distributions are entirely based on the Riemannian geometry of the univariate normal model, so that they can be thought of as “Riemannian priors”. Precisely, if {pθ ; θ ∈ Θ} is any parametrization of the univariate normal model, the paper considers prior distributions G( θ - , γ with hyperparameters θ - ∈ Θ and γ > 0, whose density with respect to Riemannian volume is proportional to exp(−d2(θ, θ - /2γ2, where d2(θ, θ - is the square of Rao’s Riemannian distance. The distributions G( θ - , γ are termed Gaussian distributions on the univariate normal model. The motivation for considering a distribution G( θ - , γ is that this distribution gives a geometric representation of a class or cluster of univariate normal populations. Indeed, G( θ - , γ has a unique mode θ - (precisely, θ - is the unique Riemannian center of mass of G( θ - , γ, as shown in the paper, and its dispersion away from θ - is given by γ. Therefore, one thinks of members of the class represented by G( θ - , γ as being centered around θ - and lying within a typical distance determined by γ. The paper defines rigorously the Gaussian distributions G( θ - , γ and describes an algorithm for computing maximum likelihood estimates of their hyperparameters. Based on this algorithm and on the Laplace approximation, it describes how the distributions G( θ - , γ can be used as prior distributions for Bayesian classification of large univariate normal populations. In a concrete application to texture image classification, it is shown that this leads to an improvement in performance over the use of conjugate priors.
Pre-Aggregation with Probability Distributions

DEFF Research Database (Denmark)

Timko, Igor; Dyreson, Curtis E.; Pedersen, Torben Bach

2006-01-01

Motivated by the increasing need to analyze complex, uncertain multidimensional data this paper proposes probabilistic OLAP queries that are computed using probability distributions rather than atomic values. The paper describes how to create probability distributions from base data, and how...... the distributions can be subsequently used in pre-aggregation. Since the probability distributions can become large, we show how to achieve good time and space efficiency by approximating the distributions. We present the results of several experiments that demonstrate the effectiveness of our methods. The work...... is motivated with a real-world case study, based on our collaboration with a leading Danish vendor of location-based services. This paper is the first to consider the approximate processing of probabilistic OLAP queries over probability distributions....
Automatic Image Segmentation Using Active Contours with Univariate Marginal Distribution

Directory of Open Access Journals (Sweden)

I. Cruz-Aceves

2013-01-01

Full Text Available This paper presents a novel automatic image segmentation method based on the theory of active contour models and estimation of distribution algorithms. The proposed method uses the univariate marginal distribution model to infer statistical dependencies between the control points on different active contours. These contours have been generated through an alignment process of reference shape priors, in order to increase the exploration and exploitation capabilities regarding different interactive segmentation techniques. This proposed method is applied in the segmentation of the hollow core in microscopic images of photonic crystal fibers and it is also used to segment the human heart and ventricular areas from datasets of computed tomography and magnetic resonance images, respectively. Moreover, to evaluate the performance of the medical image segmentations compared to regions outlined by experts, a set of similarity measures has been adopted. The experimental results suggest that the proposed image segmentation method outperforms the traditional active contour model and the interactive Tseng method in terms of segmentation accuracy and stability.
Pre-aggregation for Probability Distributions

DEFF Research Database (Denmark)

Timko, Igor; Dyreson, Curtis E.; Pedersen, Torben Bach

Motivated by the increasing need to analyze complex uncertain multidimensional data (e.g., in order to optimize and personalize location-based services), this paper proposes novel types of {\\em probabilistic} OLAP queries that operate on aggregate values that are probability distributions...... and the techniques to process these queries. The paper also presents the methods for computing the probability distributions, which enables pre-aggregation, and for using the pre-aggregated distributions for further aggregation. In order to achieve good time and space efficiency, the methods perform approximate...... multidimensional data analysis that is considered in this paper (i.e., approximate processing of probabilistic OLAP queries over probability distributions)....
Bayesian optimization for computationally extensive probability distributions.

Science.gov (United States)

Tamura, Ryo; Hukushima, Koji

2018-01-01

An efficient method for finding a better maximizer of computationally extensive probability distributions is proposed on the basis of a Bayesian optimization technique. A key idea of the proposed method is to use extreme values of acquisition functions by Gaussian processes for the next training phase, which should be located near a local maximum or a global maximum of the probability distribution. Our Bayesian optimization technique is applied to the posterior distribution in the effective physical model estimation, which is a computationally extensive probability distribution. Even when the number of sampling points on the posterior distributions is fixed to be small, the Bayesian optimization provides a better maximizer of the posterior distributions in comparison to those by the random search method, the steepest descent method, or the Monte Carlo method. Furthermore, the Bayesian optimization improves the results efficiently by combining the steepest descent method and thus it is a powerful tool to search for a better maximizer of computationally extensive probability distributions.
Lower bounds on the run time of the univariate marginal distribution algorithm on OneMax

DEFF Research Database (Denmark)

Krejca, Martin S.; Witt, Carsten

2017-01-01

The Univariate Marginal Distribution Algorithm (UMDA), a popular estimation of distribution algorithm, is studied from a run time perspective. On the classical OneMax benchmark function, a lower bound of Ω(μ√n + n log n), where μ is the population size, on its expected run time is proved...... values maintained by the algorithm, including carefully designed potential functions. These techniques may prove useful in advancing the field of run time analysis for estimation of distribution algorithms in general........ This is the first direct lower bound on the run time of the UMDA. It is stronger than the bounds that follow from general black-box complexity theory and is matched by the run time of many evolutionary algorithms. The results are obtained through advanced analyses of the stochastic change of the frequencies of bit...
Univariate and multivariate skewness and kurtosis for measuring nonnormality: Prevalence, influence and estimation.

Science.gov (United States)

Cain, Meghan K; Zhang, Zhiyong; Yuan, Ke-Hai

2017-10-01

Nonnormality of univariate data has been extensively examined previously (Blanca et al., Methodology: European Journal of Research Methods for the Behavioral and Social Sciences, 9(2), 78-84, 2013; Miceeri, Psychological Bulletin, 105(1), 156, 1989). However, less is known of the potential nonnormality of multivariate data although multivariate analysis is commonly used in psychological and educational research. Using univariate and multivariate skewness and kurtosis as measures of nonnormality, this study examined 1,567 univariate distriubtions and 254 multivariate distributions collected from authors of articles published in Psychological Science and the American Education Research Journal. We found that 74 % of univariate distributions and 68 % multivariate distributions deviated from normal distributions. In a simulation study using typical values of skewness and kurtosis that we collected, we found that the resulting type I error rates were 17 % in a t-test and 30 % in a factor analysis under some conditions. Hence, we argue that it is time to routinely report skewness and kurtosis along with other summary statistics such as means and variances. To facilitate future report of skewness and kurtosis, we provide a tutorial on how to compute univariate and multivariate skewness and kurtosis by SAS, SPSS, R and a newly developed Web application.
Joint Probability Distributions for a Class of Non-Markovian Processes

OpenAIRE

Baule, A.; Friedrich, R.

2004-01-01

We consider joint probability distributions for the class of coupled Langevin equations introduced by Fogedby [H.C. Fogedby, Phys. Rev. E 50, 1657 (1994)]. We generalize well-known results for the single time probability distributions to the case of N-time joint probability distributions. It is shown that these probability distribution functions can be obtained by an integral transform from distributions of a Markovian process. The integral kernel obeys a partial differential equation with fr...
Fitness Probability Distribution of Bit-Flip Mutation.

Science.gov (United States)

Chicano, Francisco; Sutton, Andrew M; Whitley, L Darrell; Alba, Enrique

2015-01-01

Bit-flip mutation is a common mutation operator for evolutionary algorithms applied to optimize functions over binary strings. In this paper, we develop results from the theory of landscapes and Krawtchouk polynomials to exactly compute the probability distribution of fitness values of a binary string undergoing uniform bit-flip mutation. We prove that this probability distribution can be expressed as a polynomial in p, the probability of flipping each bit. We analyze these polynomials and provide closed-form expressions for an easy linear problem (Onemax), and an NP-hard problem, MAX-SAT. We also discuss a connection of the results with runtime analysis.
Joint probability distributions for a class of non-Markovian processes.

Science.gov (United States)

Baule, A; Friedrich, R

2005-02-01

We consider joint probability distributions for the class of coupled Langevin equations introduced by Fogedby [H. C. Fogedby, Phys. Rev. E 50, 1657 (1994)]. We generalize well-known results for the single-time probability distributions to the case of N -time joint probability distributions. It is shown that these probability distribution functions can be obtained by an integral transform from distributions of a Markovian process. The integral kernel obeys a partial differential equation with fractional time derivatives reflecting the non-Markovian character of the process.
Bayesian Prior Probability Distributions for Internal Dosimetry

Energy Technology Data Exchange (ETDEWEB)

Miller, G.; Inkret, W.C.; Little, T.T.; Martz, H.F.; Schillaci, M.E

2001-07-01

The problem of choosing a prior distribution for the Bayesian interpretation of measurements (specifically internal dosimetry measurements) is considered using a theoretical analysis and by examining historical tritium and plutonium urine bioassay data from Los Alamos. Two models for the prior probability distribution are proposed: (1) the log-normal distribution, when there is some additional information to determine the scale of the true result, and (2) the 'alpha' distribution (a simplified variant of the gamma distribution) when there is not. These models have been incorporated into version 3 of the Bayesian internal dosimetric code in use at Los Alamos (downloadable from our web site). Plutonium internal dosimetry at Los Alamos is now being done using prior probability distribution parameters determined self-consistently from population averages of Los Alamos data. (author)
Some applications of the fractional Poisson probability distribution

International Nuclear Information System (INIS)

Laskin, Nick

2009-01-01

Physical and mathematical applications of the recently invented fractional Poisson probability distribution have been presented. As a physical application, a new family of quantum coherent states has been introduced and studied. As mathematical applications, we have developed the fractional generalization of Bell polynomials, Bell numbers, and Stirling numbers of the second kind. The appearance of fractional Bell polynomials is natural if one evaluates the diagonal matrix element of the evolution operator in the basis of newly introduced quantum coherent states. Fractional Stirling numbers of the second kind have been introduced and applied to evaluate the skewness and kurtosis of the fractional Poisson probability distribution function. A representation of the Bernoulli numbers in terms of fractional Stirling numbers of the second kind has been found. In the limit case when the fractional Poisson probability distribution becomes the Poisson probability distribution, all of the above listed developments and implementations turn into the well-known results of the quantum optics and the theory of combinatorial numbers.
Incorporating Skew into RMS Surface Roughness Probability Distribution

Science.gov (United States)

Stahl, Mark T.; Stahl, H. Philip.

2013-01-01

The standard treatment of RMS surface roughness data is the application of a Gaussian probability distribution. This handling of surface roughness ignores the skew present in the surface and overestimates the most probable RMS of the surface, the mode. Using experimental data we confirm the Gaussian distribution overestimates the mode and application of an asymmetric distribution provides a better fit. Implementing the proposed asymmetric distribution into the optical manufacturing process would reduce the polishing time required to meet surface roughness specifications.

Probability Distributome: A Web Computational Infrastructure for Exploring the Properties, Interrelations, and Applications of Probability Distributions.

Science.gov (United States)

Dinov, Ivo D; Siegrist, Kyle; Pearl, Dennis K; Kalinin, Alexandr; Christou, Nicolas

2016-06-01

Probability distributions are useful for modeling, simulation, analysis, and inference on varieties of natural processes and physical phenomena. There are uncountably many probability distributions. However, a few dozen families of distributions are commonly defined and are frequently used in practice for problem solving, experimental applications, and theoretical studies. In this paper, we present a new computational and graphical infrastructure, the Distributome , which facilitates the discovery, exploration and application of diverse spectra of probability distributions. The extensible Distributome infrastructure provides interfaces for (human and machine) traversal, search, and navigation of all common probability distributions. It also enables distribution modeling, applications, investigation of inter-distribution relations, as well as their analytical representations and computational utilization. The entire Distributome framework is designed and implemented as an open-source, community-built, and Internet-accessible infrastructure. It is portable, extensible and compatible with HTML5 and Web2.0 standards (http://Distributome.org). We demonstrate two types of applications of the probability Distributome resources: computational research and science education. The Distributome tools may be employed to address five complementary computational modeling applications (simulation, data-analysis and inference, model-fitting, examination of the analytical, mathematical and computational properties of specific probability distributions, and exploration of the inter-distributional relations). Many high school and college science, technology, engineering and mathematics (STEM) courses may be enriched by the use of modern pedagogical approaches and technology-enhanced methods. The Distributome resources provide enhancements for blended STEM education by improving student motivation, augmenting the classical curriculum with interactive webapps, and overhauling the
Proposal for Modified Damage Probability Distribution Functions

DEFF Research Database (Denmark)

Pedersen, Preben Terndrup; Hansen, Peter Friis

1996-01-01

Immidiately following the Estonia disaster, the Nordic countries establishe a project entitled "Safety of Passenger/RoRo Vessels" As part of this project the present proposal for modified damage stability probability distribution functions has been developed. and submitted to "Sub-committee on st......Immidiately following the Estonia disaster, the Nordic countries establishe a project entitled "Safety of Passenger/RoRo Vessels" As part of this project the present proposal for modified damage stability probability distribution functions has been developed. and submitted to "Sub...
Converting dose distributions into tumour control probability

International Nuclear Information System (INIS)

Nahum, A.E.

1996-01-01

The endpoints in radiotherapy that are truly of relevance are not dose distributions but the probability of local control, sometimes known as the Tumour Control Probability (TCP) and the Probability of Normal Tissue Complications (NTCP). A model for the estimation of TCP based on simple radiobiological considerations is described. It is shown that incorporation of inter-patient heterogeneity into the radiosensitivity parameter a through s a can result in a clinically realistic slope for the dose-response curve. The model is applied to inhomogeneous target dose distributions in order to demonstrate the relationship between dose uniformity and s a . The consequences of varying clonogenic density are also explored. Finally the model is applied to the target-volume DVHs for patients in a clinical trial of conformal pelvic radiotherapy; the effect of dose inhomogeneities on distributions of TCP are shown as well as the potential benefits of customizing the target dose according to normal-tissue DVHs. (author). 37 refs, 9 figs
Converting dose distributions into tumour control probability

Energy Technology Data Exchange (ETDEWEB)

Nahum, A E [The Royal Marsden Hospital, London (United Kingdom). Joint Dept. of Physics

1996-08-01

The endpoints in radiotherapy that are truly of relevance are not dose distributions but the probability of local control, sometimes known as the Tumour Control Probability (TCP) and the Probability of Normal Tissue Complications (NTCP). A model for the estimation of TCP based on simple radiobiological considerations is described. It is shown that incorporation of inter-patient heterogeneity into the radiosensitivity parameter a through s{sub a} can result in a clinically realistic slope for the dose-response curve. The model is applied to inhomogeneous target dose distributions in order to demonstrate the relationship between dose uniformity and s{sub a}. The consequences of varying clonogenic density are also explored. Finally the model is applied to the target-volume DVHs for patients in a clinical trial of conformal pelvic radiotherapy; the effect of dose inhomogeneities on distributions of TCP are shown as well as the potential benefits of customizing the target dose according to normal-tissue DVHs. (author). 37 refs, 9 figs.
STADIC: a computer code for combining probability distributions

International Nuclear Information System (INIS)

Cairns, J.J.; Fleming, K.N.

1977-03-01

The STADIC computer code uses a Monte Carlo simulation technique for combining probability distributions. The specific function for combination of the input distribution is defined by the user by introducing the appropriate FORTRAN statements to the appropriate subroutine. The code generates a Monte Carlo sampling from each of the input distributions and combines these according to the user-supplied function to provide, in essence, a random sampling of the combined distribution. When the desired number of samples is obtained, the output routine calculates the mean, standard deviation, and confidence limits for the resultant distribution. This method of combining probability distributions is particularly useful in cases where analytical approaches are either too difficult or undefined
High throughput nonparametric probability density estimation.

Science.gov (United States)

Farmer, Jenny; Jacobs, Donald

2018-01-01

In high throughput applications, such as those found in bioinformatics and finance, it is important to determine accurate probability distribution functions despite only minimal information about data characteristics, and without using human subjectivity. Such an automated process for univariate data is implemented to achieve this goal by merging the maximum entropy method with single order statistics and maximum likelihood. The only required properties of the random variables are that they are continuous and that they are, or can be approximated as, independent and identically distributed. A quasi-log-likelihood function based on single order statistics for sampled uniform random data is used to empirically construct a sample size invariant universal scoring function. Then a probability density estimate is determined by iteratively improving trial cumulative distribution functions, where better estimates are quantified by the scoring function that identifies atypical fluctuations. This criterion resists under and over fitting data as an alternative to employing the Bayesian or Akaike information criterion. Multiple estimates for the probability density reflect uncertainties due to statistical fluctuations in random samples. Scaled quantile residual plots are also introduced as an effective diagnostic to visualize the quality of the estimated probability densities. Benchmark tests show that estimates for the probability density function (PDF) converge to the true PDF as sample size increases on particularly difficult test probability densities that include cases with discontinuities, multi-resolution scales, heavy tails, and singularities. These results indicate the method has general applicability for high throughput statistical inference.
Evidence for Truncated Exponential Probability Distribution of Earthquake Slip

KAUST Repository

Thingbaijam, Kiran Kumar; Mai, Paul Martin

2016-01-01

Earthquake ruptures comprise spatially varying slip on the fault surface, where slip represents the displacement discontinuity between the two sides of the rupture plane. In this study, we analyze the probability distribution of coseismic slip, which provides important information to better understand earthquake source physics. Although the probability distribution of slip is crucial for generating realistic rupture scenarios for simulation-based seismic and tsunami-hazard analysis, the statistical properties of earthquake slip have received limited attention so far. Here, we use the online database of earthquake source models (SRCMOD) to show that the probability distribution of slip follows the truncated exponential law. This law agrees with rupture-specific physical constraints limiting the maximum possible slip on the fault, similar to physical constraints on maximum earthquake magnitudes.We show the parameters of the best-fitting truncated exponential distribution scale with average coseismic slip. This scaling property reflects the control of the underlying stress distribution and fault strength on the rupture dimensions, which determines the average slip. Thus, the scale-dependent behavior of slip heterogeneity is captured by the probability distribution of slip. We conclude that the truncated exponential law accurately quantifies coseismic slip distribution and therefore allows for more realistic modeling of rupture scenarios. © 2016, Seismological Society of America. All rights reserverd.
Evidence for Truncated Exponential Probability Distribution of Earthquake Slip

KAUST Repository

Thingbaijam, Kiran K. S.

2016-07-13

Earthquake ruptures comprise spatially varying slip on the fault surface, where slip represents the displacement discontinuity between the two sides of the rupture plane. In this study, we analyze the probability distribution of coseismic slip, which provides important information to better understand earthquake source physics. Although the probability distribution of slip is crucial for generating realistic rupture scenarios for simulation-based seismic and tsunami-hazard analysis, the statistical properties of earthquake slip have received limited attention so far. Here, we use the online database of earthquake source models (SRCMOD) to show that the probability distribution of slip follows the truncated exponential law. This law agrees with rupture-specific physical constraints limiting the maximum possible slip on the fault, similar to physical constraints on maximum earthquake magnitudes.We show the parameters of the best-fitting truncated exponential distribution scale with average coseismic slip. This scaling property reflects the control of the underlying stress distribution and fault strength on the rupture dimensions, which determines the average slip. Thus, the scale-dependent behavior of slip heterogeneity is captured by the probability distribution of slip. We conclude that the truncated exponential law accurately quantifies coseismic slip distribution and therefore allows for more realistic modeling of rupture scenarios. © 2016, Seismological Society of America. All rights reserverd.
APPROXIMATION OF PROBABILITY DISTRIBUTIONS IN QUEUEING MODELS

Directory of Open Access Journals (Sweden)

T. I. Aliev

2013-03-01

Full Text Available For probability distributions with variation coefficient, not equal to unity, mathematical dependences for approximating distributions on the basis of first two moments are derived by making use of multi exponential distributions. It is proposed to approximate distributions with coefficient of variation less than unity by using hypoexponential distribution, which makes it possible to generate random variables with coefficient of variation, taking any value in a range (0; 1, as opposed to Erlang distribution, having only discrete values of coefficient of variation.
Probability distributions with truncated, log and bivariate extensions

CERN Document Server

Thomopoulos, Nick T

2018-01-01

This volume presents a concise and practical overview of statistical methods and tables not readily available in other publications. It begins with a review of the commonly used continuous and discrete probability distributions. Several useful distributions that are not so common and less understood are described with examples and applications in full detail: discrete normal, left-partial, right-partial, left-truncated normal, right-truncated normal, lognormal, bivariate normal, and bivariate lognormal. Table values are provided with examples that enable researchers to easily apply the distributions to real applications and sample data. The left- and right-truncated normal distributions offer a wide variety of shapes in contrast to the symmetrically shaped normal distribution, and a newly developed spread ratio enables analysts to determine which of the three distributions best fits a particular set of sample data. The book will be highly useful to anyone who does statistical and probability analysis. This in...
Fitting the Probability Distribution Functions to Model Particulate Matter Concentrations

International Nuclear Information System (INIS)

El-Shanshoury, Gh.I.

2017-01-01

The main objective of this study is to identify the best probability distribution and the plotting position formula for modeling the concentrations of Total Suspended Particles (TSP) as well as the Particulate Matter with an aerodynamic diameter<10 μm (PM 10 ). The best distribution provides the estimated probabilities that exceed the threshold limit given by the Egyptian Air Quality Limit value (EAQLV) as well the number of exceedance days is estimated. The standard limits of the EAQLV for TSP and PM 10 concentrations are 24-h average of 230 μg/m 3 and 70 μg/m 3 , respectively. Five frequency distribution functions with seven formula of plotting positions (empirical cumulative distribution functions) are compared to fit the average of daily TSP and PM 10 concentrations in year 2014 for Ain Sokhna city. The Quantile-Quantile plot (Q-Q plot) is used as a method for assessing how closely a data set fits a particular distribution. A proper probability distribution that represents the TSP and PM 10 has been chosen based on the statistical performance indicator values. The results show that Hosking and Wallis plotting position combined with Frechet distribution gave the highest fit for TSP and PM 10 concentrations. Burr distribution with the same plotting position follows Frechet distribution. The exceedance probability and days over the EAQLV are predicted using Frechet distribution. In 2014, the exceedance probability and days for TSP concentrations are 0.052 and 19 days, respectively. Furthermore, the PM 10 concentration is found to exceed the threshold limit by 174 days
Predictive probability methods for interim monitoring in clinical trials with longitudinal outcomes.

Science.gov (United States)

Zhou, Ming; Tang, Qi; Lang, Lixin; Xing, Jun; Tatsuoka, Kay

2018-04-17

In clinical research and development, interim monitoring is critical for better decision-making and minimizing the risk of exposing patients to possible ineffective therapies. For interim futility or efficacy monitoring, predictive probability methods are widely adopted in practice. Those methods have been well studied for univariate variables. However, for longitudinal studies, predictive probability methods using univariate information from only completers may not be most efficient, and data from on-going subjects can be utilized to improve efficiency. On the other hand, leveraging information from on-going subjects could allow an interim analysis to be potentially conducted once a sufficient number of subjects reach an earlier time point. For longitudinal outcomes, we derive closed-form formulas for predictive probabilities, including Bayesian predictive probability, predictive power, and conditional power and also give closed-form solutions for predictive probability of success in a future trial and the predictive probability of success of the best dose. When predictive probabilities are used for interim monitoring, we study their distributions and discuss their analytical cutoff values or stopping boundaries that have desired operating characteristics. We show that predictive probabilities utilizing all longitudinal information are more efficient for interim monitoring than that using information from completers only. To illustrate their practical application for longitudinal data, we analyze 2 real data examples from clinical trials. Copyright © 2018 John Wiley & Sons, Ltd.
Segmentation of Coronary Angiograms Using Gabor Filters and Boltzmann Univariate Marginal Distribution Algorithm

Directory of Open Access Journals (Sweden)

Fernando Cervantes-Sanchez

2016-01-01

Full Text Available This paper presents a novel method for improving the training step of the single-scale Gabor filters by using the Boltzmann univariate marginal distribution algorithm (BUMDA in X-ray angiograms. Since the single-scale Gabor filters (SSG are governed by three parameters, the optimal selection of the SSG parameters is highly desirable in order to maximize the detection performance of coronary arteries while reducing the computational time. To obtain the best set of parameters for the SSG, the area (Az under the receiver operating characteristic curve is used as fitness function. Moreover, to classify vessel and nonvessel pixels from the Gabor filter response, the interclass variance thresholding method has been adopted. The experimental results using the proposed method obtained the highest detection rate with Az=0.9502 over a training set of 40 images and Az=0.9583 with a test set of 40 images. In addition, the experimental results of vessel segmentation provided an accuracy of 0.944 with the test set of angiograms.
Modeling highway travel time distribution with conditional probability models

Energy Technology Data Exchange (ETDEWEB)

Oliveira Neto, Francisco Moraes [ORNL; Chin, Shih-Miao [ORNL; Hwang, Ho-Ling [ORNL; Han, Lee [University of Tennessee, Knoxville (UTK)

2014-01-01

ABSTRACT Under the sponsorship of the Federal Highway Administration's Office of Freight Management and Operations, the American Transportation Research Institute (ATRI) has developed performance measures through the Freight Performance Measures (FPM) initiative. Under this program, travel speed information is derived from data collected using wireless based global positioning systems. These telemetric data systems are subscribed and used by trucking industry as an operations management tool. More than one telemetric operator submits their data dumps to ATRI on a regular basis. Each data transmission contains truck location, its travel time, and a clock time/date stamp. Data from the FPM program provides a unique opportunity for studying the upstream-downstream speed distributions at different locations, as well as different time of the day and day of the week. This research is focused on the stochastic nature of successive link travel speed data on the continental United States Interstates network. Specifically, a method to estimate route probability distributions of travel time is proposed. This method uses the concepts of convolution of probability distributions and bivariate, link-to-link, conditional probability to estimate the expected distributions for the route travel time. Major contribution of this study is the consideration of speed correlation between upstream and downstream contiguous Interstate segments through conditional probability. The established conditional probability distributions, between successive segments, can be used to provide travel time reliability measures. This study also suggests an adaptive method for calculating and updating route travel time distribution as new data or information is added. This methodology can be useful to estimate performance measures as required by the recent Moving Ahead for Progress in the 21st Century Act (MAP 21).
Calculating Cumulative Binomial-Distribution Probabilities

Science.gov (United States)

Scheuer, Ernest M.; Bowerman, Paul N.

1989-01-01

Cumulative-binomial computer program, CUMBIN, one of set of three programs, calculates cumulative binomial probability distributions for arbitrary inputs. CUMBIN, NEWTONP (NPO-17556), and CROSSER (NPO-17557), used independently of one another. Reliabilities and availabilities of k-out-of-n systems analyzed. Used by statisticians and users of statistical procedures, test planners, designers, and numerical analysts. Used for calculations of reliability and availability. Program written in C.
Modeling the probability distribution of peak discharge for infiltrating hillslopes

Science.gov (United States)

Baiamonte, Giorgio; Singh, Vijay P.

2017-07-01

Hillslope response plays a fundamental role in the prediction of peak discharge at the basin outlet. The peak discharge for the critical duration of rainfall and its probability distribution are needed for designing urban infrastructure facilities. This study derives the probability distribution, denoted as GABS model, by coupling three models: (1) the Green-Ampt model for computing infiltration, (2) the kinematic wave model for computing discharge hydrograph from the hillslope, and (3) the intensity-duration-frequency (IDF) model for computing design rainfall intensity. The Hortonian mechanism for runoff generation is employed for computing the surface runoff hydrograph. Since the antecedent soil moisture condition (ASMC) significantly affects the rate of infiltration, its effect on the probability distribution of peak discharge is investigated. Application to a watershed in Sicily, Italy, shows that with the increase of probability, the expected effect of ASMC to increase the maximum discharge diminishes. Only for low values of probability, the critical duration of rainfall is influenced by ASMC, whereas its effect on the peak discharge seems to be less for any probability. For a set of parameters, the derived probability distribution of peak discharge seems to be fitted by the gamma distribution well. Finally, an application to a small watershed, with the aim to test the possibility to arrange in advance the rational runoff coefficient tables to be used for the rational method, and a comparison between peak discharges obtained by the GABS model with those measured in an experimental flume for a loamy-sand soil were carried out.
Most probable degree distribution at fixed structural entropy

Indian Academy of Sciences (India)

Here we derive the most probable degree distribution emerging ... the structural entropy of power-law networks is an increasing function of the expo- .... tition function Z of the network as the sum over all degree distributions, with given energy.
Geometry of q-Exponential Family of Probability Distributions

Directory of Open Access Journals (Sweden)

Shun-ichi Amari

2011-06-01

Full Text Available The Gibbs distribution of statistical physics is an exponential family of probability distributions, which has a mathematical basis of duality in the form of the Legendre transformation. Recent studies of complex systems have found lots of distributions obeying the power law rather than the standard Gibbs type distributions. The Tsallis q-entropy is a typical example capturing such phenomena. We treat the q-Gibbs distribution or the q-exponential family by generalizing the exponential function to the q-family of power functions, which is useful for studying various complex or non-standard physical phenomena. We give a new mathematical structure to the q-exponential family different from those previously given. It has a dually flat geometrical structure derived from the Legendre transformation and the conformal geometry is useful for understanding it. The q-version of the maximum entropy theorem is naturally induced from the q-Pythagorean theorem. We also show that the maximizer of the q-escort distribution is a Bayesian MAP (Maximum A posteriori Probability estimator.
Comparative analysis through probability distributions of a data set

Science.gov (United States)

Cristea, Gabriel; Constantinescu, Dan Mihai

2018-02-01

In practice, probability distributions are applied in such diverse fields as risk analysis, reliability engineering, chemical engineering, hydrology, image processing, physics, market research, business and economic research, customer support, medicine, sociology, demography etc. This article highlights important aspects of fitting probability distributions to data and applying the analysis results to make informed decisions. There are a number of statistical methods available which can help us to select the best fitting model. Some of the graphs display both input data and fitted distributions at the same time, as probability density and cumulative distribution. The goodness of fit tests can be used to determine whether a certain distribution is a good fit. The main used idea is to measure the "distance" between the data and the tested distribution, and compare that distance to some threshold values. Calculating the goodness of fit statistics also enables us to order the fitted distributions accordingly to how good they fit to data. This particular feature is very helpful for comparing the fitted models. The paper presents a comparison of most commonly used goodness of fit tests as: Kolmogorov-Smirnov, Anderson-Darling, and Chi-Squared. A large set of data is analyzed and conclusions are drawn by visualizing the data, comparing multiple fitted distributions and selecting the best model. These graphs should be viewed as an addition to the goodness of fit tests.
The return period analysis of natural disasters with statistical modeling of bivariate joint probability distribution.

Science.gov (United States)

Li, Ning; Liu, Xueqin; Xie, Wei; Wu, Jidong; Zhang, Peng

2013-01-01

New features of natural disasters have been observed over the last several years. The factors that influence the disasters' formation mechanisms, regularity of occurrence and main characteristics have been revealed to be more complicated and diverse in nature than previously thought. As the uncertainty involved increases, the variables need to be examined further. This article discusses the importance and the shortage of multivariate analysis of natural disasters and presents a method to estimate the joint probability of the return periods and perform a risk analysis. Severe dust storms from 1990 to 2008 in Inner Mongolia were used as a case study to test this new methodology, as they are normal and recurring climatic phenomena on Earth. Based on the 79 investigated events and according to the dust storm definition with bivariate, the joint probability distribution of severe dust storms was established using the observed data of maximum wind speed and duration. The joint return periods of severe dust storms were calculated, and the relevant risk was analyzed according to the joint probability. The copula function is able to simulate severe dust storm disasters accurately. The joint return periods generated are closer to those observed in reality than the univariate return periods and thus have more value in severe dust storm disaster mitigation, strategy making, program design, and improvement of risk management. This research may prove useful in risk-based decision making. The exploration of multivariate analysis methods can also lay the foundation for further applications in natural disaster risk analysis. © 2012 Society for Risk Analysis.

Predicting the probability of slip in gait: methodology and distribution study.

Science.gov (United States)

Gragg, Jared; Yang, James

2016-01-01

The likelihood of a slip is related to the available and required friction for a certain activity, here gait. Classical slip and fall analysis presumed that a walking surface was safe if the difference between the mean available and required friction coefficients exceeded a certain threshold. Previous research was dedicated to reformulating the classical slip and fall theory to include the stochastic variation of the available and required friction when predicting the probability of slip in gait. However, when predicting the probability of a slip, previous researchers have either ignored the variation in the required friction or assumed the available and required friction to be normally distributed. Also, there are no published results that actually give the probability of slip for various combinations of required and available frictions. This study proposes a modification to the equation for predicting the probability of slip, reducing the previous equation from a double-integral to a more convenient single-integral form. Also, a simple numerical integration technique is provided to predict the probability of slip in gait: the trapezoidal method. The effect of the random variable distributions on the probability of slip is also studied. It is shown that both the required and available friction distributions cannot automatically be assumed as being normally distributed. The proposed methods allow for any combination of distributions for the available and required friction, and numerical results are compared to analytical solutions for an error analysis. The trapezoidal method is shown to be highly accurate and efficient. The probability of slip is also shown to be sensitive to the input distributions of the required and available friction. Lastly, a critical value for the probability of slip is proposed based on the number of steps taken by an average person in a single day.
Assigning probability distributions to input parameters of performance assessment models

Energy Technology Data Exchange (ETDEWEB)

Mishra, Srikanta [INTERA Inc., Austin, TX (United States)

2002-02-01

This study presents an overview of various approaches for assigning probability distributions to input parameters and/or future states of performance assessment models. Specifically,three broad approaches are discussed for developing input distributions: (a) fitting continuous distributions to data, (b) subjective assessment of probabilities, and (c) Bayesian updating of prior knowledge based on new information. The report begins with a summary of the nature of data and distributions, followed by a discussion of several common theoretical parametric models for characterizing distributions. Next, various techniques are presented for fitting continuous distributions to data. These include probability plotting, method of moments, maximum likelihood estimation and nonlinear least squares analysis. The techniques are demonstrated using data from a recent performance assessment study for the Yucca Mountain project. Goodness of fit techniques are also discussed, followed by an overview of how distribution fitting is accomplished in commercial software packages. The issue of subjective assessment of probabilities is dealt with in terms of the maximum entropy distribution selection approach, as well as some common rules for codifying informal expert judgment. Formal expert elicitation protocols are discussed next, and are based primarily on the guidance provided by the US NRC. The Bayesian framework for updating prior distributions (beliefs) when new information becomes available is discussed. A simple numerical approach is presented for facilitating practical applications of the Bayes theorem. Finally, a systematic framework for assigning distributions is presented: (a) for the situation where enough data are available to define an empirical CDF or fit a parametric model to the data, and (b) to deal with the situation where only a limited amount of information is available.
Assigning probability distributions to input parameters of performance assessment models

International Nuclear Information System (INIS)

Mishra, Srikanta

2002-02-01

This study presents an overview of various approaches for assigning probability distributions to input parameters and/or future states of performance assessment models. Specifically,three broad approaches are discussed for developing input distributions: (a) fitting continuous distributions to data, (b) subjective assessment of probabilities, and (c) Bayesian updating of prior knowledge based on new information. The report begins with a summary of the nature of data and distributions, followed by a discussion of several common theoretical parametric models for characterizing distributions. Next, various techniques are presented for fitting continuous distributions to data. These include probability plotting, method of moments, maximum likelihood estimation and nonlinear least squares analysis. The techniques are demonstrated using data from a recent performance assessment study for the Yucca Mountain project. Goodness of fit techniques are also discussed, followed by an overview of how distribution fitting is accomplished in commercial software packages. The issue of subjective assessment of probabilities is dealt with in terms of the maximum entropy distribution selection approach, as well as some common rules for codifying informal expert judgment. Formal expert elicitation protocols are discussed next, and are based primarily on the guidance provided by the US NRC. The Bayesian framework for updating prior distributions (beliefs) when new information becomes available is discussed. A simple numerical approach is presented for facilitating practical applications of the Bayes theorem. Finally, a systematic framework for assigning distributions is presented: (a) for the situation where enough data are available to define an empirical CDF or fit a parametric model to the data, and (b) to deal with the situation where only a limited amount of information is available
Multivariate phase type distributions - Applications and parameter estimation

DEFF Research Database (Denmark)

Meisch, David

The best known univariate probability distribution is the normal distribution. It is used throughout the literature in a broad field of applications. In cases where it is not sensible to use the normal distribution alternative distributions are at hand and well understood, many of these belonging...... and statistical inference, is the multivariate normal distribution. Unfortunately only little is known about the general class of multivariate phase type distribution. Considering the results concerning parameter estimation and inference theory of univariate phase type distributions, the class of multivariate...... projects and depend on reliable cost estimates. The Successive Principle is a group analysis method primarily used for analyzing medium to large projects in relation to cost or duration. We believe that the mathematical modeling used in the Successive Principle can be improved. We suggested a novel...
Probability Distribution for Flowing Interval Spacing

International Nuclear Information System (INIS)

Kuzio, S.

2001-01-01

The purpose of this analysis is to develop a probability distribution for flowing interval spacing. A flowing interval is defined as a fractured zone that transmits flow in the Saturated Zone (SZ), as identified through borehole flow meter surveys (Figure 1). This analysis uses the term ''flowing interval spacing'' as opposed to fractured spacing, which is typically used in the literature. The term fracture spacing was not used in this analysis because the data used identify a zone (or a flowing interval) that contains fluid-conducting fractures but does not distinguish how many or which fractures comprise the flowing interval. The flowing interval spacing is measured between the midpoints of each flowing interval. Fracture spacing within the SZ is defined as the spacing between fractures, with no regard to which fractures are carrying flow. The Development Plan associated with this analysis is entitled, ''Probability Distribution for Flowing Interval Spacing'', (CRWMS M and O 2000a). The parameter from this analysis may be used in the TSPA SR/LA Saturated Zone Flow and Transport Work Direction and Planning Documents: (1) ''Abstraction of Matrix Diffusion for SZ Flow and Transport Analyses'' (CRWMS M and O 1999a) and (2) ''Incorporation of Heterogeneity in SZ Flow and Transport Analyses'', (CRWMS M and O 1999b). A limitation of this analysis is that the probability distribution of flowing interval spacing may underestimate the effect of incorporating matrix diffusion processes in the SZ transport model because of the possible overestimation of the flowing interval spacing. Larger flowing interval spacing results in a decrease in the matrix diffusion processes. This analysis may overestimate the flowing interval spacing because the number of fractures that contribute to a flowing interval cannot be determined from the data. Because each flowing interval probably has more than one fracture contributing to a flowing interval, the true flowing interval spacing could be
Information-theoretic methods for estimating of complicated probability distributions

CERN Document Server

Zong, Zhi

2006-01-01

Mixing up various disciplines frequently produces something that are profound and far-reaching. Cybernetics is such an often-quoted example. Mix of information theory, statistics and computing technology proves to be very useful, which leads to the recent development of information-theory based methods for estimating complicated probability distributions. Estimating probability distribution of a random variable is the fundamental task for quite some fields besides statistics, such as reliability, probabilistic risk analysis (PSA), machine learning, pattern recognization, image processing, neur
A Probability Distribution over Latent Causes, in the Orbitofrontal Cortex.

Science.gov (United States)

Chan, Stephanie C Y; Niv, Yael; Norman, Kenneth A

2016-07-27

The orbitofrontal cortex (OFC) has been implicated in both the representation of "state," in studies of reinforcement learning and decision making, and also in the representation of "schemas," in studies of episodic memory. Both of these cognitive constructs require a similar inference about the underlying situation or "latent cause" that generates our observations at any given time. The statistically optimal solution to this inference problem is to use Bayes' rule to compute a posterior probability distribution over latent causes. To test whether such a posterior probability distribution is represented in the OFC, we tasked human participants with inferring a probability distribution over four possible latent causes, based on their observations. Using fMRI pattern similarity analyses, we found that BOLD activity in the OFC is best explained as representing the (log-transformed) posterior distribution over latent causes. Furthermore, this pattern explained OFC activity better than other task-relevant alternatives, such as the most probable latent cause, the most recent observation, or the uncertainty over latent causes. Our world is governed by hidden (latent) causes that we cannot observe, but which generate the observations we see. A range of high-level cognitive processes require inference of a probability distribution (or "belief distribution") over the possible latent causes that might be generating our current observations. This is true for reinforcement learning and decision making (where the latent cause comprises the true "state" of the task), and for episodic memory (where memories are believed to be organized by the inferred situation or "schema"). Using fMRI, we show that this belief distribution over latent causes is encoded in patterns of brain activity in the orbitofrontal cortex, an area that has been separately implicated in the representations of both states and schemas. Copyright © 2016 the authors 0270-6474/16/367817-12$15.00/0.
Probability distributions for Markov chain based quantum walks

Science.gov (United States)

Balu, Radhakrishnan; Liu, Chaobin; Venegas-Andraca, Salvador E.

2018-01-01

We analyze the probability distributions of the quantum walks induced from Markov chains by Szegedy (2004). The first part of this paper is devoted to the quantum walks induced from finite state Markov chains. It is shown that the probability distribution on the states of the underlying Markov chain is always convergent in the Cesaro sense. In particular, we deduce that the limiting distribution is uniform if the transition matrix is symmetric. In the case of a non-symmetric Markov chain, we exemplify that the limiting distribution of the quantum walk is not necessarily identical with the stationary distribution of the underlying irreducible Markov chain. The Szegedy scheme can be extended to infinite state Markov chains (random walks). In the second part, we formulate the quantum walk induced from a lazy random walk on the line. We then obtain the weak limit of the quantum walk. It is noted that the current quantum walk appears to spread faster than its counterpart-quantum walk on the line driven by the Grover coin discussed in literature. The paper closes with an outlook on possible future directions.
Evaluation of burst probability for tubes by Weibull distributions

International Nuclear Information System (INIS)

Kao, S.

1975-10-01

The investigations of candidate distributions that best describe the burst pressure failure probability characteristics of nuclear power steam generator tubes has been continued. To date it has been found that the Weibull distribution provides an acceptable fit for the available data from both the statistical and physical viewpoints. The reasons for the acceptability of the Weibull distribution are stated together with the results of tests for the suitability of fit. In exploring the acceptability of the Weibull distribution for the fitting, a graphical method to be called the ''density-gram'' is employed instead of the usual histogram. With this method a more sensible graphical observation on the empirical density may be made for cases where the available data is very limited. Based on these methods estimates of failure pressure are made for the left-tail probabilities
Confidence intervals for the lognormal probability distribution

International Nuclear Information System (INIS)

Smith, D.L.; Naberejnev, D.G.

2004-01-01

The present communication addresses the topic of symmetric confidence intervals for the lognormal probability distribution. This distribution is frequently utilized to characterize inherently positive, continuous random variables that are selected to represent many physical quantities in applied nuclear science and technology. The basic formalism is outlined herein and a conjured numerical example is provided for illustration. It is demonstrated that when the uncertainty reflected in a lognormal probability distribution is large, the use of a confidence interval provides much more useful information about the variable used to represent a particular physical quantity than can be had by adhering to the notion that the mean value and standard deviation of the distribution ought to be interpreted as best value and corresponding error, respectively. Furthermore, it is shown that if the uncertainty is very large a disturbing anomaly can arise when one insists on interpreting the mean value and standard deviation as the best value and corresponding error, respectively. Reliance on using the mode and median as alternative parameters to represent the best available knowledge of a variable with large uncertainties is also shown to entail limitations. Finally, a realistic physical example involving the decay of radioactivity over a time period that spans many half-lives is presented and analyzed to further illustrate the concepts discussed in this communication
Simulation of Daily Weather Data Using Theoretical Probability Distributions.

Science.gov (United States)

Bruhn, J. A.; Fry, W. E.; Fick, G. W.

1980-09-01

A computer simulation model was constructed to supply daily weather data to a plant disease management model for potato late blight. In the weather model Monte Carlo techniques were employed to generate daily values of precipitation, maximum temperature, minimum temperature, minimum relative humidity and total solar radiation. Each weather variable is described by a known theoretical probability distribution but the values of the parameters describing each distribution are dependent on the occurrence of rainfall. Precipitation occurrence is described by a first-order Markov chain. The amount of rain, given that rain has occurred, is described by a gamma probability distribution. Maximum and minimum temperature are simulated with a trivariate normal probability distribution involving maximum temperature on the previous day, maximum temperature on the current day and minimum temperature on the current day. Parameter values for this distribution are dependent on the occurrence of rain on the previous day. Both minimum relative humidity and total solar radiation are assumed to be normally distributed. The values of the parameters describing the distribution of minimum relative humidity is dependent on rainfall occurrence on the previous day and current day. Parameter values for total solar radiation are dependent on the occurrence of rain on the current day. The assumptions made during model construction were found to be appropriate for actual weather data from Geneva, New York. The performance of the weather model was evaluated by comparing the cumulative frequency distributions of simulated weather data with the distributions of actual weather data from Geneva, New York and Fort Collins, Colorado. For each location, simulated weather data were similar to actual weather data in terms of mean response, variability and autocorrelation. The possible applications of this model when used with models of other components of the agro-ecosystem are discussed.
Multiobjective fuzzy stochastic linear programming problems with inexact probability distribution

Energy Technology Data Exchange (ETDEWEB)

Hamadameen, Abdulqader Othman [Optimization, Department of Mathematical Sciences, Faculty of Science, UTM (Malaysia); Zainuddin, Zaitul Marlizawati [Department of Mathematical Sciences, Faculty of Science, UTM (Malaysia)

2014-06-19

This study deals with multiobjective fuzzy stochastic linear programming problems with uncertainty probability distribution which are defined as fuzzy assertions by ambiguous experts. The problem formulation has been presented and the two solutions strategies are; the fuzzy transformation via ranking function and the stochastic transformation when α{sup –}. cut technique and linguistic hedges are used in the uncertainty probability distribution. The development of Sen’s method is employed to find a compromise solution, supported by illustrative numerical example.
Time dependent and asymptotic neutron number probability distribution calculation using discrete Fourier transform

International Nuclear Information System (INIS)

Humbert, Ph.

2005-01-01

In this paper we consider the probability distribution of neutrons in a multiplying assembly. The problem is studied using a space independent one group neutron point reactor model without delayed neutrons. We recall the generating function methodology and analytical results obtained by G.I. Bell when the c 2 approximation is used and we present numerical solutions in the general case, without this approximation. The neutron source induced distribution is calculated using the single initial neutron distribution which satisfies a master (Kolmogorov backward) equation. This equation is solved using the generating function method. The generating function satisfies a differential equation and the probability distribution is derived by inversion of the generating function. Numerical results are obtained using the same methodology where the generating function is the Fourier transform of the probability distribution. Discrete Fourier transforms are used to calculate the discrete time dependent distributions and continuous Fourier transforms are used to calculate the asymptotic continuous probability distributions. Numerical applications are presented to illustrate the method. (author)
The exact probability distribution of the rank product statistics for replicated experiments.

Science.gov (United States)

Eisinga, Rob; Breitling, Rainer; Heskes, Tom

2013-03-18

The rank product method is a widely accepted technique for detecting differentially regulated genes in replicated microarray experiments. To approximate the sampling distribution of the rank product statistic, the original publication proposed a permutation approach, whereas recently an alternative approximation based on the continuous gamma distribution was suggested. However, both approximations are imperfect for estimating small tail probabilities. In this paper we relate the rank product statistic to number theory and provide a derivation of its exact probability distribution and the true tail probabilities. Copyright © 2013 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.
Feynman quasi probability distribution for spin-(1/2), and its generalizations

International Nuclear Information System (INIS)

Colucci, M.

1999-01-01

It has been examined the Feynman's paper Negative probability, in which, after a discussion about the possibility of attributing a real physical meaning to quasi probability distributions, he introduces a new kind of distribution for spin-(1/2), with a possible method of generalization to systems with arbitrary number of states. The principal aim of this article is to shed light upon the method of construction of these distributions, taking into consideration their application to some experiments, and discussing their positive and negative aspects
Influence of dose distribution homogeneity on the tumor control probability in heavy-ion radiotherapy

International Nuclear Information System (INIS)

Wen Xiaoqiong; Li Qiang; Zhou Guangming; Li Wenjian; Wei Zengquan

2001-01-01

In order to estimate the influence of the un-uniform dose distribution on the clinical treatment result, the Influence of dose distribution homogeneity on the tumor control probability was investigated. Basing on the formula deduced previously for survival fraction of cells irradiated by the un-uniform heavy-ion irradiation field and the theory of tumor control probability, the tumor control probability was calculated for a tumor mode exposed to different dose distribution homogeneity. The results show that the tumor control probability responding to the same total dose will decrease if the dose distribution homogeneity gets worse. In clinical treatment, the dose distribution homogeneity should be better than 95%
Separating the contributions of variability and parameter uncertainty in probability distributions

International Nuclear Information System (INIS)

Sankararaman, S.; Mahadevan, S.

2013-01-01

This paper proposes a computational methodology to quantify the individual contributions of variability and distribution parameter uncertainty to the overall uncertainty in a random variable. Even if the distribution type is assumed to be known, sparse or imprecise data leads to uncertainty about the distribution parameters. If uncertain distribution parameters are represented using probability distributions, then the random variable can be represented using a family of probability distributions. The family of distributions concept has been used to obtain qualitative, graphical inference of the contributions of natural variability and distribution parameter uncertainty. The proposed methodology provides quantitative estimates of the contributions of the two types of uncertainty. Using variance-based global sensitivity analysis, the contributions of variability and distribution parameter uncertainty to the overall uncertainty are computed. The proposed method is developed at two different levels; first, at the level of a variable whose distribution parameters are uncertain, and second, at the level of a model output whose inputs have uncertain distribution parameters
VC-dimension of univariate decision trees.

Science.gov (United States)

Yildiz, Olcay Taner

2015-02-01

In this paper, we give and prove the lower bounds of the Vapnik-Chervonenkis (VC)-dimension of the univariate decision tree hypothesis class. The VC-dimension of the univariate decision tree depends on the VC-dimension values of its subtrees and the number of inputs. Via a search algorithm that calculates the VC-dimension of univariate decision trees exhaustively, we show that our VC-dimension bounds are tight for simple trees. To verify that the VC-dimension bounds are useful, we also use them to get VC-generalization bounds for complexity control using structural risk minimization in decision trees, i.e., pruning. Our simulation results show that structural risk minimization pruning using the VC-dimension bounds finds trees that are more accurate as those pruned using cross validation.
The distributed failure probability approach to dependent failure analysis, and its application

International Nuclear Information System (INIS)

Hughes, R.P.

1989-01-01

The Distributed Failure Probability (DFP) approach to the problem of dependent failures in systems is presented. The basis of the approach is that the failure probability of a component is a variable. The source of this variability is the change in the 'environment' of the component, where the term 'environment' is used to mean not only obvious environmental factors such as temperature etc., but also such factors as the quality of maintenance and manufacture. The failure probability is distributed among these various 'environments' giving rise to the Distributed Failure Probability method. Within the framework which this method represents, modelling assumptions can be made, based both on engineering judgment and on the data directly. As such, this DFP approach provides a soundly based and scrutable technique by which dependent failures can be quantitatively assessed. (orig.)
Superthermal photon bunching in terms of simple probability distributions

Science.gov (United States)

Lettau, T.; Leymann, H. A. M.; Melcher, B.; Wiersig, J.

2018-05-01

We analyze the second-order photon autocorrelation function g(2 ) with respect to the photon probability distribution and discuss the generic features of a distribution that results in superthermal photon bunching [g(2 )(0 ) >2 ]. Superthermal photon bunching has been reported for a number of optical microcavity systems that exhibit processes such as superradiance or mode competition. We show that a superthermal photon number distribution cannot be constructed from the principle of maximum entropy if only the intensity and the second-order autocorrelation are given. However, for bimodal systems, an unbiased superthermal distribution can be constructed from second-order correlations and the intensities alone. Our findings suggest modeling superthermal single-mode distributions by a mixture of a thermal and a lasinglike state and thus reveal a generic mechanism in the photon probability distribution responsible for creating superthermal photon bunching. We relate our general considerations to a physical system, i.e., a (single-emitter) bimodal laser, and show that its statistics can be approximated and understood within our proposed model. Furthermore, the excellent agreement of the statistics of the bimodal laser and our model reveals that the bimodal laser is an ideal source of bunched photons, in the sense that it can generate statistics that contain no other features but the superthermal bunching.

Generalization of Poisson distribution for the case of changing probability of consequential events

International Nuclear Information System (INIS)

Kushnirenko, E.

1995-01-01

The generalization of the Poisson distribution for the case of changing probabilities of the consequential events is done. It is shown that the classical Poisson distribution is the special case of this generalized distribution when the probabilities of the consequential events are constant. The using of the generalized Poisson distribution gives the possibility in some cases to obtain analytical result instead of making Monte-Carlo calculation
Family of probability distributions derived from maximal entropy principle with scale invariant restrictions.

Science.gov (United States)

Sonnino, Giorgio; Steinbrecher, György; Cardinali, Alessandro; Sonnino, Alberto; Tlidi, Mustapha

2013-01-01

Using statistical thermodynamics, we derive a general expression of the stationary probability distribution for thermodynamic systems driven out of equilibrium by several thermodynamic forces. The local equilibrium is defined by imposing the minimum entropy production and the maximum entropy principle under the scale invariance restrictions. The obtained probability distribution presents a singularity that has immediate physical interpretation in terms of the intermittency models. The derived reference probability distribution function is interpreted as time and ensemble average of the real physical one. A generic family of stochastic processes describing noise-driven intermittency, where the stationary density distribution coincides exactly with the one resulted from entropy maximization, is presented.
Study on probability distribution of fire scenarios in risk assessment to emergency evacuation

International Nuclear Information System (INIS)

Chu Guanquan; Wang Jinhui

2012-01-01

Event tree analysis (ETA) is a frequently-used technique to analyze the probability of probable fire scenario. The event probability is usually characterized by definite value. It is not appropriate to use definite value as these estimates may be the result of poor quality statistics and limited knowledge. Without addressing uncertainties, ETA will give imprecise results. The credibility of risk assessment will be undermined. This paper presents an approach to address event probability uncertainties and analyze probability distribution of probable fire scenario. ETA is performed to construct probable fire scenarios. The activation time of every event is characterized as stochastic variable by considering uncertainties of fire growth rate and other input variables. To obtain probability distribution of probable fire scenario, Markov Chain is proposed to combine with ETA. To demonstrate the approach, a case study is presented.
A new expression of the probability distribution in Incomplete Statistics and fundamental thermodynamic relations

International Nuclear Information System (INIS)

Huang Zhifu; Lin Bihong; ChenJincan

2009-01-01

In order to overcome the limitations of the original expression of the probability distribution appearing in literature of Incomplete Statistics, a new expression of the probability distribution is derived, where the Lagrange multiplier β introduced here is proved to be identical with that introduced in the second and third choices for the internal energy constraint in Tsallis' statistics and to be just equal to the physical inverse temperature. It is expounded that the probability distribution described by the new expression is invariant through uniform translation of the energy spectrum. Moreover, several fundamental thermodynamic relations are given and the relationship between the new and the original expressions of the probability distribution is discussed.
Collective motions of globally coupled oscillators and some probability distributions on circle

Energy Technology Data Exchange (ETDEWEB)

Jaćimović, Vladimir [Faculty of Natural Sciences and Mathematics, University of Montenegro, Cetinjski put, bb., 81000 Podgorica (Montenegro); Crnkić, Aladin, E-mail: aladin.crnkic@hotmail.com [Faculty of Technical Engineering, University of Bihać, Ljubijankićeva, bb., 77000 Bihać, Bosnia and Herzegovina (Bosnia and Herzegovina)

2017-06-28

In 2010 Kato and Jones described a new family of probability distributions on circle, obtained as Möbius transformation of von Mises distribution. We present the model demonstrating that these distributions appear naturally in study of populations of coupled oscillators. We use this opportunity to point out certain relations between Directional Statistics and collective motion of coupled oscillators. - Highlights: • We specify probability distributions on circle that arise in Kuramoto model. • We study how the mean-field coupling affects the shape of distribution of phases. • We discuss potential applications in some experiments on cell cycle. • We apply Directional Statistics to study collective dynamics of coupled oscillators.
How Can Histograms Be Useful for Introducing Continuous Probability Distributions?

Science.gov (United States)

Derouet, Charlotte; Parzysz, Bernard

2016-01-01

The teaching of probability has changed a great deal since the end of the last century. The development of technologies is indeed part of this evolution. In France, continuous probability distributions began to be studied in 2002 by scientific 12th graders, but this subject was marginal and appeared only as an application of integral calculus.…
Calculation of ruin probabilities for a dense class of heavy tailed distributions

DEFF Research Database (Denmark)

Bladt, Mogens; Nielsen, Bo Friis; Samorodnitsky, Gennady

2015-01-01

In this paper, we propose a class of infinite-dimensional phase-type distributions with finitely many parameters as models for heavy tailed distributions. The class of finite-dimensional phase-type distributions is dense in the class of distributions on the positive reals and may hence approximate...... any such distribution. We prove that formulas from renewal theory, and with a particular attention to ruin probabilities, which are true for common phase-type distributions also hold true for the infinite-dimensional case. We provide algorithms for calculating functionals of interest...... such as the renewal density and the ruin probability. It might be of interest to approximate a given heavy tailed distribution of some other type by a distribution from the class of infinite-dimensional phase-type distributions and to this end we provide a calibration procedure which works for the approximation...
Probability distribution of extreme share returns in Malaysia

Science.gov (United States)

Zin, Wan Zawiah Wan; Safari, Muhammad Aslam Mohd; Jaaman, Saiful Hafizah; Yie, Wendy Ling Shin

2014-09-01

The objective of this study is to investigate the suitable probability distribution to model the extreme share returns in Malaysia. To achieve this, weekly and monthly maximum daily share returns are derived from share prices data obtained from Bursa Malaysia over the period of 2000 to 2012. The study starts with summary statistics of the data which will provide a clue on the likely candidates for the best fitting distribution. Next, the suitability of six extreme value distributions, namely the Gumbel, Generalized Extreme Value (GEV), Generalized Logistic (GLO) and Generalized Pareto (GPA), the Lognormal (GNO) and the Pearson (PE3) distributions are evaluated. The method of L-moments is used in parameter estimation. Based on several goodness of fit tests and L-moment diagram test, the Generalized Pareto distribution and the Pearson distribution are found to be the best fitted distribution to represent the weekly and monthly maximum share returns in Malaysia stock market during the studied period, respectively.
Probability, conditional probability and complementary cumulative distribution functions in performance assessment for radioactive waste disposal

International Nuclear Information System (INIS)

Helton, J.C.

1996-03-01

A formal description of the structure of several recent performance assessments (PAs) for the Waste Isolation Pilot Plant (WIPP) is given in terms of the following three components: a probability space (S st , S st , p st ) for stochastic uncertainty, a probability space (S su , S su , p su ) for subjective uncertainty and a function (i.e., a random variable) defined on the product space associated with (S st , S st , p st ) and (S su , S su , p su ). The explicit recognition of the existence of these three components allows a careful description of the use of probability, conditional probability and complementary cumulative distribution functions within the WIPP PA. This usage is illustrated in the context of the U.S. Environmental Protection Agency's standard for the geologic disposal of radioactive waste (40 CFR 191, Subpart B). The paradigm described in this presentation can also be used to impose a logically consistent structure on PAs for other complex systems
Probability, conditional probability and complementary cumulative distribution functions in performance assessment for radioactive waste disposal

International Nuclear Information System (INIS)

Helton, J.C.

1996-01-01

A formal description of the structure of several recent performance assessments (PAs) for the Waste Isolation Pilot Plant (WIPP) is given in terms of the following three components: a probability space (S st , L st , P st ) for stochastic uncertainty, a probability space (S su , L su , P su ) for subjective uncertainty and a function (i.e., a random variable) defined on the product space associated with (S st , L st , P st ) and (S su , L su , P su ). The explicit recognition of the existence of these three components allows a careful description of the use of probability, conditional probability and complementary cumulative distribution functions within the WIPP PA. This usage is illustrated in the context of the US Environmental Protection Agency's standard for the geologic disposal of radioactive waste (40 CFR 191, Subpart B). The paradigm described in this presentation can also be used to impose a logically consistent structure on PAs for other complex systems
A formalism to generate probability distributions for performance-assessment modeling

International Nuclear Information System (INIS)

Kaplan, P.G.

1990-01-01

A formalism is presented for generating probability distributions of parameters used in performance-assessment modeling. The formalism is used when data are either sparse or nonexistent. The appropriate distribution is a function of the known or estimated constraints and is chosen to maximize a quantity known as Shannon's informational entropy. The formalism is applied to a parameter used in performance-assessment modeling. The functional form of the model that defines the parameter, data from the actual field site, and natural analog data are analyzed to estimate the constraints. A beta probability distribution of the example parameter is generated after finding four constraints. As an example of how the formalism is applied to the site characterization studies of Yucca Mountain, the distribution is generated for an input parameter in a performance-assessment model currently used to estimate compliance with disposal of high-level radioactive waste in geologic repositories, 10 CFR 60.113(a)(2), commonly known as the ground water travel time criterion. 8 refs., 2 figs
Statistical models based on conditional probability distributions

International Nuclear Information System (INIS)

Narayanan, R.S.

1991-10-01

We present a formulation of statistical mechanics models based on conditional probability distribution rather than a Hamiltonian. We show that it is possible to realize critical phenomena through this procedure. Closely linked with this formulation is a Monte Carlo algorithm, in which a configuration generated is guaranteed to be statistically independent from any other configuration for all values of the parameters, in particular near the critical point. (orig.)
Probability Distribution and Deviation Information Fusion Driven Support Vector Regression Model and Its Application

Directory of Open Access Journals (Sweden)

Changhao Fan

2017-01-01

Full Text Available In modeling, only information from the deviation between the output of the support vector regression (SVR model and the training sample is considered, whereas the other prior information of the training sample, such as probability distribution information, is ignored. Probabilistic distribution information describes the overall distribution of sample data in a training sample that contains different degrees of noise and potential outliers, as well as helping develop a high-accuracy model. To mine and use the probability distribution information of a training sample, a new support vector regression model that incorporates probability distribution information weight SVR (PDISVR is proposed. In the PDISVR model, the probability distribution of each sample is considered as the weight and is then introduced into the error coefficient and slack variables of SVR. Thus, the deviation and probability distribution information of the training sample are both used in the PDISVR model to eliminate the influence of noise and outliers in the training sample and to improve predictive performance. Furthermore, examples with different degrees of noise were employed to demonstrate the performance of PDISVR, which was then compared with those of three SVR-based methods. The results showed that PDISVR performs better than the three other methods.
Quantitative non-monotonic modeling of economic uncertainty by probability and possibility distributions

DEFF Research Database (Denmark)

Schjær-Jacobsen, Hans

2012-01-01

uncertainty can be calculated. The possibility approach is particular well suited for representation of uncertainty of a non-statistical nature due to lack of knowledge and requires less information than the probability approach. Based on the kind of uncertainty and knowledge present, these aspects...... to the understanding of similarities and differences of the two approaches as well as practical applications. The probability approach offers a good framework for representation of randomness and variability. Once the probability distributions of uncertain parameters and their correlations are known the resulting...... are thoroughly discussed in the case of rectangular representation of uncertainty by the uniform probability distribution and the interval, respectively. Also triangular representations are dealt with and compared. Calculation of monotonic as well as non-monotonic functions of variables represented...
WIENER-HOPF SOLVER WITH SMOOTH PROBABILITY DISTRIBUTIONS OF ITS COMPONENTS

Directory of Open Access Journals (Sweden)

Mr. Vladimir A. Smagin

2016-12-01

Full Text Available The Wiener – Hopf solver with smooth probability distributions of its component is presented. The method is based on hyper delta approximations of initial distributions. The use of Fourier series transformation and characteristic function allows working with the random variable method concentrated in transversal axis of absc.
Probability distribution of long-run indiscriminate felling of trees in ...

African Journals Online (AJOL)

The study was undertaken to determine the probability distribution of Long-run indiscriminate felling of trees in northern senatorial district of Adamawa State. Specifically, the study focused on examining the future direction of indiscriminate felling of trees as well as its equilibrium distribution. A multi-stage and simple random ...
Theoretical derivation of wind power probability distribution function and applications

International Nuclear Information System (INIS)

Altunkaynak, Abdüsselam; Erdik, Tarkan; Dabanlı, İsmail; Şen, Zekai

2012-01-01

Highlights: ► Derivation of wind power stochastic characteristics are standard deviation and the dimensionless skewness. ► The perturbation is expressions for the wind power statistics from Weibull probability distribution function (PDF). ► Comparisons with the corresponding characteristics of wind speed PDF abides by the Weibull PDF. ► The wind power abides with the Weibull-PDF. -- Abstract: The instantaneous wind power contained in the air current is directly proportional with the cube of the wind speed. In practice, there is a record of wind speeds in the form of a time series. It is, therefore, necessary to develop a formulation that takes into consideration the statistical parameters of such a time series. The purpose of this paper is to derive the general wind power formulation in terms of the statistical parameters by using the perturbation theory, which leads to a general formulation of the wind power expectation and other statistical parameter expressions such as the standard deviation and the coefficient of variation. The formulation is very general and can be applied specifically for any wind speed probability distribution function. Its application to two-parameter Weibull probability distribution of wind speeds is presented in full detail. It is concluded that provided wind speed is distributed according to a Weibull distribution, the wind power could be derived based on wind speed data. It is possible to determine wind power at any desired risk level, however, in practical studies most often 5% or 10% risk levels are preferred and the necessary simple procedure is presented for this purpose in this paper.
Numerical Loading of a Maxwellian Probability Distribution Function

International Nuclear Information System (INIS)

Lewandowski, J.L.V.

2003-01-01

A renormalization procedure for the numerical loading of a Maxwellian probability distribution function (PDF) is formulated. The procedure, which involves the solution of three coupled nonlinear equations, yields a numerically loaded PDF with improved properties for higher velocity moments. This method is particularly useful for low-noise particle-in-cell simulations with electron dynamics
On the probability distribution of the stochastic saturation scale in QCD

International Nuclear Information System (INIS)

Marquet, C.; Soyez, G.; Xiao Bowen

2006-01-01

It was recently noticed that high-energy scattering processes in QCD have a stochastic nature. An event-by-event scattering amplitude is characterised by a saturation scale which is a random variable. The statistical ensemble of saturation scales formed with all the events is distributed according to a probability law whose cumulants have been recently computed. In this work, we obtain the probability distribution from the cumulants. We prove that it can be considered as Gaussian over a large domain that we specify and our results are confirmed by numerical simulations
Calculation of magnetization curves and probability distribution for monoclinic and uniaxial systems

International Nuclear Information System (INIS)

Sobh, Hala A.; Aly, Samy H.; Yehia, Sherif

2013-01-01

We present the application of a simple classical statistical mechanics-based model to selected monoclinic and hexagonal model systems. In this model, we treat the magnetization as a classical vector whose angular orientation is dictated by the laws of equilibrium classical statistical mechanics. We calculate for these anisotropic systems, the magnetization curves, energy landscapes and probability distribution for different sets of relevant parameters and magnetic fields of different strengths and directions. Our results demonstrate a correlation between the most probable orientation of the magnetization vector, the system's parameters, and the external magnetic field. -- Highlights: ► We calculate magnetization curves and probability angular distribution of the magnetization. ► The magnetization curves are consistent with probability results for the studied systems. ► Monoclinic and hexagonal systems behave differently due to their different anisotropies

Probability, conditional probability and complementary cumulative distribution functions in performance assessment for radioactive waste disposal

Energy Technology Data Exchange (ETDEWEB)

Helton, J.C. [Arizona State Univ., Tempe, AZ (United States)

1996-03-01

A formal description of the structure of several recent performance assessments (PAs) for the Waste Isolation Pilot Plant (WIPP) is given in terms of the following three components: a probability space (S{sub st}, S{sub st}, p{sub st}) for stochastic uncertainty, a probability space (S{sub su}, S{sub su}, p{sub su}) for subjective uncertainty and a function (i.e., a random variable) defined on the product space associated with (S{sub st}, S{sub st}, p{sub st}) and (S{sub su}, S{sub su}, p{sub su}). The explicit recognition of the existence of these three components allows a careful description of the use of probability, conditional probability and complementary cumulative distribution functions within the WIPP PA. This usage is illustrated in the context of the U.S. Environmental Protection Agency`s standard for the geologic disposal of radioactive waste (40 CFR 191, Subpart B). The paradigm described in this presentation can also be used to impose a logically consistent structure on PAs for other complex systems.
Quantum Fourier transform, Heisenberg groups and quasi-probability distributions

International Nuclear Information System (INIS)

Patra, Manas K; Braunstein, Samuel L

2011-01-01

This paper aims to explore the inherent connection between Heisenberg groups, quantum Fourier transform (QFT) and (quasi-probability) distribution functions. Distribution functions for continuous and finite quantum systems are examined from three perspectives and all of them lead to Weyl-Gabor-Heisenberg groups. The QFT appears as the intertwining operator of two equivalent representations arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of the Wigner function from the marginal distributions via inverse Radon transform giving explicit formulae. We consider some applications of our approach to quantum information processing and quantum process tomography.
New family of probability distributions with applications to Monte Carlo studies

International Nuclear Information System (INIS)

Johnson, M.E.; Tietjen, G.L.; Beckman, R.J.

1980-01-01

A new probability distribution is presented that offers considerable potential for providing stochastic inputs to Monte Carlo simulation studies. The distribution includes the exponential power family as a special case. An efficient computational strategy is proposed for random variate generation. An example for testing the hypothesis of unit variance illustrates the advantages of the proposed distribution
Precipitation intensity probability distribution modelling for hydrological and construction design purposes

International Nuclear Information System (INIS)

Koshinchanov, Georgy; Dimitrov, Dobri

2008-01-01

The characteristics of rainfall intensity are important for many purposes, including design of sewage and drainage systems, tuning flood warning procedures, etc. Those estimates are usually statistical estimates of the intensity of precipitation realized for certain period of time (e.g. 5, 10 min., etc) with different return period (e.g. 20, 100 years, etc). The traditional approach in evaluating the mentioned precipitation intensities is to process the pluviometer's records and fit probability distribution to samples of intensities valid for certain locations ore regions. Those estimates further become part of the state regulations to be used for various economic activities. Two problems occur using the mentioned approach: 1. Due to various factors the climate conditions are changed and the precipitation intensity estimates need regular update; 2. As far as the extremes of the probability distribution are of particular importance for the practice, the methodology of the distribution fitting needs specific attention to those parts of the distribution. The aim of this paper is to make review of the existing methodologies for processing the intensive rainfalls and to refresh some of the statistical estimates for the studied areas. The methodologies used in Bulgaria for analyzing the intensive rainfalls and produce relevant statistical estimates: - The method of the maximum intensity, used in the National Institute of Meteorology and Hydrology to process and decode the pluviometer's records, followed by distribution fitting for each precipitation duration period; - As the above, but with separate modeling of probability distribution for the middle and high probability quantiles. - Method is similar to the first one, but with a threshold of 0,36 mm/min of intensity; - Another method proposed by the Russian hydrologist G. A. Aleksiev for regionalization of estimates over some territory, improved and adapted by S. Gerasimov for Bulgaria; - Next method is considering only
Evaluation of the probability distribution of intake from a single measurement on a personal air sampler

International Nuclear Information System (INIS)

Birchall, A.; Muirhead, C.R.; James, A.C.

1988-01-01

An analytical expression has been derived for the k-sum distribution, formed by summing k random variables from a lognormal population. Poisson statistics are used with this distribution to derive distribution of intake when breathing an atmosphere with a constant particle number concentration. Bayesian inference is then used to calculate the posterior probability distribution of concentrations from a given measurement. This is combined with the above intake distribution to give the probability distribution of intake resulting from a single measurement of activity made by an ideal sampler. It is shown that the probability distribution of intake is very dependent on the prior distribution used in Bayes' theorem. The usual prior assumption, that all number concentrations are equally probable, leads to an imbalance in the posterior intake distribution. This can be resolved if a new prior proportional to w -2/3 is used, where w is the expected number of particles collected. (author)
Exact probability distribution function for the volatility of cumulative production

Science.gov (United States)

Zadourian, Rubina; Klümper, Andreas

2018-04-01

In this paper we study the volatility and its probability distribution function for the cumulative production based on the experience curve hypothesis. This work presents a generalization of the study of volatility in Lafond et al. (2017), which addressed the effects of normally distributed noise in the production process. Due to its wide applicability in industrial and technological activities we present here the mathematical foundation for an arbitrary distribution function of the process, which we expect will pave the future research on forecasting of the production process.
Bounds for the probability distribution function of the linear ACD process

OpenAIRE

Fernandes, Marcelo

2003-01-01

Rio de Janeiro This paper derives both lower and upper bounds for the probability distribution function of stationary ACD(p, q) processes. For the purpose of illustration, I specialize the results to the main parent distributions in duration analysis. Simulations show that the lower bound is much tighter than the upper bound.
On Selection of the Probability Distribution for Representing the Maximum Annual Wind Speed in East Cairo, Egypt

International Nuclear Information System (INIS)

El-Shanshoury, Gh. I.; El-Hemamy, S.T.

2013-01-01

The main objective of this paper is to identify an appropriate probability model and best plotting position formula which represent the maximum annual wind speed in east Cairo. This model can be used to estimate the extreme wind speed and return period at a particular site as well as to determine the radioactive release distribution in case of accident occurrence at a nuclear power plant. Wind speed probabilities can be estimated by using probability distributions. An accurate determination of probability distribution for maximum wind speed data is very important in expecting the extreme value . The probability plots of the maximum annual wind speed (MAWS) in east Cairo are fitted to six major statistical distributions namely: Gumbel, Weibull, Normal, Log-Normal, Logistic and Log- Logistic distribution, while eight plotting positions of Hosking and Wallis, Hazen, Gringorten, Cunnane, Blom, Filliben, Benard and Weibull are used for determining exceedance of their probabilities. A proper probability distribution for representing the MAWS is selected by the statistical test criteria in frequency analysis. Therefore, the best plotting position formula which can be used to select appropriate probability model representing the MAWS data must be determined. The statistical test criteria which represented in: the probability plot correlation coefficient (PPCC), the root mean square error (RMSE), the relative root mean square error (RRMSE) and the maximum absolute error (MAE) are used to select the appropriate probability position and distribution. The data obtained show that the maximum annual wind speed in east Cairo vary from 44.3 Km/h to 96.1 Km/h within duration of 39 years . Weibull plotting position combined with Normal distribution gave the highest fit, most reliable, accurate predictions and determination of the wind speed in the study area having the highest value of PPCC and lowest values of RMSE, RRMSE and MAE
Measurement of probability distributions for internal stresses in dislocated crystals

Energy Technology Data Exchange (ETDEWEB)

Wilkinson, Angus J.; Tarleton, Edmund; Vilalta-Clemente, Arantxa; Collins, David M. [Department of Materials, University of Oxford, Parks Road, Oxford OX1 3PH (United Kingdom); Jiang, Jun; Britton, T. Benjamin [Department of Materials, Imperial College London, Royal School of Mines, Exhibition Road, London SW7 2AZ (United Kingdom)

2014-11-03

Here, we analyse residual stress distributions obtained from various crystal systems using high resolution electron backscatter diffraction (EBSD) measurements. Histograms showing stress probability distributions exhibit tails extending to very high stress levels. We demonstrate that these extreme stress values are consistent with the functional form that should be expected for dislocated crystals. Analysis initially developed by Groma and co-workers for X-ray line profile analysis and based on the so-called “restricted second moment of the probability distribution” can be used to estimate the total dislocation density. The generality of the results are illustrated by application to three quite different systems, namely, face centred cubic Cu deformed in uniaxial tension, a body centred cubic steel deformed to larger strain by cold rolling, and hexagonal InAlN layers grown on misfitting sapphire and silicon carbide substrates.
Fitting statistical distributions the generalized lambda distribution and generalized bootstrap methods

CERN Document Server

Karian, Zaven A

2000-01-01

Throughout the physical and social sciences, researchers face the challenge of fitting statistical distributions to their data. Although the study of statistical modelling has made great strides in recent years, the number and variety of distributions to choose from-all with their own formulas, tables, diagrams, and general properties-continue to create problems. For a specific application, which of the dozens of distributions should one use? What if none of them fit well?Fitting Statistical Distributions helps answer those questions. Focusing on techniques used successfully across many fields, the authors present all of the relevant results related to the Generalized Lambda Distribution (GLD), the Generalized Bootstrap (GB), and Monte Carlo simulation (MC). They provide the tables, algorithms, and computer programs needed for fitting continuous probability distributions to data in a wide variety of circumstances-covering bivariate as well as univariate distributions, and including situations where moments do...
Rank-Ordered Multifractal Analysis (ROMA of probability distributions in fluid turbulence

Directory of Open Access Journals (Sweden)

C. C. Wu

2011-04-01

Full Text Available Rank-Ordered Multifractal Analysis (ROMA was introduced by Chang and Wu (2008 to describe the multifractal characteristic of intermittent events. The procedure provides a natural connection between the rank-ordered spectrum and the idea of one-parameter scaling for monofractals. This technique has successfully been applied to MHD turbulence simulations and turbulence data observed in various space plasmas. In this paper, the technique is applied to the probability distributions in the inertial range of the turbulent fluid flow, as given in the vast Johns Hopkins University (JHU turbulence database. In addition, a new way of finding the continuous ROMA spectrum and the scaled probability distribution function (PDF simultaneously is introduced.
Probability distributions for first neighbor distances between resonances that belong to two different families

International Nuclear Information System (INIS)

Difilippo, F.C.

1994-01-01

For a mixture of two families of resonances, we found the probability distribution for the distance, as first neighbors, between resonances that belong to different families. Integration of this distribution gives the probability of accidental overlapping of resonances of one isotope by resonances of the other, provided that the resonances of each isotope belong to a single family. (author)
Univariate Lp and ɭ p Averaging, 0 < p < 1, in Polynomial Time by Utilization of Statistical Structure

Directory of Open Access Journals (Sweden)

John E. Lavery

2012-10-01

Full Text Available We present evidence that one can calculate generically combinatorially expensive Lp and lp averages, 0 < p < 1, in polynomial time by restricting the data to come from a wide class of statistical distributions. Our approach differs from the approaches in the previous literature, which are based on a priori sparsity requirements or on accepting a local minimum as a replacement for a global minimum. The functionals by which Lp averages are calculated are not convex but are radially monotonic and the functionals by which lp averages are calculated are nearly so, which are the keys to solvability in polynomial time. Analytical results for symmetric, radially monotonic univariate distributions are presented. An algorithm for univariate lp averaging is presented. Computational results for a Gaussian distribution, a class of symmetric heavy-tailed distributions and a class of asymmetric heavy-tailed distributions are presented. Many phenomena in human-based areas are increasingly known to be represented by data that have large numbers of outliers and belong to very heavy-tailed distributions. When tails of distributions are so heavy that even medians (L1 and l1 averages do not exist, one needs to consider using lp minimization principles with 0 < p < 1.
Diachronic changes in word probability distributions in daily press

Directory of Open Access Journals (Sweden)

Stanković Jelena

2006-01-01

Full Text Available Changes in probability distributions of individual words and word types were investigated within two samples of daily press in the span of fifty years. Two samples of daily press were used in this study. The one derived from the Corpus of Serbian Language (CSL /Kostić, Đ., 2001/ that covers period between 1945. and 1957. and the other derived from the Ebart Media Documentation (EBR that was complied from seven daily news and five weekly magazines from 2002. and 2003. Each sample consisted of about 1 million words. The obtained results indicate that nouns and adjectives were more frequent in the CSL, while verbs and prepositions are more frequent in the EBR sample, suggesting a decrease of sentence length in the last five decades. Conspicuous changes in probability distribution of individual words were observed for nouns and adjectives, while minimal or no changes were observed for verbs and prepositions. Such an outcome suggests that nouns and adjectives are most susceptible to diachronic changes, while verbs and prepositions appear to be resistant to such changes.
Probability distributions in conservative energy exchange models of multiple interacting agents

International Nuclear Information System (INIS)

Scafetta, Nicola; West, Bruce J

2007-01-01

Herein we study energy exchange models of multiple interacting agents that conserve energy in each interaction. The models differ regarding the rules that regulate the energy exchange and boundary effects. We find a variety of stochastic behaviours that manifest energy equilibrium probability distributions of different types and interaction rules that yield not only the exponential distributions such as the familiar Maxwell-Boltzmann-Gibbs distribution of an elastically colliding ideal particle gas, but also uniform distributions, truncated exponential distributions, Gaussian distributions, Gamma distributions, inverse power law distributions, mixed exponential and inverse power law distributions, and evolving distributions. This wide variety of distributions should be of value in determining the underlying mechanisms generating the statistical properties of complex phenomena including those to be found in complex chemical reactions
Regional probability distribution of the annual reference evapotranspiration and its effective parameters in Iran

Science.gov (United States)

Khanmohammadi, Neda; Rezaie, Hossein; Montaseri, Majid; Behmanesh, Javad

2017-10-01

The reference evapotranspiration (ET0) plays an important role in water management plans in arid or semi-arid countries such as Iran. For this reason, the regional analysis of this parameter is important. But, ET0 process is affected by several meteorological parameters such as wind speed, solar radiation, temperature and relative humidity. Therefore, the effect of distribution type of effective meteorological variables on ET0 distribution was analyzed. For this purpose, the regional probability distribution of the annual ET0 and its effective parameters were selected. Used data in this research was recorded data at 30 synoptic stations of Iran during 1960-2014. Using the probability plot correlation coefficient (PPCC) test and the L-moment method, five common distributions were compared and the best distribution was selected. The results of PPCC test and L-moment diagram indicated that the Pearson type III distribution was the best probability distribution for fitting annual ET0 and its four effective parameters. The results of RMSE showed that the ability of the PPCC test and L-moment method for regional analysis of reference evapotranspiration and its effective parameters was similar. The results also showed that the distribution type of the parameters which affected ET0 values can affect the distribution of reference evapotranspiration.
The joint probability distribution of structure factors incorporating anomalous-scattering and isomorphous-replacement data

International Nuclear Information System (INIS)

Peschar, R.; Schenk, H.

1991-01-01

A method to derive joint probability distributions of structure factors is presented which incorporates anomalous-scattering and isomorphous-replacement data in a unified procedure. The structure factors F H and F -H , whose magnitudes are different due to anomalous scattering, are shown to be isomorphously related. This leads to a definition of isomorphism by means of which isomorphous-replacement and anomalous-scattering data can be handled simultaneously. The definition and calculation of the general term of the joint probability distribution for isomorphous structure factors turns out to be crucial. Its analytical form leads to an algorithm by means of which any particular joint probability distribution of structure factors can be constructed. The calculation of the general term is discussed for the case of four isomorphous structure factors in P1, assuming the atoms to be independently and uniformly distributed. A main result is the construction of the probability distribution of the 64 triplet phase sums present in space group P1 amongst four isomorphous structure factors F H , four isomorphous F K and four isomorphous F -H-K . The procedure is readily generalized in the case where an arbitrary number of isomorphous structure factors are available for F H , F K and F -H-K . (orig.)
INVESTIGATION OF INFLUENCE OF ENCODING FUNCTION COMPLEXITY ON DISTRIBUTION OF ERROR MASKING PROBABILITY

Directory of Open Access Journals (Sweden)

A. B. Levina

2016-03-01

Full Text Available Error detection codes are mechanisms that enable robust delivery of data in unreliable communication channels and devices. Unreliable channels and devices are error-prone objects. Respectively, error detection codes allow detecting such errors. There are two classes of error detecting codes - classical codes and security-oriented codes. The classical codes have high percentage of detected errors; however, they have a high probability to miss an error in algebraic manipulation. In order, security-oriented codes are codes with a small Hamming distance and high protection to algebraic manipulation. The probability of error masking is a fundamental parameter of security-oriented codes. A detailed study of this parameter allows analyzing the behavior of the error-correcting code in the case of error injection in the encoding device. In order, the complexity of the encoding function plays an important role in the security-oriented codes. Encoding functions with less computational complexity and a low probability of masking are the best protection of encoding device against malicious acts. This paper investigates the influence of encoding function complexity on the error masking probability distribution. It will be shownthat the more complex encoding function reduces the maximum of error masking probability. It is also shown in the paper that increasing of the function complexity changes the error masking probability distribution. In particular, increasing of computational complexity decreases the difference between the maximum and average value of the error masking probability. Our resultshave shown that functions with greater complexity have smoothed maximums of error masking probability, which significantly complicates the analysis of error-correcting code by attacker. As a result, in case of complex encoding function the probability of the algebraic manipulation is reduced. The paper discusses an approach how to measure the error masking
Investigating and improving student understanding of the probability distributions for measuring physical observables in quantum mechanics

International Nuclear Information System (INIS)

Marshman, Emily; Singh, Chandralekha

2017-01-01

A solid grasp of the probability distributions for measuring physical observables is central to connecting the quantum formalism to measurements. However, students often struggle with the probability distributions of measurement outcomes for an observable and have difficulty expressing this concept in different representations. Here we first describe the difficulties that upper-level undergraduate and PhD students have with the probability distributions for measuring physical observables in quantum mechanics. We then discuss how student difficulties found in written surveys and individual interviews were used as a guide in the development of a quantum interactive learning tutorial (QuILT) to help students develop a good grasp of the probability distributions of measurement outcomes for physical observables. The QuILT strives to help students become proficient in expressing the probability distributions for the measurement of physical observables in Dirac notation and in the position representation and be able to convert from Dirac notation to position representation and vice versa. We describe the development and evaluation of the QuILT and findings about the effectiveness of the QuILT from in-class evaluations. (paper)
Statistical tests for whether a given set of independent, identically distributed draws comes from a specified probability density.

Science.gov (United States)

Tygert, Mark

2010-09-21

We discuss several tests for determining whether a given set of independent and identically distributed (i.i.d.) draws does not come from a specified probability density function. The most commonly used are Kolmogorov-Smirnov tests, particularly Kuiper's variant, which focus on discrepancies between the cumulative distribution function for the specified probability density and the empirical cumulative distribution function for the given set of i.i.d. draws. Unfortunately, variations in the probability density function often get smoothed over in the cumulative distribution function, making it difficult to detect discrepancies in regions where the probability density is small in comparison with its values in surrounding regions. We discuss tests without this deficiency, complementing the classical methods. The tests of the present paper are based on the plain fact that it is unlikely to draw a random number whose probability is small, provided that the draw is taken from the same distribution used in calculating the probability (thus, if we draw a random number whose probability is small, then we can be confident that we did not draw the number from the same distribution used in calculating the probability).

Multimode Interference: Identifying Channels and Ridges in Quantum Probability Distributions

OpenAIRE

O'Connell, Ross C.; Loinaz, Will

2004-01-01

The multimode interference technique is a simple way to study the interference patterns found in many quantum probability distributions. We demonstrate that this analysis not only explains the existence of so-called "quantum carpets," but can explain the spatial distribution of channels and ridges in the carpets. With an understanding of the factors that govern these channels and ridges we have a limited ability to produce a particular pattern of channels and ridges by carefully choosing the ...
Comparision of the different probability distributions for earthquake hazard assessment in the North Anatolian Fault Zone

Energy Technology Data Exchange (ETDEWEB)

Yilmaz, Şeyda, E-mail: seydayilmaz@ktu.edu.tr; Bayrak, Erdem, E-mail: erdmbyrk@gmail.com [Karadeniz Technical University, Trabzon (Turkey); Bayrak, Yusuf, E-mail: bayrak@ktu.edu.tr [Ağrı İbrahim Çeçen University, Ağrı (Turkey)

2016-04-18

In this study we examined and compared the three different probabilistic distribution methods for determining the best suitable model in probabilistic assessment of earthquake hazards. We analyzed a reliable homogeneous earthquake catalogue between a time period 1900-2015 for magnitude M ≥ 6.0 and estimated the probabilistic seismic hazard in the North Anatolian Fault zone (39°-41° N 30°-40° E) using three distribution methods namely Weibull distribution, Frechet distribution and three-parameter Weibull distribution. The distribution parameters suitability was evaluated Kolmogorov-Smirnov (K-S) goodness-of-fit test. We also compared the estimated cumulative probability and the conditional probabilities of occurrence of earthquakes for different elapsed time using these three distribution methods. We used Easyfit and Matlab software to calculate these distribution parameters and plotted the conditional probability curves. We concluded that the Weibull distribution method was the most suitable than other distribution methods in this region.
Probability distribution relationships

Directory of Open Access Journals (Sweden)

Yousry Abdelkader

2013-05-01

Full Text Available In this paper, we are interesting to show the most famous distributions and their relations to the other distributions in collected diagrams. Four diagrams are sketched as networks. The first one is concerned to the continuous distributions and their relations. The second one presents the discrete distributions. The third diagram is depicted the famous limiting distributions. Finally, the Balakrishnan skew-normal density and its relationship with the other distributions are shown in the fourth diagram.
The distribution function of a probability measure on a space with a fractal structure

Energy Technology Data Exchange (ETDEWEB)

Sanchez-Granero, M.A.; Galvez-Rodriguez, J.F.

2017-07-01

In this work we show how to define a probability measure with the help of a fractal structure. One of the keys of this approach is to use the completion of the fractal structure. Then we use the theory of a cumulative distribution function on a Polish ultrametric space and describe it in this context. Finally, with the help of fractal structures, we prove that a function satisfying the properties of a cumulative distribution function on a Polish ultrametric space is a cumulative distribution function with respect to some probability measure on the space. (Author)
Analysis of biopsy outcome after three-dimensional conformal radiation therapy of prostate cancer using dose-distribution variables and tumor control probability models

International Nuclear Information System (INIS)

Levegruen, Sabine; Jackson, Andrew; Zelefsky, Michael J.; Venkatraman, Ennapadam S.; Skwarchuk, Mark W.; Schlegel, Wolfgang; Fuks, Zvi; Leibel, Steven A.; Ling, C. Clifton

2000-01-01

Purpose: To investigate tumor control following three-dimensional conformal radiation therapy (3D-CRT) of prostate cancer and to identify dose-distribution variables that correlate with local control assessed through posttreatment prostate biopsies. Methods and Material: Data from 132 patients, treated at Memorial Sloan-Kettering Cancer Center (MSKCC), who had a prostate biopsy 2.5 years or more after 3D-CRT for T1c-T3 prostate cancer with prescription doses of 64.8-81 Gy were analyzed. Variables derived from the dose distribution in the PTV included: minimum dose (Dmin), maximum dose (Dmax), mean dose (Dmean), dose to n% of the PTV (Dn), where n = 1%, ..., 99%. The concept of the equivalent uniform dose (EUD) was evaluated for different values of the surviving fraction at 2 Gy (SF 2 ). Four tumor control probability (TCP) models (one phenomenologic model using a logistic function and three Poisson cell kill models) were investigated using two sets of input parameters, one for low and one for high T-stage tumors. Application of both sets to all patients was also investigated. In addition, several tumor-related prognostic variables were examined (including T-stage, Gleason score). Univariate and multivariate logistic regression analyses were performed. The ability of the logistic regression models (univariate and multivariate) to predict the biopsy result correctly was tested by performing cross-validation analyses and evaluating the results in terms of receiver operating characteristic (ROC) curves. Results: In univariate analysis, prescription dose (Dprescr), Dmax, Dmean, dose to n% of the PTV with n of 70% or less correlate with outcome (p 2 : EUD correlates significantly with outcome for SF 2 of 0.4 or more, but not for lower SF 2 values. Using either of the two input parameters sets, all TCP models correlate with outcome (p 2 , is limited because the low dose region may not coincide with the tumor location. Instead, for MSKCC prostate cancer patients with their
Digital simulation of two-dimensional random fields with arbitrary power spectra and non-Gaussian probability distribution functions

DEFF Research Database (Denmark)

Yura, Harold; Hanson, Steen Grüner

2012-01-01

with the desired spectral distribution, after which this colored Gaussian probability distribution is transformed via an inverse transform into the desired probability distribution. In most cases the method provides satisfactory results and can thus be considered an engineering approach. Several illustrative...
Univariate normalization of bispectrum using Hölder's inequality.

Science.gov (United States)

Shahbazi, Forooz; Ewald, Arne; Nolte, Guido

2014-08-15

Considering that many biological systems including the brain are complex non-linear systems, suitable methods capable of detecting these non-linearities are required to study the dynamical properties of these systems. One of these tools is the third order cummulant or cross-bispectrum, which is a measure of interfrequency interactions between three signals. For convenient interpretation, interaction measures are most commonly normalized to be independent of constant scales of the signals such that its absolute values are bounded by one, with this limit reflecting perfect coupling. Although many different normalization factors for cross-bispectra were suggested in the literature these either do not lead to bounded measures or are themselves dependent on the coupling and not only on the scale of the signals. In this paper we suggest a normalization factor which is univariate, i.e., dependent only on the amplitude of each signal and not on the interactions between signals. Using a generalization of Hölder's inequality it is proven that the absolute value of this univariate bicoherence is bounded by zero and one. We compared three widely used normalizations to the univariate normalization concerning the significance of bicoherence values gained from resampling tests. Bicoherence values are calculated from real EEG data recorded in an eyes closed experiment from 10 subjects. The results show slightly more significant values for the univariate normalization but in general, the differences are very small or even vanishing in some subjects. Therefore, we conclude that the normalization factor does not play an important role in the bicoherence values with regard to statistical power, although a univariate normalization is the only normalization factor which fulfills all the required conditions of a proper normalization. Copyright © 2014 Elsevier B.V. All rights reserved.
On the Meta Distribution of Coverage Probability in Uplink Cellular Networks

KAUST Repository

Elsawy, Hesham; Alouini, Mohamed-Slim

2017-01-01

This letter studies the meta distribution of coverage probability (CP), within a stochastic geometry framework, for cellular uplink transmission with fractional path-loss inversion power control. Using the widely accepted Poisson point process (PPP
The p-sphere and the geometric substratum of power-law probability distributions

International Nuclear Information System (INIS)

Vignat, C.; Plastino, A.

2005-01-01

Links between power law probability distributions and marginal distributions of uniform laws on p-spheres in R n show that a mathematical derivation of the Boltzmann-Gibbs distribution necessarily passes through power law ones. Results are also given that link parameters p and n to the value of the non-extensivity parameter q that characterizes these power laws in the context of non-extensive statistics
Landslide Probability Assessment by the Derived Distributions Technique

Science.gov (United States)

Muñoz, E.; Ochoa, A.; Martínez, H.

2012-12-01

Landslides are potentially disastrous events that bring along human and economic losses; especially in cities where an accelerated and unorganized growth leads to settlements on steep and potentially unstable areas. Among the main causes of landslides are geological, geomorphological, geotechnical, climatological, hydrological conditions and anthropic intervention. This paper studies landslides detonated by rain, commonly known as "soil-slip", which characterize by having a superficial failure surface (Typically between 1 and 1.5 m deep) parallel to the slope face and being triggered by intense and/or sustained periods of rain. This type of landslides is caused by changes on the pore pressure produced by a decrease in the suction when a humid front enters, as a consequence of the infiltration initiated by rain and ruled by the hydraulic characteristics of the soil. Failure occurs when this front reaches a critical depth and the shear strength of the soil in not enough to guarantee the stability of the mass. Critical rainfall thresholds in combination with a slope stability model are widely used for assessing landslide probability. In this paper we present a model for the estimation of the occurrence of landslides based on the derived distributions technique. Since the works of Eagleson in the 1970s the derived distributions technique has been widely used in hydrology to estimate the probability of occurrence of extreme flows. The model estimates the probability density function (pdf) of the Factor of Safety (FOS) from the statistical behavior of the rainfall process and some slope parameters. The stochastic character of the rainfall is transformed by means of a deterministic failure model into FOS pdf. Exceedance probability and return period estimation is then straightforward. The rainfall process is modeled as a Rectangular Pulses Poisson Process (RPPP) with independent exponential pdf for mean intensity and duration of the storms. The Philip infiltration model
Digital simulation of two-dimensional random fields with arbitrary power spectra and non-Gaussian probability distribution functions.

Science.gov (United States)

Yura, Harold T; Hanson, Steen G

2012-04-01

Methods for simulation of two-dimensional signals with arbitrary power spectral densities and signal amplitude probability density functions are disclosed. The method relies on initially transforming a white noise sample set of random Gaussian distributed numbers into a corresponding set with the desired spectral distribution, after which this colored Gaussian probability distribution is transformed via an inverse transform into the desired probability distribution. In most cases the method provides satisfactory results and can thus be considered an engineering approach. Several illustrative examples with relevance for optics are given.
Estimating probable flaw distributions in PWR steam generator tubes

International Nuclear Information System (INIS)

Gorman, J.A.; Turner, A.P.L.

1997-01-01

This paper describes methods for estimating the number and size distributions of flaws of various types in PWR steam generator tubes. These estimates are needed when calculating the probable primary to secondary leakage through steam generator tubes under postulated accidents such as severe core accidents and steam line breaks. The paper describes methods for two types of predictions: (1) the numbers of tubes with detectable flaws of various types as a function of time, and (2) the distributions in size of these flaws. Results are provided for hypothetical severely affected, moderately affected and lightly affected units. Discussion is provided regarding uncertainties and assumptions in the data and analyses
Predicting dihedral angle probability distributions for protein coil residues from primary sequence using neural networks

DEFF Research Database (Denmark)

Helles, Glennie; Fonseca, Rasmus

2009-01-01

residue in the input-window. The trained neural network shows a significant improvement (4-68%) in predicting the most probable bin (covering a 30°×30° area of the dihedral angle space) for all amino acids in the data set compared to first order statistics. An accuracy comparable to that of secondary...... seem to have a significant influence on the dihedral angles adopted by the individual amino acids in coil segments. In this work we attempt to predict a probability distribution of these dihedral angles based on the flanking residues. While attempts to predict dihedral angles of coil segments have been...... done previously, none have, to our knowledge, presented comparable results for the probability distribution of dihedral angles. Results: In this paper we develop an artificial neural network that uses an input-window of amino acids to predict a dihedral angle probability distribution for the middle...
A measure of mutual divergence among a number of probability distributions

Directory of Open Access Journals (Sweden)

J. N. Kapur

1987-01-01

major inequalities due to Shannon, Renyi and Holder. The inequalities are then used to obtain some useful results in information theory. In particular measures are obtained to measure the mutual divergence among two or more probability distributions.
Optimal methods for fitting probability distributions to propagule retention time in studies of zoochorous dispersal.

Science.gov (United States)

Viana, Duarte S; Santamaría, Luis; Figuerola, Jordi

2016-02-01

Propagule retention time is a key factor in determining propagule dispersal distance and the shape of "seed shadows". Propagules dispersed by animal vectors are either ingested and retained in the gut until defecation or attached externally to the body until detachment. Retention time is a continuous variable, but it is commonly measured at discrete time points, according to pre-established sampling time-intervals. Although parametric continuous distributions have been widely fitted to these interval-censored data, the performance of different fitting methods has not been evaluated. To investigate the performance of five different fitting methods, we fitted parametric probability distributions to typical discretized retention-time data with known distribution using as data-points either the lower, mid or upper bounds of sampling intervals, as well as the cumulative distribution of observed values (using either maximum likelihood or non-linear least squares for parameter estimation); then compared the estimated and original distributions to assess the accuracy of each method. We also assessed the robustness of these methods to variations in the sampling procedure (sample size and length of sampling time-intervals). Fittings to the cumulative distribution performed better for all types of parametric distributions (lognormal, gamma and Weibull distributions) and were more robust to variations in sample size and sampling time-intervals. These estimated distributions had negligible deviations of up to 0.045 in cumulative probability of retention times (according to the Kolmogorov-Smirnov statistic) in relation to original distributions from which propagule retention time was simulated, supporting the overall accuracy of this fitting method. In contrast, fitting the sampling-interval bounds resulted in greater deviations that ranged from 0.058 to 0.273 in cumulative probability of retention times, which may introduce considerable biases in parameter estimates. We
Outage probability of distributed beamforming with co-channel interference

KAUST Repository

Yang, Liang

2012-03-01

In this letter, we consider a distributed beamforming scheme (DBF) in the presence of equal-power co-channel interferers for both amplify-and-forward and decode-and-forward relaying protocols over Rayleigh fading channels. We first derive outage probability expressions for the DBF systems. We then present a performance analysis for a scheme relying on source selection. Numerical results are finally presented to verify our analysis. © 2011 IEEE.
A transmission probability method for calculation of neutron flux distributions in hexagonal geometry

International Nuclear Information System (INIS)

Wasastjerna, F.; Lux, I.

1980-03-01

A transmission probability method implemented in the program TPHEX is described. This program was developed for the calculation of neutron flux distributions in hexagonal light water reactor fuel assemblies. The accuracy appears to be superior to diffusion theory, and the computation time is shorter than that of the collision probability method. (author)
Gas Hydrate Formation Probability Distributions: The Effect of Shear and Comparisons with Nucleation Theory.

Science.gov (United States)

May, Eric F; Lim, Vincent W; Metaxas, Peter J; Du, Jianwei; Stanwix, Paul L; Rowland, Darren; Johns, Michael L; Haandrikman, Gert; Crosby, Daniel; Aman, Zachary M

2018-03-13

Gas hydrate formation is a stochastic phenomenon of considerable significance for any risk-based approach to flow assurance in the oil and gas industry. In principle, well-established results from nucleation theory offer the prospect of predictive models for hydrate formation probability in industrial production systems. In practice, however, heuristics are relied on when estimating formation risk for a given flowline subcooling or when quantifying kinetic hydrate inhibitor (KHI) performance. Here, we present statistically significant measurements of formation probability distributions for natural gas hydrate systems under shear, which are quantitatively compared with theoretical predictions. Distributions with over 100 points were generated using low-mass, Peltier-cooled pressure cells, cycled in temperature between 40 and -5 °C at up to 2 K·min -1 and analyzed with robust algorithms that automatically identify hydrate formation and initial growth rates from dynamic pressure data. The application of shear had a significant influence on the measured distributions: at 700 rpm mass-transfer limitations were minimal, as demonstrated by the kinetic growth rates observed. The formation probability distributions measured at this shear rate had mean subcoolings consistent with theoretical predictions and steel-hydrate-water contact angles of 14-26°. However, the experimental distributions were substantially wider than predicted, suggesting that phenomena acting on macroscopic length scales are responsible for much of the observed stochastic formation. Performance tests of a KHI provided new insights into how such chemicals can reduce the risk of hydrate blockage in flowlines. Our data demonstrate that the KHI not only reduces the probability of formation (by both shifting and sharpening the distribution) but also reduces hydrate growth rates by a factor of 2.
Probability an introduction

CERN Document Server

Goldberg, Samuel

1960-01-01

Excellent basic text covers set theory, probability theory for finite sample spaces, binomial theorem, probability distributions, means, standard deviations, probability function of binomial distribution, more. Includes 360 problems with answers for half.
Neighbor-dependent Ramachandran probability distributions of amino acids developed from a hierarchical Dirichlet process model.

Directory of Open Access Journals (Sweden)

Daniel Ting

2010-04-01

Full Text Available Distributions of the backbone dihedral angles of proteins have been studied for over 40 years. While many statistical analyses have been presented, only a handful of probability densities are publicly available for use in structure validation and structure prediction methods. The available distributions differ in a number of important ways, which determine their usefulness for various purposes. These include: 1 input data size and criteria for structure inclusion (resolution, R-factor, etc.; 2 filtering of suspect conformations and outliers using B-factors or other features; 3 secondary structure of input data (e.g., whether helix and sheet are included; whether beta turns are included; 4 the method used for determining probability densities ranging from simple histograms to modern nonparametric density estimation; and 5 whether they include nearest neighbor effects on the distribution of conformations in different regions of the Ramachandran map. In this work, Ramachandran probability distributions are presented for residues in protein loops from a high-resolution data set with filtering based on calculated electron densities. Distributions for all 20 amino acids (with cis and trans proline treated separately have been determined, as well as 420 left-neighbor and 420 right-neighbor dependent distributions. The neighbor-independent and neighbor-dependent probability densities have been accurately estimated using Bayesian nonparametric statistical analysis based on the Dirichlet process. In particular, we used hierarchical Dirichlet process priors, which allow sharing of information between densities for a particular residue type and different neighbor residue types. The resulting distributions are tested in a loop modeling benchmark with the program Rosetta, and are shown to improve protein loop conformation prediction significantly. The distributions are available at http://dunbrack.fccc.edu/hdp.

Probabilities of filaments in a Poissonian distribution of points -I

International Nuclear Information System (INIS)

Betancort-Rijo, J.

1989-01-01

Statistical techniques are devised to assess the likelihood of a Poisson sample of points in two and three dimensions, containing specific filamentary structures. For that purpose, the expression of Otto et al (1986. Astrophys. J., 304) for the probability density of clumps in a Poissonian distribution of points is generalized for any value of the density contrast. A way of counting filaments differing from that of Otto et al. is proposed, because at low density contrast the filaments counted by Otto et al. are distributed in a clumpy fashion, each clump of filaments corresponding to a distinct observed filament. (author)
A microcomputer program for energy assessment and aggregation using the triangular probability distribution

Science.gov (United States)

Crovelli, R.A.; Balay, R.H.

1991-01-01

A general risk-analysis method was developed for petroleum-resource assessment and other applications. The triangular probability distribution is used as a model with an analytic aggregation methodology based on probability theory rather than Monte-Carlo simulation. Among the advantages of the analytic method are its computational speed and flexibility, and the saving of time and cost on a microcomputer. The input into the model consists of a set of components (e.g. geologic provinces) and, for each component, three potential resource estimates: minimum, most likely (mode), and maximum. Assuming a triangular probability distribution, the mean, standard deviation, and seven fractiles (F100, F95, F75, F50, F25, F5, and F0) are computed for each component, where for example, the probability of more than F95 is equal to 0.95. The components are aggregated by combining the means, standard deviations, and respective fractiles under three possible siutations (1) perfect positive correlation, (2) complete independence, and (3) any degree of dependence between these two polar situations. A package of computer programs named the TRIAGG system was written in the Turbo Pascal 4.0 language for performing the analytic probabilistic methodology. The system consists of a program for processing triangular probability distribution assessments and aggregations, and a separate aggregation routine for aggregating aggregations. The user's documentation and program diskette of the TRIAGG system are available from USGS Open File Services. TRIAGG requires an IBM-PC/XT/AT compatible microcomputer with 256kbyte of main memory, MS-DOS 3.1 or later, either two diskette drives or a fixed disk, and a 132 column printer. A graphics adapter and color display are optional. ?? 1991.
Idealized models of the joint probability distribution of wind speeds

Science.gov (United States)

Monahan, Adam H.

2018-05-01

The joint probability distribution of wind speeds at two separate locations in space or points in time completely characterizes the statistical dependence of these two quantities, providing more information than linear measures such as correlation. In this study, we consider two models of the joint distribution of wind speeds obtained from idealized models of the dependence structure of the horizontal wind velocity components. The bivariate Rice distribution follows from assuming that the wind components have Gaussian and isotropic fluctuations. The bivariate Weibull distribution arises from power law transformations of wind speeds corresponding to vector components with Gaussian, isotropic, mean-zero variability. Maximum likelihood estimates of these distributions are compared using wind speed data from the mid-troposphere, from different altitudes at the Cabauw tower in the Netherlands, and from scatterometer observations over the sea surface. While the bivariate Rice distribution is more flexible and can represent a broader class of dependence structures, the bivariate Weibull distribution is mathematically simpler and may be more convenient in many applications. The complexity of the mathematical expressions obtained for the joint distributions suggests that the development of explicit functional forms for multivariate speed distributions from distributions of the components will not be practical for more complicated dependence structure or more than two speed variables.
Probability distribution functions of turbulence in seepage-affected alluvial channel

Energy Technology Data Exchange (ETDEWEB)

Sharma, Anurag; Kumar, Bimlesh, E-mail: anurag.sharma@iitg.ac.in, E-mail: bimk@iitg.ac.in [Department of Civil Engineering, Indian Institute of Technology Guwahati, 781039 (India)

2017-02-15

The present experimental study is carried out on the probability distribution functions (PDFs) of turbulent flow characteristics within near-bed-surface and away-from-bed surfaces for both no seepage and seepage flow. Laboratory experiments were conducted in the plane sand bed for no seepage (NS), 10% seepage (10%S) and 15% seepage (15%) cases. The experimental calculation of the PDFs of turbulent parameters such as Reynolds shear stress, velocity fluctuations, and bursting events is compared with theoretical expression obtained by Gram–Charlier (GC)-based exponential distribution. Experimental observations follow the computed PDF distributions for both no seepage and seepage cases. Jensen-Shannon divergence (JSD) method is used to measure the similarity between theoretical and experimental PDFs. The value of JSD for PDFs of velocity fluctuation lies between 0.0005 to 0.003 while the JSD value for PDFs of Reynolds shear stress varies between 0.001 to 0.006. Even with the application of seepage, the PDF distribution of bursting events, sweeps and ejections are well characterized by the exponential distribution of the GC series, except that a slight deflection of inward and outward interactions is observed which may be due to weaker events. The value of JSD for outward and inward interactions ranges from 0.0013 to 0.032, while the JSD value for sweep and ejection events varies between 0.0001 to 0.0025. The theoretical expression for the PDF of turbulent intensity is developed in the present study, which agrees well with the experimental observations and JSD lies between 0.007 and 0.015. The work presented is potentially applicable to the probability distribution of mobile-bed sediments in seepage-affected alluvial channels typically characterized by the various turbulent parameters. The purpose of PDF estimation from experimental data is that it provides a complete numerical description in the areas of turbulent flow either at a single or finite number of points
Parametric Probability Distribution Functions for Axon Diameters of Corpus Callosum

Directory of Open Access Journals (Sweden)

Farshid eSepehrband

2016-05-01

Full Text Available Axon diameter is an important neuroanatomical characteristic of the nervous system that alters in the course of neurological disorders such as multiple sclerosis. Axon diameters vary, even within a fiber bundle, and are not normally distributed. An accurate distribution function is therefore beneficial, either to describe axon diameters that are obtained from a direct measurement technique (e.g., microscopy, or to infer them indirectly (e.g., using diffusion-weighted MRI. The gamma distribution is a common choice for this purpose (particularly for the inferential approach because it resembles the distribution profile of measured axon diameters which has been consistently shown to be non-negative and right-skewed. In this study we compared a wide range of parametric probability distribution functions against empirical data obtained from electron microscopy images. We observed that the gamma distribution fails to accurately describe the main characteristics of the axon diameter distribution, such as location and scale of the mode and the profile of distribution tails. We also found that the generalized extreme value distribution consistently fitted the measured distribution better than other distribution functions. This suggests that there may be distinct subpopulations of axons in the corpus callosum, each with their own distribution profiles. In addition, we observed that several other distributions outperformed the gamma distribution, yet had the same number of unknown parameters; these were the inverse Gaussian, log normal, log logistic and Birnbaum-Saunders distributions.
Comparison of spectrum normalization techniques for univariate ...

Indian Academy of Sciences (India)

Laser-induced breakdown spectroscopy; univariate study; normalization models; stainless steel; standard error of prediction. Abstract. Analytical performance of six different spectrum normalization techniques, namelyinternal normalization, normalization with total light, normalization with background along with their ...
Non-Gaussian probability distributions of solar wind fluctuations

Directory of Open Access Journals (Sweden)

E. Marsch

Full Text Available The probability distributions of field differences ∆x(τ=x(t+τ-x(t, where the variable x(t may denote any solar wind scalar field or vector field component at time t, have been calculated from time series of Helios data obtained in 1976 at heliocentric distances near 0.3 AU. It is found that for comparatively long time lag τ, ranging from a few hours to 1 day, the differences are normally distributed according to a Gaussian. For shorter time lags, of less than ten minutes, significant changes in shape are observed. The distributions are often spikier and narrower than the equivalent Gaussian distribution with the same standard deviation, and they are enhanced for large, reduced for intermediate and enhanced for very small values of ∆x. This result is in accordance with fluid observations and numerical simulations. Hence statistical properties are dominated at small scale τ by large fluctuation amplitudes that are sparsely distributed, which is direct evidence for spatial intermittency of the fluctuations. This is in agreement with results from earlier analyses of the structure functions of ∆x. The non-Gaussian features are differently developed for the various types of fluctuations. The relevance of these observations to the interpretation and understanding of the nature of solar wind magnetohydrodynamic (MHD turbulence is pointed out, and contact is made with existing theoretical concepts of intermittency in fluid turbulence.
Count data, detection probabilities, and the demography, dynamics, distribution, and decline of amphibians.

Science.gov (United States)

Schmidt, Benedikt R

2003-08-01

The evidence for amphibian population declines is based on count data that were not adjusted for detection probabilities. Such data are not reliable even when collected using standard methods. The formula C = Np (where C is a count, N the true parameter value, and p is a detection probability) relates count data to demography, population size, or distributions. With unadjusted count data, one assumes a linear relationship between C and N and that p is constant. These assumptions are unlikely to be met in studies of amphibian populations. Amphibian population data should be based on methods that account for detection probabilities.
Introduction to probability with Mathematica

CERN Document Server

Hastings, Kevin J

2009-01-01

Discrete ProbabilityThe Cast of Characters Properties of Probability Simulation Random SamplingConditional ProbabilityIndependenceDiscrete DistributionsDiscrete Random Variables, Distributions, and ExpectationsBernoulli and Binomial Random VariablesGeometric and Negative Binomial Random Variables Poisson DistributionJoint, Marginal, and Conditional Distributions More on ExpectationContinuous ProbabilityFrom the Finite to the (Very) Infinite Continuous Random Variables and DistributionsContinuous ExpectationContinuous DistributionsThe Normal Distribution Bivariate Normal DistributionNew Random Variables from OldOrder Statistics Gamma DistributionsChi-Square, Student's t, and F-DistributionsTransformations of Normal Random VariablesAsymptotic TheoryStrong and Weak Laws of Large Numbers Central Limit TheoremStochastic Processes and ApplicationsMarkov ChainsPoisson Processes QueuesBrownian MotionFinancial MathematicsAppendixIntroduction to Mathematica Glossary of Mathematica Commands for Probability Short Answers...
Extreme points of the convex set of joint probability distributions with ...

Indian Academy of Sciences (India)

Here we address the following problem: If G is a standard ... convex set of all joint probability distributions on the product Borel space (X1 ×X2, F1 ⊗. F2) which .... cannot be identically zero when X and Y vary in A1 and u and v vary in H2. Thus.
Flux-probability distributions from the master equation for radiation transport in stochastic media

International Nuclear Information System (INIS)

Franke, Brian C.; Prinja, Anil K.

2011-01-01

We present numerical investigations into the accuracy of approximations in the master equation for radiation transport in discrete binary random media. Our solutions of the master equation yield probability distributions of particle flux at each element of phase space. We employ the Levermore-Pomraning interface closure and evaluate the effectiveness of closures for the joint conditional flux distribution for estimating scattering integrals. We propose a parameterized model for this joint-pdf closure, varying between correlation neglect and a full-correlation model. The closure is evaluated for a variety of parameter settings. Comparisons are made with benchmark results obtained through suites of fixed-geometry realizations of random media in rod problems. All calculations are performed using Monte Carlo techniques. Accuracy of the approximations in the master equation is assessed by examining the probability distributions for reflection and transmission and by evaluating the moments of the pdfs. The results suggest the correlation-neglect setting in our model performs best and shows improved agreement in the atomic-mix limit. (author)
Multivariate Matrix-Exponential Distributions

DEFF Research Database (Denmark)

Bladt, Mogens; Nielsen, Bo Friis

2010-01-01

be written as linear combinations of the elements in the exponential of a matrix. For this reason we shall refer to multivariate distributions with rational Laplace transform as multivariate matrix-exponential distributions (MVME). The marginal distributions of an MVME are univariate matrix......-exponential distributions. We prove a characterization that states that a distribution is an MVME distribution if and only if all non-negative, non-null linear combinations of the coordinates have a univariate matrix-exponential distribution. This theorem is analog to a well-known characterization theorem...
A method for the calculation of the cumulative failure probability distribution of complex repairable systems

International Nuclear Information System (INIS)

Caldarola, L.

1976-01-01

A method is proposed for the analytical evaluation of the cumulative failure probability distribution of complex repairable systems. The method is based on a set of integral equations each one referring to a specific minimal cut set of the system. Each integral equation links the unavailability of a minimal cut set to its failure probability density distribution and to the probability that the minimal cut set is down at the time t under the condition that it was down at time t'(t'<=t). The limitations for the applicability of the method are also discussed. It has been concluded that the method is applicable if the process describing the failure of a minimal cut set is a 'delayed semi-regenerative process'. (Auth.)
The force distribution probability function for simple fluids by density functional theory.

Science.gov (United States)

Rickayzen, G; Heyes, D M

2013-02-28

Classical density functional theory (DFT) is used to derive a formula for the probability density distribution function, P(F), and probability distribution function, W(F), for simple fluids, where F is the net force on a particle. The final formula for P(F) ∝ exp(-AF(2)), where A depends on the fluid density, the temperature, and the Fourier transform of the pair potential. The form of the DFT theory used is only applicable to bounded potential fluids. When combined with the hypernetted chain closure of the Ornstein-Zernike equation, the DFT theory for W(F) agrees with molecular dynamics computer simulations for the Gaussian and bounded soft sphere at high density. The Gaussian form for P(F) is still accurate at lower densities (but not too low density) for the two potentials, but with a smaller value for the constant, A, than that predicted by the DFT theory.
Application of the Unbounded Probability Distribution of the Johnson System for Floods Estimation

Directory of Open Access Journals (Sweden)

Campos-Aranda Daniel Francisco

2015-09-01

Full Text Available Floods designs constitute a key to estimate the sizing of new water works and to review the hydrological security of existing ones. The most reliable method for estimating their magnitudes associated with certain return periods is to fit a probabilistic model to available records of maximum annual flows. Since such model is at first unknown, several models need to be tested in order to select the most appropriate one according to an arbitrary statistical index, commonly the standard error of fit. Several probability distributions have shown versatility and consistency of results when processing floods records and therefore, its application has been established as a norm or precept. The Johnson System has three families of distributions, one of which is the Log–Normal model with three parameters of fit, which is also the border between the bounded distributions and those with no upper limit. These families of distributions have four adjustment parameters and converge to the standard normal distribution, so that their predictions are obtained with such a model. Having contrasted the three probability distributions established by precept in 31 historical records of hydrological events, the Johnson system is applied to such data. The results of the unbounded distribution of the Johnson system (SJU are compared to the optimal results from the three distributions. It was found that the predictions of the SJU distribution are similar to those obtained with the other models in the low return periods ( 1000 years. Because of its theoretical support, the SJU model is recommended in flood estimation.
Joint probability distributions and fluctuation theorems

International Nuclear Information System (INIS)

García-García, Reinaldo; Kolton, Alejandro B; Domínguez, Daniel; Lecomte, Vivien

2012-01-01

We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady state by using joint probability distribution symmetries of different entropy production decompositions. The analytical approach is applied to diverse problems such as the description of the fluctuations induced by experimental errors, for unveiling symmetries of correlation functions appearing in fluctuation–dissipation relations recently generalized to non-equilibrium steady states, and also for mapping averages between different trajectory-based dynamical ensembles. Many known fluctuation theorems arise as special instances of our approach for particular twofold decompositions of the total entropy production. As a complement, we also briefly review and synthesize the variety of fluctuation theorems applying to stochastic dynamics of both continuous systems described by a Langevin dynamics and discrete systems obeying a Markov dynamics, emphasizing how these results emerge from distinct symmetries of the dynamical entropy of the trajectory followed by the system. For Langevin dynamics, we embed the 'dual dynamics' with a physical meaning, and for Markov systems we show how the fluctuation theorems translate into symmetries of modified evolution operators
THREE-MOMENT BASED APPROXIMATION OF PROBABILITY DISTRIBUTIONS IN QUEUEING SYSTEMS

Directory of Open Access Journals (Sweden)

T. I. Aliev

2014-03-01

Full Text Available The paper deals with the problem of approximation of probability distributions of random variables defined in positive area of real numbers with coefficient of variation different from unity. While using queueing systems as models for computer networks, calculation of characteristics is usually performed at the level of expectation and variance. At the same time, one of the main characteristics of multimedia data transmission quality in computer networks is delay jitter. For jitter calculation the function of packets time delay distribution should be known. It is shown that changing the third moment of distribution of packets delay leads to jitter calculation difference in tens or hundreds of percent, with the same values of the first two moments – expectation value and delay variation coefficient. This means that delay distribution approximation for the calculation of jitter should be performed in accordance with the third moment of delay distribution. For random variables with coefficients of variation greater than unity, iterative approximation algorithm with hyper-exponential two-phase distribution based on three moments of approximated distribution is offered. It is shown that for random variables with coefficients of variation less than unity, the impact of the third moment of distribution becomes negligible, and for approximation of such distributions Erlang distribution with two first moments should be used. This approach gives the possibility to obtain upper bounds for relevant characteristics, particularly, the upper bound of delay jitter.
Quantile selection procedure and assoiated distribution of ratios of order statistics from a restricted family of probability distributions

International Nuclear Information System (INIS)

Gupta, S.S.; Panchapakesan, S.

1975-01-01

A quantile selection procedure in reliability problems pertaining to a restricted family of probability distributions is discussed. This family is assumed to be star-ordered with respect to the standard normal distribution folded at the origin. Motivation for this formulation of the problem is described. Both exact and asymptotic results dealing with the distribution of the maximum of ratios of order statistics from such a family are obtained and tables of the appropriate constants, percentiles of this statistic, are given in order to facilitate the use of the selection procedure
The probability distribution of intergranular stress corrosion cracking life for sensitized 304 stainless steels in high temperature, high purity water

International Nuclear Information System (INIS)

Akashi, Masatsune; Kenjyo, Takao; Matsukura, Shinji; Kawamoto, Teruaki

1984-01-01

In order to discuss the probability distribution of intergranular stress corrsion carcking life for sensitized 304 stainless steels, a series of the creviced bent beem (CBB) and the uni-axial constant load tests were carried out in oxygenated high temperature, high purity water. The following concludions were resulted; (1) The initiation process of intergranular stress corrosion cracking has been assumed to be approximated by the Poisson stochastic process, based on the CBB test results. (2) The probability distribution of intergranular stress corrosion cracking life may consequently be approximated by the exponential probability distribution. (3) The experimental data could be fitted to the exponential probability distribution. (author)
Transient Properties of Probability Distribution for a Markov Process with Size-dependent Additive Noise

Science.gov (United States)

Yamada, Yuhei; Yamazaki, Yoshihiro

2018-04-01

This study considered a stochastic model for cluster growth in a Markov process with a cluster size dependent additive noise. According to this model, the probability distribution of the cluster size transiently becomes an exponential or a log-normal distribution depending on the initial condition of the growth. In this letter, a master equation is obtained for this model, and derivation of the distributions is discussed.

On the issues of probability distribution of GPS carrier phase observations

Science.gov (United States)

Luo, X.; Mayer, M.; Heck, B.

2009-04-01

In common practice the observables related to Global Positioning System (GPS) are assumed to follow a Gauss-Laplace normal distribution. Actually, full knowledge of the observables' distribution is not required for parameter estimation by means of the least-squares algorithm based on the functional relation between observations and unknown parameters as well as the associated variance-covariance matrix. However, the probability distribution of GPS observations plays a key role in procedures for quality control (e.g. outlier and cycle slips detection, ambiguity resolution) and in reliability-related assessments of the estimation results. Under non-ideal observation conditions with respect to the factors impacting GPS data quality, for example multipath effects and atmospheric delays, the validity of the normal distribution postulate of GPS observations is in doubt. This paper presents a detailed analysis of the distribution properties of GPS carrier phase observations using double difference residuals. For this purpose 1-Hz observation data from the permanent SAPOS
Exact solutions and symmetry analysis for the limiting probability distribution of quantum walks

International Nuclear Information System (INIS)

Xu, Xin-Ping; Ide, Yusuke

2016-01-01

In the literature, there are numerous studies of one-dimensional discrete-time quantum walks (DTQWs) using a moving shift operator. However, there is no exact solution for the limiting probability distributions of DTQWs on cycles using a general coin or swapping shift operator. In this paper, we derive exact solutions for the limiting probability distribution of quantum walks using a general coin and swapping shift operator on cycles for the first time. Based on the exact solutions, we show how to generate symmetric quantum walks and determine the condition under which a symmetric quantum walk appears. Our results suggest that choosing various coin and initial state parameters can achieve a symmetric quantum walk. By defining a quantity to measure the variation of symmetry, deviation and mixing time of symmetric quantum walks are also investigated.
Exact solutions and symmetry analysis for the limiting probability distribution of quantum walks

Energy Technology Data Exchange (ETDEWEB)

Xu, Xin-Ping, E-mail: xuxp@mail.ihep.ac.cn [School of Physical Science and Technology, Soochow University, Suzhou 215006 (China); Ide, Yusuke [Department of Information Systems Creation, Faculty of Engineering, Kanagawa University, Yokohama, Kanagawa, 221-8686 (Japan)

2016-10-15

In the literature, there are numerous studies of one-dimensional discrete-time quantum walks (DTQWs) using a moving shift operator. However, there is no exact solution for the limiting probability distributions of DTQWs on cycles using a general coin or swapping shift operator. In this paper, we derive exact solutions for the limiting probability distribution of quantum walks using a general coin and swapping shift operator on cycles for the first time. Based on the exact solutions, we show how to generate symmetric quantum walks and determine the condition under which a symmetric quantum walk appears. Our results suggest that choosing various coin and initial state parameters can achieve a symmetric quantum walk. By defining a quantity to measure the variation of symmetry, deviation and mixing time of symmetric quantum walks are also investigated.
Examining barrier distributions and, in extension, energy derivative of probabilities for surrogate experiments

International Nuclear Information System (INIS)

Romain, P.; Duarte, H.; Morillon, B.

2012-01-01

The energy derivatives of probabilities are functions suited to a best understanding of certain mechanisms. Applied to compound nuclear reactions, they can bring information on fusion barrier distributions as originally introduced, and also, as presented here, on fission barrier distributions and heights. Extendedly, they permit to access the compound nucleus spin-parity states preferentially populated according to an entrance channel, at a given energy. (authors)
A least squares approach to estimating the probability distribution of unobserved data in multiphoton microscopy

Science.gov (United States)

Salama, Paul

2008-02-01

Multi-photon microscopy has provided biologists with unprecedented opportunities for high resolution imaging deep into tissues. Unfortunately deep tissue multi-photon microscopy images are in general noisy since they are acquired at low photon counts. To aid in the analysis and segmentation of such images it is sometimes necessary to initially enhance the acquired images. One way to enhance an image is to find the maximum a posteriori (MAP) estimate of each pixel comprising an image, which is achieved by finding a constrained least squares estimate of the unknown distribution. In arriving at the distribution it is assumed that the noise is Poisson distributed, the true but unknown pixel values assume a probability mass function over a finite set of non-negative values, and since the observed data also assumes finite values because of low photon counts, the sum of the probabilities of the observed pixel values (obtained from the histogram of the acquired pixel values) is less than one. Experimental results demonstrate that it is possible to closely estimate the unknown probability mass function with these assumptions.
Probability distribution for the Gaussian curvature of the zero level surface of a random function

Science.gov (United States)

Hannay, J. H.

2018-04-01

A rather natural construction for a smooth random surface in space is the level surface of value zero, or ‘nodal’ surface f(x,y,z) = 0, of a (real) random function f; the interface between positive and negative regions of the function. A physically significant local attribute at a point of a curved surface is its Gaussian curvature (the product of its principal curvatures) because, when integrated over the surface it gives the Euler characteristic. Here the probability distribution for the Gaussian curvature at a random point on the nodal surface f = 0 is calculated for a statistically homogeneous (‘stationary’) and isotropic zero mean Gaussian random function f. Capitalizing on the isotropy, a ‘fixer’ device for axes supplies the probability distribution directly as a multiple integral. Its evaluation yields an explicit algebraic function with a simple average. Indeed, this average Gaussian curvature has long been known. For a non-zero level surface instead of the nodal one, the probability distribution is not fully tractable, but is supplied as an integral expression.
The Impact of an Instructional Intervention Designed to Support Development of Stochastic Understanding of Probability Distribution

Science.gov (United States)

Conant, Darcy Lynn

2013-01-01

Stochastic understanding of probability distribution undergirds development of conceptual connections between probability and statistics and supports development of a principled understanding of statistical inference. This study investigated the impact of an instructional course intervention designed to support development of stochastic…
A Bernstein-Von Mises Theorem for discrete probability distributions

OpenAIRE

Boucheron, S.; Gassiat, E.

2008-01-01

We investigate the asymptotic normality of the posterior distribution in the discrete setting, when model dimension increases with sample size. We consider a probability mass function θ0 on ℕ∖{0} and a sequence of truncation levels (kn)n satisfying kn3≤ninf i≤knθ0(i). Let θ̂ denote the maximum likelihood estimate of (θ0(i))i≤kn and let Δn(θ0) denote the kn-dimensional vector which i-th coordinate is defined by $\\sqrt{n}(\\hat{\\theta}_{n}(i)-\\theta_{0}(i))$ for 1≤i≤kn. We check that under mild ...
Characterizing single-molecule FRET dynamics with probability distribution analysis.

Science.gov (United States)

Santoso, Yusdi; Torella, Joseph P; Kapanidis, Achillefs N

2010-07-12

Probability distribution analysis (PDA) is a recently developed statistical tool for predicting the shapes of single-molecule fluorescence resonance energy transfer (smFRET) histograms, which allows the identification of single or multiple static molecular species within a single histogram. We used a generalized PDA method to predict the shapes of FRET histograms for molecules interconverting dynamically between multiple states. This method is tested on a series of model systems, including both static DNA fragments and dynamic DNA hairpins. By fitting the shape of this expected distribution to experimental data, the timescale of hairpin conformational fluctuations can be recovered, in good agreement with earlier published results obtained using different techniques. This method is also applied to studying the conformational fluctuations in the unliganded Klenow fragment (KF) of Escherichia coli DNA polymerase I, which allows both confirmation of the consistency of a simple, two-state kinetic model with the observed smFRET distribution of unliganded KF and extraction of a millisecond fluctuation timescale, in good agreement with rates reported elsewhere. We expect this method to be useful in extracting rates from processes exhibiting dynamic FRET, and in hypothesis-testing models of conformational dynamics against experimental data.
Probability and stochastic modeling

CERN Document Server

Rotar, Vladimir I

2012-01-01

Basic NotionsSample Space and EventsProbabilitiesCounting TechniquesIndependence and Conditional ProbabilityIndependenceConditioningThe Borel-Cantelli TheoremDiscrete Random VariablesRandom Variables and VectorsExpected ValueVariance and Other Moments. Inequalities for DeviationsSome Basic DistributionsConvergence of Random Variables. The Law of Large NumbersConditional ExpectationGenerating Functions. Branching Processes. Random Walk RevisitedBranching Processes Generating Functions Branching Processes Revisited More on Random WalkMarkov ChainsDefinitions and Examples. Probability Distributions of Markov ChainsThe First Step Analysis. Passage TimesVariables Defined on a Markov ChainErgodicity and Stationary DistributionsA Classification of States and ErgodicityContinuous Random VariablesContinuous DistributionsSome Basic Distributions Continuous Multivariate Distributions Sums of Independent Random Variables Conditional Distributions and ExpectationsDistributions in the General Case. SimulationDistribution F...
Ruin Probabilities and Aggregrate Claims Distributions for Shot Noise Cox Processes

DEFF Research Database (Denmark)

Albrecher, H.; Asmussen, Søren

claim size is investigated under these assumptions. For both light-tailed and heavy-tailed claim size distributions, asymptotic estimates for infinite-time and finite-time ruin probabilities are derived. Moreover, we discuss an extension of the model to an adaptive premium rule that is dynamically......We consider a risk process Rt where the claim arrival process is a superposition of a homogeneous Poisson process and a Cox process with a Poisson shot noise intensity process, capturing the effect of sudden increases of the claim intensity due to external events. The distribution of the aggregate...... adjusted according to past claims experience....
Probability distribution functions for intermittent scrape-off layer plasma fluctuations

Science.gov (United States)

Theodorsen, A.; Garcia, O. E.

2018-03-01

A stochastic model for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas has been constructed based on a super-position of uncorrelated pulses arriving according to a Poisson process. In the most common applications of the model, the pulse amplitudes are assumed exponentially distributed, supported by conditional averaging of large-amplitude fluctuations in experimental measurement data. This basic assumption has two potential limitations. First, statistical analysis of measurement data using conditional averaging only reveals the tail of the amplitude distribution to be exponentially distributed. Second, exponentially distributed amplitudes leads to a positive definite signal which cannot capture fluctuations in for example electric potential and radial velocity. Assuming pulse amplitudes which are not positive definite often make finding a closed form for the probability density function (PDF) difficult, even if the characteristic function remains relatively simple. Thus estimating model parameters requires an approach based on the characteristic function, not the PDF. In this contribution, the effect of changing the amplitude distribution on the moments, PDF and characteristic function of the process is investigated and a parameter estimation method using the empirical characteristic function is presented and tested on synthetically generated data. This proves valuable for describing intermittent fluctuations of all plasma parameters in the boundary region of magnetized plasmas.
Audio feature extraction using probability distribution function

Science.gov (United States)

Suhaib, A.; Wan, Khairunizam; Aziz, Azri A.; Hazry, D.; Razlan, Zuradzman M.; Shahriman A., B.

2015-05-01

Voice recognition has been one of the popular applications in robotic field. It is also known to be recently used for biometric and multimedia information retrieval system. This technology is attained from successive research on audio feature extraction analysis. Probability Distribution Function (PDF) is a statistical method which is usually used as one of the processes in complex feature extraction methods such as GMM and PCA. In this paper, a new method for audio feature extraction is proposed which is by using only PDF as a feature extraction method itself for speech analysis purpose. Certain pre-processing techniques are performed in prior to the proposed feature extraction method. Subsequently, the PDF result values for each frame of sampled voice signals obtained from certain numbers of individuals are plotted. From the experimental results obtained, it can be seen visually from the plotted data that each individuals' voice has comparable PDF values and shapes.
Subspace Learning via Local Probability Distribution for Hyperspectral Image Classification

Directory of Open Access Journals (Sweden)

Huiwu Luo

2015-01-01

Full Text Available The computational procedure of hyperspectral image (HSI is extremely complex, not only due to the high dimensional information, but also due to the highly correlated data structure. The need of effective processing and analyzing of HSI has met many difficulties. It has been evidenced that dimensionality reduction has been found to be a powerful tool for high dimensional data analysis. Local Fisher’s liner discriminant analysis (LFDA is an effective method to treat HSI processing. In this paper, a novel approach, called PD-LFDA, is proposed to overcome the weakness of LFDA. PD-LFDA emphasizes the probability distribution (PD in LFDA, where the maximum distance is replaced with local variance for the construction of weight matrix and the class prior probability is applied to compute the affinity matrix. The proposed approach increases the discriminant ability of the transformed features in low dimensional space. Experimental results on Indian Pines 1992 data indicate that the proposed approach significantly outperforms the traditional alternatives.
Forecasting electricity spot-prices using linear univariate time-series models

International Nuclear Information System (INIS)

Cuaresma, Jesus Crespo; Hlouskova, Jaroslava; Kossmeier, Stephan; Obersteiner, Michael

2004-01-01

This paper studies the forecasting abilities of a battery of univariate models on hourly electricity spot prices, using data from the Leipzig Power Exchange. The specifications studied include autoregressive models, autoregressive-moving average models and unobserved component models. The results show that specifications, where each hour of the day is modelled separately present uniformly better forecasting properties than specifications for the whole time-series, and that the inclusion of simple probabilistic processes for the arrival of extreme price events can lead to improvements in the forecasting abilities of univariate models for electricity spot prices. (Author)
PHOTOMETRIC REDSHIFT PROBABILITY DISTRIBUTIONS FOR GALAXIES IN THE SDSS DR8

International Nuclear Information System (INIS)

Sheldon, Erin S.; Cunha, Carlos E.; Mandelbaum, Rachel; Brinkmann, J.; Weaver, Benjamin A.

2012-01-01

We present redshift probability distributions for galaxies in the Sloan Digital Sky Survey (SDSS) Data Release 8 imaging data. We used the nearest-neighbor weighting algorithm to derive the ensemble redshift distribution N(z), and individual redshift probability distributions P(z) for galaxies with r < 21.8 and u < 29.0. As part of this technique, we calculated weights for a set of training galaxies with known redshifts such that their density distribution in five-dimensional color-magnitude space was proportional to that of the photometry-only sample, producing a nearly fair sample in that space. We estimated the ensemble N(z) of the photometric sample by constructing a weighted histogram of the training-set redshifts. We derived P(z)'s for individual objects by using training-set objects from the local color-magnitude space around each photometric object. Using the P(z) for each galaxy can reduce the statistical error in measurements that depend on the redshifts of individual galaxies. The spectroscopic training sample is substantially larger than that used for the DR7 release. The newly added PRIMUS catalog is now the most important training set used in this analysis by a wide margin. We expect the primary sources of error in the N(z) reconstruction to be sample variance and spectroscopic failures: The training sets are drawn from relatively small volumes of space, and some samples have large incompleteness. Using simulations we estimated the uncertainty in N(z) due to sample variance at a given redshift to be ∼10%-15%. The uncertainty on calculations incorporating N(z) or P(z) depends on how they are used; we discuss the case of weak lensing measurements. The P(z) catalog is publicly available from the SDSS Web site.
Introduction to probability

CERN Document Server

Freund, John E

1993-01-01

Thorough, lucid coverage of permutations and factorials, probabilities and odds, frequency interpretation, mathematical expectation, decision making, postulates of probability, rule of elimination, binomial distribution, geometric distribution, standard deviation, law of large numbers, and much more. Exercises with some solutions. Summary. Bibliography. Includes 42 black-and-white illustrations. 1973 edition.
The limiting conditional probability distribution in a stochastic model of T cell repertoire maintenance.

Science.gov (United States)

Stirk, Emily R; Lythe, Grant; van den Berg, Hugo A; Hurst, Gareth A D; Molina-París, Carmen

2010-04-01

The limiting conditional probability distribution (LCD) has been much studied in the field of mathematical biology, particularly in the context of epidemiology and the persistence of epidemics. However, it has not yet been applied to the immune system. One of the characteristic features of the T cell repertoire is its diversity. This diversity declines in old age, whence the concepts of extinction and persistence are also relevant to the immune system. In this paper we model T cell repertoire maintenance by means of a continuous-time birth and death process on the positive integers, where the origin is an absorbing state. We show that eventual extinction is guaranteed. The late-time behaviour of the process before extinction takes place is modelled by the LCD, which we prove always exists for the process studied here. In most cases, analytic expressions for the LCD cannot be computed but the probability distribution may be approximated by means of the stationary probability distributions of two related processes. We show how these approximations are related to the LCD of the original process and use them to study the LCD in two special cases. We also make use of the large N expansion to derive a further approximation to the LCD. The accuracy of the various approximations is then analysed. (c) 2009 Elsevier Inc. All rights reserved.
A brief introduction to probability.

Science.gov (United States)

Di Paola, Gioacchino; Bertani, Alessandro; De Monte, Lavinia; Tuzzolino, Fabio

2018-02-01

The theory of probability has been debated for centuries: back in 1600, French mathematics used the rules of probability to place and win bets. Subsequently, the knowledge of probability has significantly evolved and is now an essential tool for statistics. In this paper, the basic theoretical principles of probability will be reviewed, with the aim of facilitating the comprehension of statistical inference. After a brief general introduction on probability, we will review the concept of the "probability distribution" that is a function providing the probabilities of occurrence of different possible outcomes of a categorical or continuous variable. Specific attention will be focused on normal distribution that is the most relevant distribution applied to statistical analysis.
Scoring Rules for Subjective Probability Distributions

DEFF Research Database (Denmark)

Harrison, Glenn W.; Martínez-Correa, Jimmy; Swarthout, J. Todd

The theoretical literature has a rich characterization of scoring rules for eliciting the subjective beliefs that an individual has for continuous events, but under the restrictive assumption of risk neutrality. It is well known that risk aversion can dramatically affect the incentives to correctly...... report the true subjective probability of a binary event, even under Subjective Expected Utility. To address this one can “calibrate” inferences about true subjective probabilities from elicited subjective probabilities over binary events, recognizing the incentives that risk averse agents have...... to distort reports. We characterize the comparable implications of the general case of a risk averse agent when facing a popular scoring rule over continuous events, and find that these concerns do not apply with anything like the same force. For empirically plausible levels of risk aversion, one can...

Ruin probabilities

DEFF Research Database (Denmark)

Asmussen, Søren; Albrecher, Hansjörg

The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramér-Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities......, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially...... updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber–Shiu functions and dependence....
Impact of spike train autostructure on probability distribution of joint spike events.

Science.gov (United States)

Pipa, Gordon; Grün, Sonja; van Vreeswijk, Carl

2013-05-01

The discussion whether temporally coordinated spiking activity really exists and whether it is relevant has been heated over the past few years. To investigate this issue, several approaches have been taken to determine whether synchronized events occur significantly above chance, that is, whether they occur more often than expected if the neurons fire independently. Most investigations ignore or destroy the autostructure of the spiking activity of individual cells or assume Poissonian spiking as a model. Such methods that ignore the autostructure can significantly bias the coincidence statistics. Here, we study the influence of the autostructure on the probability distribution of coincident spiking events between tuples of mutually independent non-Poisson renewal processes. In particular, we consider two types of renewal processes that were suggested as appropriate models of experimental spike trains: a gamma and a log-normal process. For a gamma process, we characterize the shape of the distribution analytically with the Fano factor (FFc). In addition, we perform Monte Carlo estimations to derive the full shape of the distribution and the probability for false positives if a different process type is assumed as was actually present. We also determine how manipulations of such spike trains, here dithering, used for the generation of surrogate data change the distribution of coincident events and influence the significance estimation. We find, first, that the width of the coincidence count distribution and its FFc depend critically and in a nontrivial way on the detailed properties of the structure of the spike trains as characterized by the coefficient of variation CV. Second, the dependence of the FFc on the CV is complex and mostly nonmonotonic. Third, spike dithering, even if as small as a fraction of the interspike interval, can falsify the inference on coordinated firing.
Probability Distribution and Projected Trends of Daily Precipitation in China

Institute of Scientific and Technical Information of China (English)

CAO; Li-Ge; ZHONG; Jun; SU; Bu-Da; ZHAI; Jian-Qing; Macro; GEMMER

2013-01-01

Based on observed daily precipitation data of 540 stations and 3,839 gridded data from the high-resolution regional climate model COSMO-Climate Limited-area Modeling(CCLM)for 1961–2000,the simulation ability of CCLM on daily precipitation in China is examined,and the variation of daily precipitation distribution pattern is revealed.By applying the probability distribution and extreme value theory to the projected daily precipitation(2011–2050)under SRES A1B scenario with CCLM,trends of daily precipitation series and daily precipitation extremes are analyzed.Results show that except for the western Qinghai-Tibetan Plateau and South China,distribution patterns of the kurtosis and skewness calculated from the simulated and observed series are consistent with each other;their spatial correlation coefcients are above 0.75.The CCLM can well capture the distribution characteristics of daily precipitation over China.It is projected that in some parts of the Jianghuai region,central-eastern Northeast China and Inner Mongolia,the kurtosis and skewness will increase significantly,and precipitation extremes will increase during 2011–2050.The projected increase of maximum daily rainfall and longest non-precipitation period during flood season in the aforementioned regions,also show increasing trends of droughts and floods in the next 40 years.
Comparison of different Methods for Univariate Time Series Imputation in R

OpenAIRE

Moritz, Steffen; Sardá, Alexis; Bartz-Beielstein, Thomas; Zaefferer, Martin; Stork, Jörg

2015-01-01

Missing values in datasets are a well-known problem and there are quite a lot of R packages offering imputation functions. But while imputation in general is well covered within R, it is hard to find functions for imputation of univariate time series. The problem is, most standard imputation techniques can not be applied directly. Most algorithms rely on inter-attribute correlations, while univariate time series imputation needs to employ time dependencies. This paper provides an overview of ...
Variation in the standard deviation of the lure rating distribution: Implications for estimates of recollection probability.

Science.gov (United States)

Dopkins, Stephen; Varner, Kaitlin; Hoyer, Darin

2017-10-01

In word recognition semantic priming of test words increased the false-alarm rate and the mean of confidence ratings to lures. Such priming also increased the standard deviation of confidence ratings to lures and the slope of the z-ROC function, suggesting that the priming increased the standard deviation of the lure evidence distribution. The Unequal Variance Signal Detection (UVSD) model interpreted the priming as increasing the standard deviation of the lure evidence distribution. Without additional parameters the Dual Process Signal Detection (DPSD) model could only accommodate the results by fitting the data for related and unrelated primes separately, interpreting the priming, implausibly, as decreasing the probability of target recollection (DPSD). With an additional parameter, for the probability of false (lure) recollection the model could fit the data for related and unrelated primes together, interpreting the priming as increasing the probability of false recollection. These results suggest that DPSD estimates of target recollection probability will decrease with increases in the lure confidence/evidence standard deviation unless a parameter is included for false recollection. Unfortunately the size of a given lure confidence/evidence standard deviation relative to other possible lure confidence/evidence standard deviations is often unspecified by context. Hence the model often has no way of estimating false recollection probability and thereby correcting its estimates of target recollection probability.
Decoding auditory spatial and emotional information encoding using multivariate versus univariate techniques.

Science.gov (United States)

Kryklywy, James H; Macpherson, Ewan A; Mitchell, Derek G V

2018-04-01

Emotion can have diverse effects on behaviour and perception, modulating function in some circumstances, and sometimes having little effect. Recently, it was identified that part of the heterogeneity of emotional effects could be due to a dissociable representation of emotion in dual pathway models of sensory processing. Our previous fMRI experiment using traditional univariate analyses showed that emotion modulated processing in the auditory 'what' but not 'where' processing pathway. The current study aims to further investigate this dissociation using a more recently emerging multi-voxel pattern analysis searchlight approach. While undergoing fMRI, participants localized sounds of varying emotional content. A searchlight multi-voxel pattern analysis was conducted to identify activity patterns predictive of sound location and/or emotion. Relative to the prior univariate analysis, MVPA indicated larger overlapping spatial and emotional representations of sound within early secondary regions associated with auditory localization. However, consistent with the univariate analysis, these two dimensions were increasingly segregated in late secondary and tertiary regions of the auditory processing streams. These results, while complimentary to our original univariate analyses, highlight the utility of multiple analytic approaches for neuroimaging, particularly for neural processes with known representations dependent on population coding.
Scarred resonances and steady probability distribution in a chaotic microcavity

International Nuclear Information System (INIS)

Lee, Soo-Young; Rim, Sunghwan; Kim, Chil-Min; Ryu, Jung-Wan; Kwon, Tae-Yoon

2005-01-01

We investigate scarred resonances of a stadium-shaped chaotic microcavity. It is shown that two components with different chirality of the scarring pattern are slightly rotated in opposite ways from the underlying unstable periodic orbit, when the incident angles of the scarring pattern are close to the critical angle for total internal reflection. In addition, the correspondence of emission pattern with the scarring pattern disappears when the incident angles are much larger than the critical angle. The steady probability distribution gives a consistent explanation about these interesting phenomena and makes it possible to expect the emission pattern in the latter case
Loaded dice in Monte Carlo : importance sampling in phase space integration and probability distributions for discrepancies

NARCIS (Netherlands)

Hameren, Andreas Ferdinand Willem van

2001-01-01

Discrepancies play an important role in the study of uniformity properties of point sets. Their probability distributions are a help in the analysis of the efficiency of the Quasi Monte Carlo method of numerical integration, which uses point sets that are distributed more uniformly than sets of
The Probability Distribution for a Biased Spinner

Science.gov (United States)

Foster, Colin

2012-01-01

This article advocates biased spinners as an engaging context for statistics students. Calculating the probability of a biased spinner landing on a particular side makes valuable connections between probability and other areas of mathematics. (Contains 2 figures and 1 table.)
Chaos optimization algorithms based on chaotic maps with different probability distribution and search speed for global optimization

Science.gov (United States)

Yang, Dixiong; Liu, Zhenjun; Zhou, Jilei

2014-04-01

Chaos optimization algorithms (COAs) usually utilize the chaotic map like Logistic map to generate the pseudo-random numbers mapped as the design variables for global optimization. Many existing researches indicated that COA can more easily escape from the local minima than classical stochastic optimization algorithms. This paper reveals the inherent mechanism of high efficiency and superior performance of COA, from a new perspective of both the probability distribution property and search speed of chaotic sequences generated by different chaotic maps. The statistical property and search speed of chaotic sequences are represented by the probability density function (PDF) and the Lyapunov exponent, respectively. Meanwhile, the computational performances of hybrid chaos-BFGS algorithms based on eight one-dimensional chaotic maps with different PDF and Lyapunov exponents are compared, in which BFGS is a quasi-Newton method for local optimization. Moreover, several multimodal benchmark examples illustrate that, the probability distribution property and search speed of chaotic sequences from different chaotic maps significantly affect the global searching capability and optimization efficiency of COA. To achieve the high efficiency of COA, it is recommended to adopt the appropriate chaotic map generating the desired chaotic sequences with uniform or nearly uniform probability distribution and large Lyapunov exponent.
Study of the SEMG probability distribution of the paretic tibialis anterior muscle

Energy Technology Data Exchange (ETDEWEB)

Cherniz, AnalIa S; Bonell, Claudia E; Tabernig, Carolina B [Laboratorio de Ingenieria de Rehabilitacion e Investigaciones Neuromusculares y Sensoriales, Facultad de Ingenieria, UNER, Oro Verde (Argentina)

2007-11-15

The surface electromyographic signal is a stochastic signal that has been modeled as a Gaussian process, with a zero mean. It has been experimentally proved that this probability distribution can be adjusted with less error to a Laplacian type distribution. The selection of estimators for the detection of changes in the amplitude of the muscular signal depends, among other things, on the type of distribution. In the case of subjects with lesions to the superior motor neuron, the lack of central control affects the muscular tone, the force and the patterns of muscular movement involved in activities such as the gait cycle. In this work, the distribution types of the SEMG signal amplitudes of the tibialis anterior muscle are evaluated during gait, both in two healthy subjects and in two hemiparetic ones in order to select the estimators that best characterize them. It was observed that the Laplacian distribution function would be the one that best adjusts to the experimental data in the studied subjects, although this largely depends on the subject and on the data segment analyzed.
Study of the SEMG probability distribution of the paretic tibialis anterior muscle

International Nuclear Information System (INIS)

Cherniz, AnalIa S; Bonell, Claudia E; Tabernig, Carolina B

2007-01-01

The surface electromyographic signal is a stochastic signal that has been modeled as a Gaussian process, with a zero mean. It has been experimentally proved that this probability distribution can be adjusted with less error to a Laplacian type distribution. The selection of estimators for the detection of changes in the amplitude of the muscular signal depends, among other things, on the type of distribution. In the case of subjects with lesions to the superior motor neuron, the lack of central control affects the muscular tone, the force and the patterns of muscular movement involved in activities such as the gait cycle. In this work, the distribution types of the SEMG signal amplitudes of the tibialis anterior muscle are evaluated during gait, both in two healthy subjects and in two hemiparetic ones in order to select the estimators that best characterize them. It was observed that the Laplacian distribution function would be the one that best adjusts to the experimental data in the studied subjects, although this largely depends on the subject and on the data segment analyzed
Spectral shaping of a randomized PWM DC-DC converter using maximum entropy probability distributions

CSIR Research Space (South Africa)

Dove, Albert

2017-01-01

Full Text Available maintaining constraints in a DC-DC converter is investigated. A probability distribution whose aim is to ensure maximal harmonic spreading and yet mainaint constraints is presented. The PDFs are determined from a direct application of the method of Maximum...
Univariate characterization of the German business cycle 1955-1994

OpenAIRE

Weihs, Claus; Garczarek, Ursula

2002-01-01

We present a descriptive analysis of stylized facts for the German business cycle. We demonstrate that simple ad-hoc instructions for identifying univariate rules characterizing the German business cycle 1955-1994 lead to an error rate comparable to standard multivariate methods.
Probability evolution method for exit location distribution

Science.gov (United States)

Zhu, Jinjie; Chen, Zhen; Liu, Xianbin

2018-03-01

The exit problem in the framework of the large deviation theory has been a hot topic in the past few decades. The most probable escape path in the weak-noise limit has been clarified by the Freidlin-Wentzell action functional. However, noise in real physical systems cannot be arbitrarily small while noise with finite strength may induce nontrivial phenomena, such as noise-induced shift and noise-induced saddle-point avoidance. Traditional Monte Carlo simulation of noise-induced escape will take exponentially large time as noise approaches zero. The majority of the time is wasted on the uninteresting wandering around the attractors. In this paper, a new method is proposed to decrease the escape simulation time by an exponentially large factor by introducing a series of interfaces and by applying the reinjection on them. This method can be used to calculate the exit location distribution. It is verified by examining two classical examples and is compared with theoretical predictions. The results show that the method performs well for weak noise while may induce certain deviations for large noise. Finally, some possible ways to improve our method are discussed.
Constructing probability distributions of uncertain variables in models of the performance of the Waste Isolation Pilot Plant: The 1990 performance simulations

International Nuclear Information System (INIS)

Tierney, M.S.

1990-12-01

A five-step procedure was used in the 1990 performance simulations to construct probability distributions of the uncertain variables appearing in the mathematical models used to simulate the Waste Isolation Pilot Plant's (WIPP's) performance. This procedure provides a consistent approach to the construction of probability distributions in cases where empirical data concerning a variable are sparse or absent and minimizes the amount of spurious information that is often introduced into a distribution by assumptions of nonspecialists. The procedure gives first priority to the professional judgment of subject-matter experts and emphasizes the use of site-specific empirical data for the construction of the probability distributions when such data are available. In the absence of sufficient empirical data, the procedure employs the Maximum Entropy Formalism and the subject-matter experts' subjective estimates of the parameters of the distribution to construct a distribution that can be used in a performance simulation. (author)
Constructing probability distributions of uncertain variables in models of the performance of the Waste Isolation Pilot Plant: The 1990 performance simulations

Energy Technology Data Exchange (ETDEWEB)

Tierney, M S

1990-12-15

A five-step procedure was used in the 1990 performance simulations to construct probability distributions of the uncertain variables appearing in the mathematical models used to simulate the Waste Isolation Pilot Plant's (WIPP's) performance. This procedure provides a consistent approach to the construction of probability distributions in cases where empirical data concerning a variable are sparse or absent and minimizes the amount of spurious information that is often introduced into a distribution by assumptions of nonspecialists. The procedure gives first priority to the professional judgment of subject-matter experts and emphasizes the use of site-specific empirical data for the construction of the probability distributions when such data are available. In the absence of sufficient empirical data, the procedure employs the Maximum Entropy Formalism and the subject-matter experts' subjective estimates of the parameters of the distribution to construct a distribution that can be used in a performance simulation. (author)
On the probability distribution of daily streamflow in the United States

Science.gov (United States)

Blum, Annalise G.; Archfield, Stacey A.; Vogel, Richard M.

2017-06-01

Daily streamflows are often represented by flow duration curves (FDCs), which illustrate the frequency with which flows are equaled or exceeded. FDCs have had broad applications across both operational and research hydrology for decades; however, modeling FDCs has proven elusive. Daily streamflow is a complex time series with flow values ranging over many orders of magnitude. The identification of a probability distribution that can approximate daily streamflow would improve understanding of the behavior of daily flows and the ability to estimate FDCs at ungaged river locations. Comparisons of modeled and empirical FDCs at nearly 400 unregulated, perennial streams illustrate that the four-parameter kappa distribution provides a very good representation of daily streamflow across the majority of physiographic regions in the conterminous United States (US). Further, for some regions of the US, the three-parameter generalized Pareto and lognormal distributions also provide a good approximation to FDCs. Similar results are found for the period of record FDCs, representing the long-term hydrologic regime at a site, and median annual FDCs, representing the behavior of flows in a typical year.
Classification of Knee Joint Vibration Signals Using Bivariate Feature Distribution Estimation and Maximal Posterior Probability Decision Criterion

Directory of Open Access Journals (Sweden)

Fang Zheng

2013-04-01

Full Text Available Analysis of knee joint vibration or vibroarthrographic (VAG signals using signal processing and machine learning algorithms possesses high potential for the noninvasive detection of articular cartilage degeneration, which may reduce unnecessary exploratory surgery. Feature representation of knee joint VAG signals helps characterize the pathological condition of degenerative articular cartilages in the knee. This paper used the kernel-based probability density estimation method to model the distributions of the VAG signals recorded from healthy subjects and patients with knee joint disorders. The estimated densities of the VAG signals showed explicit distributions of the normal and abnormal signal groups, along with the corresponding contours in the bivariate feature space. The signal classifications were performed by using the Fisher’s linear discriminant analysis, support vector machine with polynomial kernels, and the maximal posterior probability decision criterion. The maximal posterior probability decision criterion was able to provide the total classification accuracy of 86.67% and the area (Az of 0.9096 under the receiver operating characteristics curve, which were superior to the results obtained by either the Fisher’s linear discriminant analysis (accuracy: 81.33%, Az: 0.8564 or the support vector machine with polynomial kernels (accuracy: 81.33%, Az: 0.8533. Such results demonstrated the merits of the bivariate feature distribution estimation and the superiority of the maximal posterior probability decision criterion for analysis of knee joint VAG signals.
Comparison of multivariate and univariate statistical process control and monitoring methods

International Nuclear Information System (INIS)

Leger, R.P.; Garland, WM.J.; Macgregor, J.F.

1996-01-01

Work in recent years has lead to the development of multivariate process monitoring schemes which use Principal Component Analysis (PCA). This research compares the performance of a univariate scheme and a multivariate PCA scheme used for monitoring a simple process with 11 measured variables. The multivariate PCA scheme was able to adequately represent the process using two principal components. This resulted in a PCA monitoring scheme which used two charts as opposed to 11 charts for the univariate scheme and therefore had distinct advantages in terms of both data representation, presentation, and fault diagnosis capabilities. (author)

Properties of the probability distribution associated with the largest event in an earthquake cluster and their implications to foreshocks

International Nuclear Information System (INIS)

Zhuang Jiancang; Ogata, Yosihiko

2006-01-01

The space-time epidemic-type aftershock sequence model is a stochastic branching process in which earthquake activity is classified into background and clustering components and each earthquake triggers other earthquakes independently according to certain rules. This paper gives the probability distributions associated with the largest event in a cluster and their properties for all three cases when the process is subcritical, critical, and supercritical. One of the direct uses of these probability distributions is to evaluate the probability of an earthquake to be a foreshock, and magnitude distributions of foreshocks and nonforeshock earthquakes. To verify these theoretical results, the Japan Meteorological Agency earthquake catalog is analyzed. The proportion of events that have 1 or more larger descendants in total events is found to be as high as about 15%. When the differences between background events and triggered event in the behavior of triggering children are considered, a background event has a probability about 8% to be a foreshock. This probability decreases when the magnitude of the background event increases. These results, obtained from a complicated clustering model, where the characteristics of background events and triggered events are different, are consistent with the results obtained in [Ogata et al., Geophys. J. Int. 127, 17 (1996)] by using the conventional single-linked cluster declustering method
Properties of the probability distribution associated with the largest event in an earthquake cluster and their implications to foreshocks.

Science.gov (United States)

Zhuang, Jiancang; Ogata, Yosihiko

2006-04-01

The space-time epidemic-type aftershock sequence model is a stochastic branching process in which earthquake activity is classified into background and clustering components and each earthquake triggers other earthquakes independently according to certain rules. This paper gives the probability distributions associated with the largest event in a cluster and their properties for all three cases when the process is subcritical, critical, and supercritical. One of the direct uses of these probability distributions is to evaluate the probability of an earthquake to be a foreshock, and magnitude distributions of foreshocks and nonforeshock earthquakes. To verify these theoretical results, the Japan Meteorological Agency earthquake catalog is analyzed. The proportion of events that have 1 or more larger descendants in total events is found to be as high as about 15%. When the differences between background events and triggered event in the behavior of triggering children are considered, a background event has a probability about 8% to be a foreshock. This probability decreases when the magnitude of the background event increases. These results, obtained from a complicated clustering model, where the characteristics of background events and triggered events are different, are consistent with the results obtained in [Ogata, Geophys. J. Int. 127, 17 (1996)] by using the conventional single-linked cluster declustering method.
Providing probability distributions for the causal pathogen of clinical mastitis using naive Bayesian networks

NARCIS (Netherlands)

Steeneveld, W.; Gaag, van der L.C.; Barkema, H.W.; Hogeveen, H.

2009-01-01

Clinical mastitis (CM) can be caused by a wide variety of pathogens and farmers must start treatment before the actual causal pathogen is known. By providing a probability distribution for the causal pathogen, naive Bayesian networks (NBN) can serve as a management tool for farmers to decide which
A methodology for more efficient tail area sampling with discrete probability distribution

International Nuclear Information System (INIS)

Park, Sang Ryeol; Lee, Byung Ho; Kim, Tae Woon

1988-01-01

Monte Carlo Method is commonly used to observe the overall distribution and to determine the lower or upper bound value in statistical approach when direct analytical calculation is unavailable. However, this method would not be efficient if the tail area of a distribution is concerned. A new method entitled 'Two Step Tail Area Sampling' is developed, which uses the assumption of discrete probability distribution and samples only the tail area without distorting the overall distribution. This method uses two step sampling procedure. First, sampling at points separated by large intervals is done and second, sampling at points separated by small intervals is done with some check points determined at first step sampling. Comparison with Monte Carlo Method shows that the results obtained from the new method converge to analytic value faster than Monte Carlo Method if the numbers of calculation of both methods are the same. This new method is applied to DNBR (Departure from Nucleate Boiling Ratio) prediction problem in design of the pressurized light water nuclear reactor
The probability distribution model of air pollution index and its dominants in Kuala Lumpur

Science.gov (United States)

AL-Dhurafi, Nasr Ahmed; Razali, Ahmad Mahir; Masseran, Nurulkamal; Zamzuri, Zamira Hasanah

2016-11-01

This paper focuses on the statistical modeling for the distributions of air pollution index (API) and its sub-indexes data observed at Kuala Lumpur in Malaysia. Five pollutants or sub-indexes are measured including, carbon monoxide (CO); sulphur dioxide (SO2); nitrogen dioxide (NO2), and; particulate matter (PM10). Four probability distributions are considered, namely log-normal, exponential, Gamma and Weibull in search for the best fit distribution to the Malaysian air pollutants data. In order to determine the best distribution for describing the air pollutants data, five goodness-of-fit criteria's are applied. This will help in minimizing the uncertainty in pollution resource estimates and improving the assessment phase of planning. The conflict in criterion results for selecting the best distribution was overcome by using the weight of ranks method. We found that the Gamma distribution is the best distribution for the majority of air pollutants data in Kuala Lumpur.
Foundations of quantization for probability distributions

CERN Document Server

Graf, Siegfried

2000-01-01

Due to the rapidly increasing need for methods of data compression, quantization has become a flourishing field in signal and image processing and information theory. The same techniques are also used in statistics (cluster analysis), pattern recognition, and operations research (optimal location of service centers). The book gives the first mathematically rigorous account of the fundamental theory underlying these applications. The emphasis is on the asymptotics of quantization errors for absolutely continuous and special classes of singular probabilities (surface measures, self-similar measures) presenting some new results for the first time. Written for researchers and graduate students in probability theory the monograph is of potential interest to all people working in the disciplines mentioned above.
Research on Energy-Saving Design of Overhead Travelling Crane Camber Based on Probability Load Distribution

Directory of Open Access Journals (Sweden)

Tong Yifei

2014-01-01

Full Text Available Crane is a mechanical device, used widely to move materials in modern production. It is reported that the energy consumptions of China are at least 5–8 times of other developing countries. Thus, energy consumption becomes an unavoidable topic. There are several reasons influencing the energy loss, and the camber of the girder is the one not to be neglected. In this paper, the problem of the deflections induced by the moving payload in the girder of overhead travelling crane is examined. The evaluation of a camber giving a counterdeflection of the girder is proposed in order to get minimum energy consumptions for trolley to move along a nonstraight support. To this aim, probabilistic payload distributions are considered instead of fixed or rated loads involved in other researches. Taking 50/10 t bridge crane as a research object, the probability loads are determined by analysis of load distribution density functions. According to load distribution, camber design under different probability loads is discussed in detail as well as energy consumptions distribution. The research results provide the design reference of reasonable camber to obtain the least energy consumption for climbing corresponding to different P0; thus energy-saving design can be achieved.
Tumour control probability (TCP) for non-uniform activity distribution in radionuclide therapy

International Nuclear Information System (INIS)

Uusijaervi, Helena; Bernhardt, Peter; Forssell-Aronsson, Eva

2008-01-01

Non-uniform radionuclide distribution in tumours will lead to a non-uniform absorbed dose. The aim of this study was to investigate how tumour control probability (TCP) depends on the radionuclide distribution in the tumour, both macroscopically and at the subcellular level. The absorbed dose in the cell nuclei of tumours was calculated for 90 Y, 177 Lu, 103m Rh and 211 At. The radionuclides were uniformly distributed within the subcellular compartment and they were uniformly, normally or log-normally distributed among the cells in the tumour. When all cells contain the same amount of activity, the cumulated activities required for TCP = 0.99 (A-tilde TCP=0.99 ) were 1.5-2 and 2-3 times higher when the activity was distributed on the cell membrane compared to in the cell nucleus for 103m Rh and 211 At, respectively. TCP for 90 Y was not affected by different radionuclide distributions, whereas for 177 Lu, it was slightly affected when the radionuclide was in the nucleus. TCP for 103m Rh and 211 At were affected by different radionuclide distributions to a great extent when the radionuclides were in the cell nucleus and to lesser extents when the radionuclides were distributed on the cell membrane or in the cytoplasm. When the activity was distributed in the nucleus, A-tilde TCP=0.99 increased when the activity distribution became more heterogeneous for 103m Rh and 211 At, and the increase was large when the activity was normally distributed compared to log-normally distributed. When the activity was distributed on the cell membrane, A-tilde TCP=0.99 was not affected for 103m Rh and 211 At when the activity distribution became more heterogeneous. A-tilde TCP=0.99 for 90 Y and 177 Lu were not affected by different activity distributions, neither macroscopic nor subcellular
Birth/birth-death processes and their computable transition probabilities with biological applications.

Science.gov (United States)

Ho, Lam Si Tung; Xu, Jason; Crawford, Forrest W; Minin, Vladimir N; Suchard, Marc A

2018-03-01

Birth-death processes track the size of a univariate population, but many biological systems involve interaction between populations, necessitating models for two or more populations simultaneously. A lack of efficient methods for evaluating finite-time transition probabilities of bivariate processes, however, has restricted statistical inference in these models. Researchers rely on computationally expensive methods such as matrix exponentiation or Monte Carlo approximation, restricting likelihood-based inference to small systems, or indirect methods such as approximate Bayesian computation. In this paper, we introduce the birth/birth-death process, a tractable bivariate extension of the birth-death process, where rates are allowed to be nonlinear. We develop an efficient algorithm to calculate its transition probabilities using a continued fraction representation of their Laplace transforms. Next, we identify several exemplary models arising in molecular epidemiology, macro-parasite evolution, and infectious disease modeling that fall within this class, and demonstrate advantages of our proposed method over existing approaches to inference in these models. Notably, the ubiquitous stochastic susceptible-infectious-removed (SIR) model falls within this class, and we emphasize that computable transition probabilities newly enable direct inference of parameters in the SIR model. We also propose a very fast method for approximating the transition probabilities under the SIR model via a novel branching process simplification, and compare it to the continued fraction representation method with application to the 17th century plague in Eyam. Although the two methods produce similar maximum a posteriori estimates, the branching process approximation fails to capture the correlation structure in the joint posterior distribution.
Random phenomena fundamentals of probability and statistics for engineers

CERN Document Server

Ogunnaike, Babatunde A

2009-01-01

PreludeApproach PhilosophyFour Basic PrinciplesI FoundationsTwo Motivating ExamplesYield Improvement in a Chemical ProcessQuality Assurance in a Glass Sheet Manufacturing ProcessOutline of a Systematic ApproachRandom Phenomena, Variability, and UncertaintyTwo Extreme Idealizations of Natural PhenomenaRandom Mass PhenomenaIntroducing ProbabilityThe Probabilistic FrameworkII ProbabilityFundamentals of Probability TheoryBuilding BlocksOperationsProbabilityConditional ProbabilityIndependenceRandom Variables and DistributionsDistributionsMathematical ExpectationCharacterizing DistributionsSpecial Derived Probability FunctionsMultidimensional Random VariablesDistributions of Several Random VariablesDistributional Characteristics of Jointly Distributed Random VariablesRandom Variable TransformationsSingle Variable TransformationsBivariate TransformationsGeneral Multivariate TransformationsApplication Case Studies I: ProbabilityMendel and HeredityWorld War II Warship Tactical Response Under AttackIII DistributionsIde...
Various models for pion probability distributions from heavy-ion collisions

International Nuclear Information System (INIS)

Mekjian, A.Z.; Mekjian, A.Z.; Schlei, B.R.; Strottman, D.; Schlei, B.R.

1998-01-01

Various models for pion multiplicity distributions produced in relativistic heavy ion collisions are discussed. The models include a relativistic hydrodynamic model, a thermodynamic description, an emitting source pion laser model, and a description which generates a negative binomial description. The approach developed can be used to discuss other cases which will be mentioned. The pion probability distributions for these various cases are compared. Comparison of the pion laser model and Bose-Einstein condensation in a laser trap and with the thermal model are made. The thermal model and hydrodynamic model are also used to illustrate why the number of pions never diverges and why the Bose-Einstein correction effects are relatively small. The pion emission strength η of a Poisson emitter and a critical density η c are connected in a thermal model by η/n c =e -m/T <1, and this fact reduces any Bose-Einstein correction effects in the number and number fluctuation of pions. Fluctuations can be much larger than Poisson in the pion laser model and for a negative binomial description. The clan representation of the negative binomial distribution due to Van Hove and Giovannini is discussed using the present description. Applications to CERN/NA44 and CERN/NA49 data are discussed in terms of the relativistic hydrodynamic model. copyright 1998 The American Physical Society
Analytical models of probability distribution and excess noise factor of solid state photomultiplier signals with crosstalk

International Nuclear Information System (INIS)

Vinogradov, S.

2012-01-01

Silicon Photomultipliers (SiPM), also called Solid State Photomultipliers (SSPM), are based on Geiger mode avalanche breakdown that is limited by a strong negative feedback. An SSPM can detect and resolve single photons due to the high gain and ultra-low excess noise of avalanche multiplication in this mode. Crosstalk and afterpulsing processes associated with the high gain introduce specific excess noise and deteriorate the photon number resolution of the SSPM. The probabilistic features of these processes are widely studied because of its significance for the SSPM design, characterization, optimization and application, but the process modeling is mostly based on Monte Carlo simulations and numerical methods. In this study, crosstalk is considered to be a branching Poisson process, and analytical models of probability distribution and excess noise factor (ENF) of SSPM signals based on the Borel distribution as an advance on the geometric distribution models are presented and discussed. The models are found to be in a good agreement with the experimental probability distributions for dark counts and a few photon spectrums in a wide range of fired pixels number as well as with observed super-linear behavior of crosstalk ENF.
The probability distribution of maintenance cost of a system affected by the gamma process of degradation: Finite time solution

International Nuclear Information System (INIS)

Cheng, Tianjin; Pandey, Mahesh D.; Weide, J.A.M. van der

2012-01-01

The stochastic gamma process has been widely used to model uncertain degradation in engineering systems and structures. The optimization of the condition-based maintenance (CBM) policy is typically based on the minimization of the asymptotic cost rate. In the financial planning of a maintenance program, however, a more accurate prediction interval for the cost is needed for prudent decision making. The prediction interval cannot be estimated unless the probability distribution of cost is known. In this context, the asymptotic cost rate has a limited utility. This paper presents the derivation of the probability distribution of maintenance cost, when the system degradation is modelled as a stochastic gamma process. A renewal equation is formulated to derive the characteristic function, then the discrete Fourier transform of the characteristic function leads to the complete probability distribution of cost in a finite time setting. The proposed approach is useful for a precise estimation of prediction limits and optimization of the maintenance cost.
Measuring sensitivity in pharmacoeconomic studies. Refining point sensitivity and range sensitivity by incorporating probability distributions.

Science.gov (United States)

Nuijten, M J

1999-07-01

The aim of the present study is to describe a refinement of a previously presented method, based on the concept of point sensitivity, to deal with uncertainty in economic studies. The original method was refined by the incorporation of probability distributions which allow a more accurate assessment of the level of uncertainty in the model. In addition, a bootstrap method was used to create a probability distribution for a fixed input variable based on a limited number of data points. The original method was limited in that the sensitivity measurement was based on a uniform distribution of the variables and that the overall sensitivity measure was based on a subjectively chosen range which excludes the impact of values outside the range on the overall sensitivity. The concepts of the refined method were illustrated using a Markov model of depression. The application of the refined method substantially changed the ranking of the most sensitive variables compared with the original method. The response rate became the most sensitive variable instead of the 'per diem' for hospitalisation. The refinement of the original method yields sensitivity outcomes, which greater reflect the real uncertainty in economic studies.
Exploring non-signalling polytopes with negative probability

International Nuclear Information System (INIS)

Oas, G; Barros, J Acacio de; Carvalhaes, C

2014-01-01

Bipartite and tripartite EPR–Bell type systems are examined via joint quasi-probability distributions where probabilities are permitted to be negative. It is shown that such distributions exist only when the no-signalling condition is satisfied. A characteristic measure, the probability mass, is introduced and, via its minimization, limits the number of quasi-distributions describing a given marginal probability distribution. The minimized probability mass is shown to be an alternative way to characterize non-local systems. Non-signalling polytopes for two to eight settings in the bipartite scenario are examined and compared to prior work. Examining perfect cloning of non-local systems within the tripartite scenario suggests defining two categories of signalling. It is seen that many properties of non-local systems can be efficiently described by quasi-probability theory. (paper)
Combinatorial bounds on the α-divergence of univariate mixture models

KAUST Repository

Nielsen, Frank; Sun, Ke

2017-01-01

We derive lower- and upper-bounds of α-divergence between univariate mixture models with components in the exponential family. Three pairs of bounds are presented in order with increasing quality and increasing computational cost. They are verified
The Use of Univariate and Multivariate Analyses in the Geochemical Exploration, Ravanj Lead Mine, Delijan, Iran

Directory of Open Access Journals (Sweden)

Mostafa Nejadhadad

2017-11-01

Full Text Available A geochemical exploration program was applied to recognize the anomalous geochemical haloes at the Ravanj lead mine, Delijan, Iran. Sampling of unweathered rocks were undertaken across rock exposures on a 10 × 10 meter grid (n = 302 as well as the accessible parts of underground mine A (n = 42. First, the threshold values of all elements were determined using the cut-off values used in the exploratory data analysis (EDA method. Then, for further studies, elements with lognormal distributions (Pb, Zn, Ag, As, Cd, Co, Cu, Sb, S, Sr, Th, Ba, Bi, Fe, Ni and Mn were selected. Robustness against outliers is achieved by application of central log ratio transformation to address the closure problems with compositional data prior to principle components analysis (PCA. Results of these analyses show that, in the Ravanj deposit, Pb mineralization is characterized by a Pb-Ba-Ag-Sb ± Zn ± Cd association. The supra-mineralization haloes are characterized by barite and tetrahedrite in a Ba- Th- Ag- Cu- Sb- As- Sr association and sub-mineralization haloes are comprised of pyrite and tetrahedrite, probably reflecting a Fe-Cu-As-Bi-Ni-Co-Mo-Mn association. Using univariate and multivariate geostatistical analyses (e.g., EDA and robust PCA, four anomalies were detected and mapped in Block A of the Ravanj deposit. Anomalies 1 and 2 are around the ancient orebodies. Anomaly 3 is located in a thin bedded limestone-shale intercalation unit that does not show significant mineralization. Drilling of the fourth anomaly suggested a low grade, non-economic Pb mineralization.
Serial Spike Time Correlations Affect Probability Distribution of Joint Spike Events.

Science.gov (United States)

Shahi, Mina; van Vreeswijk, Carl; Pipa, Gordon

2016-01-01

Detecting the existence of temporally coordinated spiking activity, and its role in information processing in the cortex, has remained a major challenge for neuroscience research. Different methods and approaches have been suggested to test whether the observed synchronized events are significantly different from those expected by chance. To analyze the simultaneous spike trains for precise spike correlation, these methods typically model the spike trains as a Poisson process implying that the generation of each spike is independent of all the other spikes. However, studies have shown that neural spike trains exhibit dependence among spike sequences, such as the absolute and relative refractory periods which govern the spike probability of the oncoming action potential based on the time of the last spike, or the bursting behavior, which is characterized by short epochs of rapid action potentials, followed by longer episodes of silence. Here we investigate non-renewal processes with the inter-spike interval distribution model that incorporates spike-history dependence of individual neurons. For that, we use the Monte Carlo method to estimate the full shape of the coincidence count distribution and to generate false positives for coincidence detection. The results show that compared to the distributions based on homogeneous Poisson processes, and also non-Poisson processes, the width of the distribution of joint spike events changes. Non-renewal processes can lead to both heavy tailed or narrow coincidence distribution. We conclude that small differences in the exact autostructure of the point process can cause large differences in the width of a coincidence distribution. Therefore, manipulations of the autostructure for the estimation of significance of joint spike events seem to be inadequate.
Evaluating the suitability of wind speed probability distribution models: A case of study of east and southeast parts of Iran

International Nuclear Information System (INIS)

Alavi, Omid; Mohammadi, Kasra; Mostafaeipour, Ali

2016-01-01

Highlights: • Suitability of different wind speed probability functions is assessed. • 5 stations distributed in east and south-east of Iran are considered as case studies. • Nakagami distribution is tested for first time and compared with 7 other functions. • Due to difference in wind features, best function is not similar for all stations. - Abstract: Precise information of wind speed probability distribution is truly significant for many wind energy applications. The objective of this study is to evaluate the suitability of different probability functions for estimating wind speed distribution at five stations, distributed in the east and southeast of Iran. Nakagami distribution function is utilized for the first time to estimate the distribution of wind speed. The performance of Nakagami function is compared with seven typically used distribution functions. The achieved results reveal that the more effective function is not similar among all stations. Wind speed characteristics, quantity and quality of the recorded wind speed data can be considered as influential parameters on the performance of the distribution functions. Also, the skewness of the recorded wind speed data may have influence on the accuracy of the Nakagami distribution. For Chabahar and Khaf stations the Nakagami distribution shows the highest performance while for Lutak, Rafsanjan and Zabol stations the Gamma, Generalized Extreme Value and Inverse-Gaussian distributions offer the best fits, respectively. Based on the analysis, the Nakagami distribution can generally be considered as an effective distribution since it provides the best fits in 2 stations and ranks 3rd to 5th in the remaining stations; however, due to the close performance of the Nakagami and Weibull distributions and also flexibility of the Weibull function as its widely proven feature, more assessments on the performance of the Nakagami distribution are required.
Failure probability under parameter uncertainty.

Science.gov (United States)

Gerrard, R; Tsanakas, A

2011-05-01

In many problems of risk analysis, failure is equivalent to the event of a random risk factor exceeding a given threshold. Failure probabilities can be controlled if a decisionmaker is able to set the threshold at an appropriate level. This abstract situation applies, for example, to environmental risks with infrastructure controls; to supply chain risks with inventory controls; and to insurance solvency risks with capital controls. However, uncertainty around the distribution of the risk factor implies that parameter error will be present and the measures taken to control failure probabilities may not be effective. We show that parameter uncertainty increases the probability (understood as expected frequency) of failures. For a large class of loss distributions, arising from increasing transformations of location-scale families (including the log-normal, Weibull, and Pareto distributions), the article shows that failure probabilities can be exactly calculated, as they are independent of the true (but unknown) parameters. Hence it is possible to obtain an explicit measure of the effect of parameter uncertainty on failure probability. Failure probability can be controlled in two different ways: (1) by reducing the nominal required failure probability, depending on the size of the available data set, and (2) by modifying of the distribution itself that is used to calculate the risk control. Approach (1) corresponds to a frequentist/regulatory view of probability, while approach (2) is consistent with a Bayesian/personalistic view. We furthermore show that the two approaches are consistent in achieving the required failure probability. Finally, we briefly discuss the effects of data pooling and its systemic risk implications. © 2010 Society for Risk Analysis.

New method for extracting tumors in PET/CT images based on the probability distribution

International Nuclear Information System (INIS)

Nitta, Shuhei; Hontani, Hidekata; Hukami, Tadanori

2006-01-01

In this report, we propose a method for extracting tumors from PET/CT images by referring to the probability distribution of pixel values in the PET image. In the proposed method, first, the organs that normally take up fluorodeoxyglucose (FDG) (e.g., the liver, kidneys, and brain) are extracted. Then, the tumors are extracted from the images. The distribution of pixel values in PET images differs in each region of the body. Therefore, the threshold for detecting tumors is adaptively determined by referring to the distribution. We applied the proposed method to 37 cases and evaluated its performance. This report also presents the results of experiments comparing the proposed method and another method in which the pixel values are normalized for extracting tumors. (author)
[A SAS marco program for batch processing of univariate Cox regression analysis for great database].

Science.gov (United States)

Yang, Rendong; Xiong, Jie; Peng, Yangqin; Peng, Xiaoning; Zeng, Xiaomin

2015-02-01

To realize batch processing of univariate Cox regression analysis for great database by SAS marco program. We wrote a SAS macro program, which can filter, integrate, and export P values to Excel by SAS9.2. The program was used for screening survival correlated RNA molecules of ovarian cancer. A SAS marco program could finish the batch processing of univariate Cox regression analysis, the selection and export of the results. The SAS macro program has potential applications in reducing the workload of statistical analysis and providing a basis for batch processing of univariate Cox regression analysis.
A comparison of the probability distribution of observed substorm magnitude with that predicted by a minimal substorm model

Directory of Open Access Journals (Sweden)

S. K. Morley

2007-11-01

Full Text Available We compare the probability distributions of substorm magnetic bay magnitudes from observations and a minimal substorm model. The observed distribution was derived previously and independently using the IL index from the IMAGE magnetometer network. The model distribution is derived from a synthetic AL index time series created using real solar wind data and a minimal substorm model, which was previously shown to reproduce observed substorm waiting times. There are two free parameters in the model which scale the contributions to AL from the directly-driven DP2 electrojet and loading-unloading DP1 electrojet, respectively. In a limited region of the 2-D parameter space of the model, the probability distribution of modelled substorm bay magnitudes is not significantly different to the observed distribution. The ranges of the two parameters giving acceptable (95% confidence level agreement are consistent with expectations using results from other studies. The approximately linear relationship between the two free parameters over these ranges implies that the substorm magnitude simply scales linearly with the solar wind power input at the time of substorm onset.
On the Meta Distribution of Coverage Probability in Uplink Cellular Networks

KAUST Repository

Elsawy, Hesham

2017-04-07

This letter studies the meta distribution of coverage probability (CP), within a stochastic geometry framework, for cellular uplink transmission with fractional path-loss inversion power control. Using the widely accepted Poisson point process (PPP) for modeling the spatial locations of base stations (BSs), we obtain the percentiles of users that achieve a target uplink CP over an arbitrary, but fixed, realization of the PPP. To this end, the effect of the users activity factor (p) and the path-loss compensation factor () on the uplink performance are analyzed. The results show that decreasing p and/or increasing reduce the CP variation around the spatially averaged value.
Conditional probability distribution associated to the E-M image reconstruction algorithm for neutron stimulated emission tomography

International Nuclear Information System (INIS)

Viana, R.S.; Yoriyaz, H.; Santos, A.

2011-01-01

The Expectation-Maximization (E-M) algorithm is an iterative computational method for maximum likelihood (M-L) estimates, useful in a variety of incomplete-data problems. Due to its stochastic nature, one of the most relevant applications of E-M algorithm is the reconstruction of emission tomography images. In this paper, the statistical formulation of the E-M algorithm was applied to the in vivo spectrographic imaging of stable isotopes called Neutron Stimulated Emission Computed Tomography (NSECT). In the process of E-M algorithm iteration, the conditional probability distribution plays a very important role to achieve high quality image. This present work proposes an alternative methodology for the generation of the conditional probability distribution associated to the E-M reconstruction algorithm, using the Monte Carlo code MCNP5 and with the application of the reciprocity theorem. (author)
Conditional probability distribution associated to the E-M image reconstruction algorithm for neutron stimulated emission tomography

Energy Technology Data Exchange (ETDEWEB)

Viana, R.S.; Yoriyaz, H.; Santos, A., E-mail: rodrigossviana@gmail.com, E-mail: hyoriyaz@ipen.br, E-mail: asantos@ipen.br [Instituto de Pesquisas Energeticas e Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil)

2011-07-01

The Expectation-Maximization (E-M) algorithm is an iterative computational method for maximum likelihood (M-L) estimates, useful in a variety of incomplete-data problems. Due to its stochastic nature, one of the most relevant applications of E-M algorithm is the reconstruction of emission tomography images. In this paper, the statistical formulation of the E-M algorithm was applied to the in vivo spectrographic imaging of stable isotopes called Neutron Stimulated Emission Computed Tomography (NSECT). In the process of E-M algorithm iteration, the conditional probability distribution plays a very important role to achieve high quality image. This present work proposes an alternative methodology for the generation of the conditional probability distribution associated to the E-M reconstruction algorithm, using the Monte Carlo code MCNP5 and with the application of the reciprocity theorem. (author)
A general formula for computing maximum proportion correct scores in various psychophysical paradigms with arbitrary probability distributions of stimulus observations.

Science.gov (United States)

Dai, Huanping; Micheyl, Christophe

2015-05-01

Proportion correct (Pc) is a fundamental measure of task performance in psychophysics. The maximum Pc score that can be achieved by an optimal (maximum-likelihood) observer in a given task is of both theoretical and practical importance, because it sets an upper limit on human performance. Within the framework of signal detection theory, analytical solutions for computing the maximum Pc score have been established for several common experimental paradigms under the assumption of Gaussian additive internal noise. However, as the scope of applications of psychophysical signal detection theory expands, the need is growing for psychophysicists to compute maximum Pc scores for situations involving non-Gaussian (internal or stimulus-induced) noise. In this article, we provide a general formula for computing the maximum Pc in various psychophysical experimental paradigms for arbitrary probability distributions of sensory activity. Moreover, easy-to-use MATLAB code implementing the formula is provided. Practical applications of the formula are illustrated, and its accuracy is evaluated, for two paradigms and two types of probability distributions (uniform and Gaussian). The results demonstrate that Pc scores computed using the formula remain accurate even for continuous probability distributions, as long as the conversion from continuous probability density functions to discrete probability mass functions is supported by a sufficiently high sampling resolution. We hope that the exposition in this article, and the freely available MATLAB code, facilitates calculations of maximum performance for a wider range of experimental situations, as well as explorations of the impact of different assumptions concerning internal-noise distributions on maximum performance in psychophysical experiments.
The probability distribution of extreme precipitation

Science.gov (United States)

Korolev, V. Yu.; Gorshenin, A. K.

2017-12-01

On the basis of the negative binomial distribution of the duration of wet periods calculated per day, an asymptotic model is proposed for distributing the maximum daily rainfall volume during the wet period, having the form of a mixture of Frechet distributions and coinciding with the distribution of the positive degree of a random variable having the Fisher-Snedecor distribution. The method of proving the corresponding result is based on limit theorems for extreme order statistics in samples of a random volume with a mixed Poisson distribution. The adequacy of the models proposed and methods of their statistical analysis is demonstrated by the example of estimating the extreme distribution parameters based on real data.
Snow-melt flood frequency analysis by means of copula based 2D probability distributions for the Narew River in Poland

Directory of Open Access Journals (Sweden)

Bogdan Ozga-Zielinski

2016-06-01

New hydrological insights for the region: The results indicated that the 2D normal probability distribution model gives a better probabilistic description of snowmelt floods characterized by the 2-dimensional random variable (Qmax,f, Vf compared to the elliptical Gaussian copula and Archimedean 1-parameter Gumbel–Hougaard copula models, in particular from the view point of probability of exceedance as well as complexity and time of computation. Nevertheless, the copula approach offers a new perspective in estimating the 2D probability distribution for multidimensional random variables. Results showed that the 2D model for snowmelt floods built using the Gumbel–Hougaard copula is much better than the model built using the Gaussian copula.
A comparison between univariate probabilistic and multivariate (logistic regression) methods for landslide susceptibility analysis: the example of the Febbraro valley (Northern Alps, Italy)

Science.gov (United States)

Rossi, M.; Apuani, T.; Felletti, F.

2009-04-01

The aim of this paper is to compare the results of two statistical methods for landslide susceptibility analysis: 1) univariate probabilistic method based on landslide susceptibility index, 2) multivariate method (logistic regression). The study area is the Febbraro valley, located in the central Italian Alps, where different types of metamorphic rocks croup out. On the eastern part of the studied basin a quaternary cover represented by colluvial and secondarily, by glacial deposits, is dominant. In this study 110 earth flows, mainly located toward NE portion of the catchment, were analyzed. They involve only the colluvial deposits and their extension mainly ranges from 36 to 3173 m2. Both statistical methods require to establish a spatial database, in which each landslide is described by several parameters that can be assigned using a main scarp central point of landslide. The spatial database is constructed using a Geographical Information System (GIS). Each landslide is described by several parameters corresponding to the value of main scarp central point of the landslide. Based on bibliographic review a total of 15 predisposing factors were utilized. The width of the intervals, in which the maps of the predisposing factors have to be reclassified, has been defined assuming constant intervals to: elevation (100 m), slope (5 °), solar radiation (0.1 MJ/cm2/year), profile curvature (1.2 1/m), tangential curvature (2.2 1/m), drainage density (0.5), lineament density (0.00126). For the other parameters have been used the results of the probability-probability plots analysis and the statistical indexes of landslides site. In particular slope length (0 ÷ 2, 2 ÷ 5, 5 ÷ 10, 10 ÷ 20, 20 ÷ 35, 35 ÷ 260), accumulation flow (0 ÷ 1, 1 ÷ 2, 2 ÷ 5, 5 ÷ 12, 12 ÷ 60, 60 ÷27265), Topographic Wetness Index 0 ÷ 0.74, 0.74 ÷ 1.94, 1.94 ÷ 2.62, 2.62 ÷ 3.48, 3.48 ÷ 6,00, 6.00 ÷ 9.44), Stream Power Index (0 ÷ 0.64, 0.64 ÷ 1.28, 1.28 ÷ 1.81, 1.81 ÷ 4.20, 4.20 ÷ 9
Acceleration techniques in the univariate Lipschitz global optimization

Science.gov (United States)

Sergeyev, Yaroslav D.; Kvasov, Dmitri E.; Mukhametzhanov, Marat S.; De Franco, Angela

2016-10-01

Univariate box-constrained Lipschitz global optimization problems are considered in this contribution. Geometric and information statistical approaches are presented. The novel powerful local tuning and local improvement techniques are described in the contribution as well as the traditional ways to estimate the Lipschitz constant. The advantages of the presented local tuning and local improvement techniques are demonstrated using the operational characteristics approach for comparing deterministic global optimization algorithms on the class of 100 widely used test functions.
Probability distribution of dose rates in the body tissue as a function of the rhytm of Sr90 administration and the age of animals

International Nuclear Information System (INIS)

Rasin, I.M.; Sarapul'tsev, I.A.

1975-01-01

The probability distribution of tissue radiation doses in the skeleton were studied in experiments on swines and dogs. When introducing Sr-90 into the organism from the day of birth till 90 days dose rate probability distribution is characterized by one, or, for adult animals, by two independent aggregates. Each of these aggregates correspond to the normal distribution law
An uncertain journey around the tails of multivariate hydrological distributions

Science.gov (United States)

Serinaldi, Francesco

2013-10-01

Moving from univariate to multivariate frequency analysis, this study extends the Klemeš' critique of the widespread belief that the increasingly refined mathematical structures of probability functions increase the accuracy and credibility of the extrapolated upper tails of the fitted distribution models. In particular, we discuss key aspects of multivariate frequency analysis applied to hydrological data such as the selection of multivariate design events (i.e., appropriate subsets or scenarios of multiplets that exhibit the same joint probability to be used in design applications) and the assessment of the corresponding uncertainty. Since these problems are often overlooked or treated separately, and sometimes confused, we attempt to clarify properties, advantages, shortcomings, and reliability of results of frequency analysis. We suggest a selection method of multivariate design events with prescribed joint probability based on simple Monte Carlo simulations that accounts for the uncertainty affecting the inference results and the multivariate extreme quantiles. It is also shown that the exploration of the p-level probability regions of a joint distribution returns a set of events that is a subset of the p-level scenarios resulting from an appropriate assessment of the sampling uncertainty, thus tending to overlook more extreme and potentially dangerous events with the same (uncertain) joint probability. Moreover, a quantitative assessment of the uncertainty of multivariate quantiles is provided by introducing the concept of joint confidence intervals. From an operational point of view, the simulated event sets describing the distribution of the multivariate p-level quantiles can be used to perform multivariate risk analysis under sampling uncertainty. As an example of the practical implications of this study, we analyze two case studies already presented in the literature.
Assessing the Adequacy of Probability Distributions for Estimating the Extreme Events of Air Temperature in Dabaa Region

International Nuclear Information System (INIS)

El-Shanshoury, Gh.I.

2015-01-01

Assessing the adequacy of probability distributions for estimating the extreme events of air temperature in Dabaa region is one of the pre-requisite s for any design purpose at Dabaa site which can be achieved by probability approach. In the present study, three extreme value distributions are considered and compared to estimate the extreme events of monthly and annual maximum and minimum temperature. These distributions include the Gumbel/Frechet distributions for estimating the extreme maximum values and Gumbel /Weibull distributions for estimating the extreme minimum values. Lieblein technique and Method of Moments are applied for estimating the distribution para meters. Subsequently, the required design values with a given return period of exceedance are obtained. Goodness-of-Fit tests involving Kolmogorov-Smirnov and Anderson-Darling are used for checking the adequacy of fitting the method/distribution for the estimation of maximum/minimum temperature. Mean Absolute Relative Deviation, Root Mean Square Error and Relative Mean Square Deviation are calculated, as the performance indicators, to judge which distribution and method of parameters estimation are the most appropriate one to estimate the extreme temperatures. The present study indicated that the Weibull distribution combined with Method of Moment estimators gives the highest fit, most reliable, accurate predictions for estimating the extreme monthly and annual minimum temperature. The Gumbel distribution combined with Method of Moment estimators showed the highest fit, accurate predictions for the estimation of the extreme monthly and annual maximum temperature except for July, August, October and November. The study shows that the combination of Frechet distribution with Method of Moment is the most accurate for estimating the extreme maximum temperature in July, August and November months while t he Gumbel distribution and Lieblein technique is the best for October
Probability distribution of pitting corrosion depth and rate in underground pipelines: A Monte Carlo study

International Nuclear Information System (INIS)

Caleyo, F.; Velazquez, J.C.; Valor, A.; Hallen, J.M.

2009-01-01

The probability distributions of external-corrosion pit depth and pit growth rate were investigated in underground pipelines using Monte Carlo simulations. The study combines a predictive pit growth model developed by the authors with the observed distributions of the model variables in a range of soils. Depending on the pipeline age, any of the three maximal extreme value distributions, i.e. Weibull, Frechet or Gumbel, can arise as the best fit to the pitting depth and rate data. The Frechet distribution best fits the corrosion data for long exposure periods. This can be explained by considering the long-term stabilization of the diffusion-controlled pit growth. The findings of the study provide reliability analysts with accurate information regarding the stochastic characteristics of the pitting damage in underground pipelines.
Probability distribution of pitting corrosion depth and rate in underground pipelines: A Monte Carlo study

Energy Technology Data Exchange (ETDEWEB)

Caleyo, F. [Departamento de Ingenieria Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, 07738 Mexico, D.F. (Mexico)], E-mail: fcaleyo@gmail.com; Velazquez, J.C. [Departamento de Ingenieria Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, 07738 Mexico, D.F. (Mexico); Valor, A. [Facultad de Fisica, Universidad de La Habana, San Lazaro y L, Vedado, 10400, La Habana (Cuba); Hallen, J.M. [Departamento de Ingenieria Metalurgica, ESIQIE, IPN, UPALM Edif. 7, Zacatenco, 07738 Mexico, D.F. (Mexico)

2009-09-15

The probability distributions of external-corrosion pit depth and pit growth rate were investigated in underground pipelines using Monte Carlo simulations. The study combines a predictive pit growth model developed by the authors with the observed distributions of the model variables in a range of soils. Depending on the pipeline age, any of the three maximal extreme value distributions, i.e. Weibull, Frechet or Gumbel, can arise as the best fit to the pitting depth and rate data. The Frechet distribution best fits the corrosion data for long exposure periods. This can be explained by considering the long-term stabilization of the diffusion-controlled pit growth. The findings of the study provide reliability analysts with accurate information regarding the stochastic characteristics of the pitting damage in underground pipelines.
A probability space for quantum models

Science.gov (United States)

Lemmens, L. F.

2017-06-01

A probability space contains a set of outcomes, a collection of events formed by subsets of the set of outcomes and probabilities defined for all events. A reformulation in terms of propositions allows to use the maximum entropy method to assign the probabilities taking some constraints into account. The construction of a probability space for quantum models is determined by the choice of propositions, choosing the constraints and making the probability assignment by the maximum entropy method. This approach shows, how typical quantum distributions such as Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein are partly related with well-known classical distributions. The relation between the conditional probability density, given some averages as constraints and the appropriate ensemble is elucidated.
FUNSTAT and statistical image representations

Science.gov (United States)

Parzen, E.

1983-01-01

General ideas of functional statistical inference analysis of one sample and two samples, univariate and bivariate are outlined. ONESAM program is applied to analyze the univariate probability distributions of multi-spectral image data.
Matrix-exponential distributions in applied probability

CERN Document Server

Bladt, Mogens

2017-01-01

This book contains an in-depth treatment of matrix-exponential (ME) distributions and their sub-class of phase-type (PH) distributions. Loosely speaking, an ME distribution is obtained through replacing the intensity parameter in an exponential distribution by a matrix. The ME distributions can also be identified as the class of non-negative distributions with rational Laplace transforms. If the matrix has the structure of a sub-intensity matrix for a Markov jump process we obtain a PH distribution which allows for nice probabilistic interpretations facilitating the derivation of exact solutions and closed form formulas. The full potential of ME and PH unfolds in their use in stochastic modelling. Several chapters on generic applications, like renewal theory, random walks and regenerative processes, are included together with some specific examples from queueing theory and insurance risk. We emphasize our intention towards applications by including an extensive treatment on statistical methods for PH distribu...
Univariate decision tree induction using maximum margin classification

OpenAIRE

Yıldız, Olcay Taner

2012-01-01

In many pattern recognition applications, first decision trees are used due to their simplicity and easily interpretable nature. In this paper, we propose a new decision tree learning algorithm called univariate margin tree where, for each continuous attribute, the best split is found using convex optimization. Our simulation results on 47 data sets show that the novel margin tree classifier performs at least as good as C4.5 and linear discriminant tree (LDT) with a similar time complexity. F...

On bivariate geometric distribution

Directory of Open Access Journals (Sweden)

K. Jayakumar

2013-05-01

Full Text Available Characterizations of bivariate geometric distribution using univariate and bivariate geometric compounding are obtained. Autoregressive models with marginals as bivariate geometric distribution are developed. Various bivariate geometric distributions analogous to important bivariate exponential distributions like, Marshall-Olkin’s bivariate exponential, Downton’s bivariate exponential and Hawkes’ bivariate exponential are presented.
Probability Distribution for Flowing Interval Spacing

International Nuclear Information System (INIS)

S. Kuzio

2004-01-01

Fracture spacing is a key hydrologic parameter in analyses of matrix diffusion. Although the individual fractures that transmit flow in the saturated zone (SZ) cannot be identified directly, it is possible to determine the fractured zones that transmit flow from flow meter survey observations. The fractured zones that transmit flow as identified through borehole flow meter surveys have been defined in this report as flowing intervals. The flowing interval spacing is measured between the midpoints of each flowing interval. The determination of flowing interval spacing is important because the flowing interval spacing parameter is a key hydrologic parameter in SZ transport modeling, which impacts the extent of matrix diffusion in the SZ volcanic matrix. The output of this report is input to the ''Saturated Zone Flow and Transport Model Abstraction'' (BSC 2004 [DIRS 170042]). Specifically, the analysis of data and development of a data distribution reported herein is used to develop the uncertainty distribution for the flowing interval spacing parameter for the SZ transport abstraction model. Figure 1-1 shows the relationship of this report to other model reports that also pertain to flow and transport in the SZ. Figure 1-1 also shows the flow of key information among the SZ reports. It should be noted that Figure 1-1 does not contain a complete representation of the data and parameter inputs and outputs of all SZ reports, nor does it show inputs external to this suite of SZ reports. Use of the developed flowing interval spacing probability distribution is subject to the limitations of the assumptions discussed in Sections 5 and 6 of this analysis report. The number of fractures in a flowing interval is not known. Therefore, the flowing intervals are assumed to be composed of one flowing zone in the transport simulations. This analysis may overestimate the flowing interval spacing because the number of fractures that contribute to a flowing interval cannot be
p-adic probability interpretation of Bell's inequality

International Nuclear Information System (INIS)

Khrennikov, A.

1995-01-01

We study the violation of Bell's inequality using a p-adic generalization of the theory of probability. p-adic probability is introduced as a limit of relative frequencies but this limit exists with respect to a p-adic metric. In particular, negative probability distributions are well defined on the basis of the frequency definition. This new type of stochastics can be used to describe hidden-variables distributions of some quantum models. If the hidden variables have a p-adic probability distribution, Bell's inequality is not valid and it is not necessary to discuss the experimental violations of this inequality. ((orig.))
Measuring Robustness of Timetables at Stations using a Probability Distribution

DEFF Research Database (Denmark)

Jensen, Lars Wittrup; Landex, Alex

Stations are often the limiting capacity factor in a railway network. This induces interdependencies, especially at at-grade junctions, causing network effects. This paper presents three traditional methods that can be used to measure the complexity of a station, indicating the robustness...... of the station’s infrastructure layout and plan of operation. However, these three methods do not take the timetable at the station into consideration. Therefore, two methods are introduced in this paper, making it possible to estimate the robustness of different timetables at a station or different...... infrastructure layouts given a timetable. These two methods provide different precision at the expense of a more complex calculation process. The advanced and more precise method is based on a probability distribution that can describe the expected delay between two trains as a function of the buffer time...
Description of atomic burials in compact globular proteins by Fermi-Dirac probability distributions.

Science.gov (United States)

Gomes, Antonio L C; de Rezende, Júlia R; Pereira de Araújo, Antônio F; Shakhnovich, Eugene I

2007-02-01

We perform a statistical analysis of atomic distributions as a function of the distance R from the molecular geometrical center in a nonredundant set of compact globular proteins. The number of atoms increases quadratically for small R, indicating a constant average density inside the core, reaches a maximum at a size-dependent distance R(max), and falls rapidly for larger R. The empirical curves turn out to be consistent with the volume increase of spherical concentric solid shells and a Fermi-Dirac distribution in which the distance R plays the role of an effective atomic energy epsilon(R) = R. The effective chemical potential mu governing the distribution increases with the number of residues, reflecting the size of the protein globule, while the temperature parameter beta decreases. Interestingly, betamu is not as strongly dependent on protein size and appears to be tuned to maintain approximately half of the atoms in the high density interior and the other half in the exterior region of rapidly decreasing density. A normalized size-independent distribution was obtained for the atomic probability as a function of the reduced distance, r = R/R(g), where R(g) is the radius of gyration. The global normalized Fermi distribution, F(r), can be reasonably decomposed in Fermi-like subdistributions for different atomic types tau, F(tau)(r), with Sigma(tau)F(tau)(r) = F(r), which depend on two additional parameters mu(tau) and h(tau). The chemical potential mu(tau) affects a scaling prefactor and depends on the overall frequency of the corresponding atomic type, while the maximum position of the subdistribution is determined by h(tau), which appears in a type-dependent atomic effective energy, epsilon(tau)(r) = h(tau)r, and is strongly correlated to available hydrophobicity scales. Better adjustments are obtained when the effective energy is not assumed to be necessarily linear, or epsilon(tau)*(r) = h(tau)*r(alpha,), in which case a correlation with hydrophobicity
Stochastic Economic Dispatch with Wind using Versatile Probability Distribution and L-BFGS-B Based Dual Decomposition

DEFF Research Database (Denmark)

Huang, Shaojun; Sun, Yuanzhang; Wu, Qiuwei

2018-01-01

This paper focuses on economic dispatch (ED) in power systems with intermittent wind power, which is a very critical issue in future power systems. A stochastic ED problem is formed based on the recently proposed versatile probability distribution (VPD) of wind power. The problem is then analyzed...
Introduction and application of non-stationary standardized precipitation index considering probability distribution function and return period

Science.gov (United States)

Park, Junehyeong; Sung, Jang Hyun; Lim, Yoon-Jin; Kang, Hyun-Suk

2018-05-01

The widely used meteorological drought index, the Standardized Precipitation Index (SPI), basically assumes stationarity, but recent changes in the climate have led to a need to review this hypothesis. In this study, a new non-stationary SPI that considers not only the modified probability distribution parameter but also the return period under the non-stationary process was proposed. The results were evaluated for two severe drought cases during the last 10 years in South Korea. As a result, SPIs considered that the non-stationary hypothesis underestimated the drought severity than the stationary SPI despite that these past two droughts were recognized as significantly severe droughts. It may be caused by that the variances of summer and autumn precipitation become larger over time then it can make the probability distribution wider than before. This implies that drought expressions by statistical index such as SPI can be distorted by stationary assumption and cautious approach is needed when deciding drought level considering climate changes.
Analyses of moments in pseudorapidity intervals at √s = 546 GeV by means of two probability distributions in pure-birth process

International Nuclear Information System (INIS)

Biyajima, M.; Shirane, K.; Suzuki, N.

1988-01-01

Moments in pseudorapidity intervals at the CERN Sp-barpS collider (√s = 546 GeV) are analyzed by means of two probability distributions in the pure-birth stochastic process. Our results show that a probability distribution obtained from the Poisson distribution as an initial condition is more useful than that obtained from the Kronecker δ function. Analyses of moments by Koba-Nielsen-Olesen scaling functions derived from solutions of the pure-birth stochastic process are also made. Moreover, analyses of preliminary data at √s = 200 and 900 GeV are added
Probability mapping of contaminants

International Nuclear Information System (INIS)

Rautman, C.A.; Kaplan, P.G.; McGraw, M.A.; Istok, J.D.; Sigda, J.M.

1994-01-01

Exhaustive characterization of a contaminated site is a physical and practical impossibility. Descriptions of the nature, extent, and level of contamination, as well as decisions regarding proposed remediation activities, must be made in a state of uncertainty based upon limited physical sampling. The probability mapping approach illustrated in this paper appears to offer site operators a reasonable, quantitative methodology for many environmental remediation decisions and allows evaluation of the risk associated with those decisions. For example, output from this approach can be used in quantitative, cost-based decision models for evaluating possible site characterization and/or remediation plans, resulting in selection of the risk-adjusted, least-cost alternative. The methodology is completely general, and the techniques are applicable to a wide variety of environmental restoration projects. The probability-mapping approach is illustrated by application to a contaminated site at the former DOE Feed Materials Production Center near Fernald, Ohio. Soil geochemical data, collected as part of the Uranium-in-Soils Integrated Demonstration Project, have been used to construct a number of geostatistical simulations of potential contamination for parcels approximately the size of a selective remediation unit (the 3-m width of a bulldozer blade). Each such simulation accurately reflects the actual measured sample values, and reproduces the univariate statistics and spatial character of the extant data. Post-processing of a large number of these equally likely statistically similar images produces maps directly showing the probability of exceeding specified levels of contamination (potential clean-up or personnel-hazard thresholds)
Probability mapping of contaminants

Energy Technology Data Exchange (ETDEWEB)

Rautman, C.A.; Kaplan, P.G. [Sandia National Labs., Albuquerque, NM (United States); McGraw, M.A. [Univ. of California, Berkeley, CA (United States); Istok, J.D. [Oregon State Univ., Corvallis, OR (United States); Sigda, J.M. [New Mexico Inst. of Mining and Technology, Socorro, NM (United States)

1994-04-01

Exhaustive characterization of a contaminated site is a physical and practical impossibility. Descriptions of the nature, extent, and level of contamination, as well as decisions regarding proposed remediation activities, must be made in a state of uncertainty based upon limited physical sampling. The probability mapping approach illustrated in this paper appears to offer site operators a reasonable, quantitative methodology for many environmental remediation decisions and allows evaluation of the risk associated with those decisions. For example, output from this approach can be used in quantitative, cost-based decision models for evaluating possible site characterization and/or remediation plans, resulting in selection of the risk-adjusted, least-cost alternative. The methodology is completely general, and the techniques are applicable to a wide variety of environmental restoration projects. The probability-mapping approach is illustrated by application to a contaminated site at the former DOE Feed Materials Production Center near Fernald, Ohio. Soil geochemical data, collected as part of the Uranium-in-Soils Integrated Demonstration Project, have been used to construct a number of geostatistical simulations of potential contamination for parcels approximately the size of a selective remediation unit (the 3-m width of a bulldozer blade). Each such simulation accurately reflects the actual measured sample values, and reproduces the univariate statistics and spatial character of the extant data. Post-processing of a large number of these equally likely statistically similar images produces maps directly showing the probability of exceeding specified levels of contamination (potential clean-up or personnel-hazard thresholds).
Extending the Generalised Pareto Distribution for Novelty Detection in High-Dimensional Spaces.

Science.gov (United States)

Clifton, David A; Clifton, Lei; Hugueny, Samuel; Tarassenko, Lionel

2014-01-01

Novelty detection involves the construction of a "model of normality", and then classifies test data as being either "normal" or "abnormal" with respect to that model. For this reason, it is often termed one-class classification. The approach is suitable for cases in which examples of "normal" behaviour are commonly available, but in which cases of "abnormal" data are comparatively rare. When performing novelty detection, we are typically most interested in the tails of the normal model, because it is in these tails that a decision boundary between "normal" and "abnormal" areas of data space usually lies. Extreme value statistics provides an appropriate theoretical framework for modelling the tails of univariate (or low-dimensional) distributions, using the generalised Pareto distribution (GPD), which can be demonstrated to be the limiting distribution for data occurring within the tails of most practically-encountered probability distributions. This paper provides an extension of the GPD, allowing the modelling of probability distributions of arbitrarily high dimension, such as occurs when using complex, multimodel, multivariate distributions for performing novelty detection in most real-life cases. We demonstrate our extension to the GPD using examples from patient physiological monitoring, in which we have acquired data from hospital patients in large clinical studies of high-acuity wards, and in which we wish to determine "abnormal" patient data, such that early warning of patient physiological deterioration may be provided.
Probability distribution of magnetization in the one-dimensional Ising model: effects of boundary conditions

Energy Technology Data Exchange (ETDEWEB)

Antal, T [Physics Department, Simon Fraser University, Burnaby, BC V5A 1S6 (Canada); Droz, M [Departement de Physique Theorique, Universite de Geneve, CH 1211 Geneva 4 (Switzerland); Racz, Z [Institute for Theoretical Physics, Eoetvoes University, 1117 Budapest, Pazmany setany 1/a (Hungary)

2004-02-06

Finite-size scaling functions are investigated both for the mean-square magnetization fluctuations and for the probability distribution of the magnetization in the one-dimensional Ising model. The scaling functions are evaluated in the limit of the temperature going to zero (T {yields} 0), the size of the system going to infinity (N {yields} {infinity}) while N[1 - tanh(J/k{sub B}T)] is kept finite (J being the nearest neighbour coupling). Exact calculations using various boundary conditions (periodic, antiperiodic, free, block) demonstrate explicitly how the scaling functions depend on the boundary conditions. We also show that the block (small part of a large system) magnetization distribution results are identical to those obtained for free boundary conditions.
Understanding the distinctively skewed and heavy tailed character of atmospheric and oceanic probability distributions

Energy Technology Data Exchange (ETDEWEB)

Sardeshmukh, Prashant D., E-mail: Prashant.D.Sardeshmukh@noaa.gov [CIRES, University of Colorado, Boulder, Colorado 80309 (United States); NOAA/Earth System Research Laboratory, Boulder, Colorado 80305 (United States); Penland, Cécile [NOAA/Earth System Research Laboratory, Boulder, Colorado 80305 (United States)

2015-03-15

The probability distributions of large-scale atmospheric and oceanic variables are generally skewed and heavy-tailed. We argue that their distinctive departures from Gaussianity arise fundamentally from the fact that in a quadratically nonlinear system with a quadratic invariant, the coupling coefficients between system components are not constant but depend linearly on the system state in a distinctive way. In particular, the skewness arises from a tendency of the system trajectory to linger near states of weak coupling. We show that the salient features of the observed non-Gaussianity can be captured in the simplest such nonlinear 2-component system. If the system is stochastically forced and linearly damped, with one component damped much more strongly than the other, then the strongly damped fast component becomes effectively decoupled from the weakly damped slow component, and its impact on the slow component can be approximated as a stochastic noise forcing plus an augmented nonlinear damping. In the limit of large time-scale separation, the nonlinear augmentation of the damping becomes small, and the noise forcing can be approximated as an additive noise plus a correlated additive and multiplicative noise (CAM noise) forcing. Much of the diversity of observed large-scale atmospheric and oceanic probability distributions can be interpreted in this minimal framework.
Towards a theoretical determination of the geographical probability distribution of meteoroid impacts on Earth

Science.gov (United States)

Zuluaga, Jorge I.; Sucerquia, Mario

2018-06-01

Tunguska and Chelyabinsk impact events occurred inside a geographical area of only 3.4 per cent of the Earth's surface. Although two events hardly constitute a statistically significant demonstration of a geographical pattern of impacts, their spatial coincidence is at least tantalizing. To understand if this concurrence reflects an underlying geographical and/or temporal pattern, we must aim at predicting the spatio-temporal distribution of meteoroid impacts on Earth. For this purpose we designed, implemented, and tested a novel numerical technique, the `Gravitational Ray Tracing' (GRT) designed to compute the relative impact probability (RIP) on the surface of any planet. GRT is inspired by the so-called ray-casting techniques used to render realistic images of complex 3D scenes. In this paper we describe the method and the results of testing it at the time of large impact events. Our findings suggest a non-trivial pattern of impact probabilities at any given time on the Earth. Locations at 60-90° from the apex are more prone to impacts, especially at midnight. Counterintuitively, sites close to apex direction have the lowest RIP, while in the antapex RIP are slightly larger than average. We present here preliminary maps of RIP at the time of Tunguska and Chelyabinsk events and found no evidence of a spatial or temporal pattern, suggesting that their coincidence was fortuitous. We apply the GRT method to compute theoretical RIP at the location and time of 394 large fireballs. Although the predicted spatio-temporal impact distribution matches marginally the observed events, we successfully predict their impact speed distribution.
Measures of dependence for multivariate Lévy distributions

Science.gov (United States)

Boland, J.; Hurd, T. R.; Pivato, M.; Seco, L.

2001-02-01

Recent statistical analysis of a number of financial databases is summarized. Increasing agreement is found that logarithmic equity returns show a certain type of asymptotic behavior of the largest events, namely that the probability density functions have power law tails with an exponent α≈3.0. This behavior does not vary much over different stock exchanges or over time, despite large variations in trading environments. The present paper proposes a class of multivariate distributions which generalizes the observed qualities of univariate time series. A new consequence of the proposed class is the "spectral measure" which completely characterizes the multivariate dependences of the extreme tails of the distribution. This measure on the unit sphere in M-dimensions, in principle completely general, can be determined empirically by looking at extreme events. If it can be observed and determined, it will prove to be of importance for scenario generation in portfolio risk management.
Multiscale probability distribution of pressure fluctuations in fluidized beds

International Nuclear Information System (INIS)

Ghasemi, Fatemeh; Sahimi, Muhammad; Reza Rahimi Tabar, M; Peinke, Joachim

2012-01-01

Analysis of flow in fluidized beds, a common chemical reactor, is of much current interest due to its fundamental as well as industrial importance. Experimental data for the successive increments of the pressure fluctuations time series in a fluidized bed are analyzed by computing a multiscale probability density function (PDF) of the increments. The results demonstrate the evolution of the shape of the PDF from the short to long time scales. The deformation of the PDF across time scales may be modeled by the log-normal cascade model. The results are also in contrast to the previously proposed PDFs for the pressure fluctuations that include a Gaussian distribution and a PDF with a power-law tail. To understand better the properties of the pressure fluctuations, we also construct the shuffled and surrogate time series for the data and analyze them with the same method. It turns out that long-range correlations play an important role in the structure of the time series that represent the pressure fluctuation. (paper)
Effect Sizes for Research Univariate and Multivariate Applications

CERN Document Server

Grissom, Robert J

2011-01-01

Noted for its comprehensive coverage, this greatly expanded new edition now covers the use of univariate and multivariate effect sizes. Many measures and estimators are reviewed along with their application, interpretation, and limitations. Noted for its practical approach, the book features numerous examples using real data for a variety of variables and designs, to help readers apply the material to their own data. Tips on the use of SPSS, SAS, R, and S-Plus are provided. The book's broad disciplinary appeal results from its inclusion of a variety of examples from psychology, medicine, educa
Combining scenarios in a calculation of the overall probability distribution of cumulative releases of radioactivity from the Waste Isolation Pilot Plant, southeastern New Mexico

International Nuclear Information System (INIS)

Tierney, M.S.

1991-11-01

The Waste Isolation Pilot Plant (WIPP), in southeastern New Mexico, is a research and development facility to demonstrate safe disposal of defense-generated transuranic waste. The US Department of Energy will designate WIPP as a disposal facility if it meets the US Environmental Protection Agency's standard for disposal of such waste; the standard includes a requirement that estimates of cumulative releases of radioactivity to the accessible environment be incorporated in an overall probability distribution. The WIPP Project has chosen an approach to calculation of an overall probability distribution that employs the concept of scenarios for release and transport of radioactivity to the accessible environment. This report reviews the use of Monte Carlo methods in the calculation of an overall probability distribution and presents a logical and mathematical foundation for use of the scenario concept in such calculations. The report also draws preliminary conclusions regarding the shape of the probability distribution for the WIPP system; preliminary conclusions are based on the possible occurrence of three events and the presence of one feature: namely, the events ''attempted boreholes over rooms and drifts,'' ''mining alters ground-water regime,'' ''water-withdrawal wells provide alternate pathways,'' and the feature ''brine pocket below room or drift.'' Calculation of the WIPP systems's overall probability distributions for only five of sixteen possible scenario classes that can be obtained by combining the four postulated events or features
Nuclear data uncertainties: I, Basic concepts of probability

Energy Technology Data Exchange (ETDEWEB)

Smith, D.L.

1988-12-01

Some basic concepts of probability theory are presented from a nuclear-data perspective, in order to provide a foundation for thorough understanding of the role of uncertainties in nuclear data research. Topics included in this report are: events, event spaces, calculus of events, randomness, random variables, random-variable distributions, intuitive and axiomatic probability, calculus of probability, conditional probability and independence, probability distributions, binomial and multinomial probability, Poisson and interval probability, normal probability, the relationships existing between these probability laws, and Bayes' theorem. This treatment emphasizes the practical application of basic mathematical concepts to nuclear data research, and it includes numerous simple examples. 34 refs.
Nuclear data uncertainties: I, Basic concepts of probability

International Nuclear Information System (INIS)

Smith, D.L.

1988-12-01

Some basic concepts of probability theory are presented from a nuclear-data perspective, in order to provide a foundation for thorough understanding of the role of uncertainties in nuclear data research. Topics included in this report are: events, event spaces, calculus of events, randomness, random variables, random-variable distributions, intuitive and axiomatic probability, calculus of probability, conditional probability and independence, probability distributions, binomial and multinomial probability, Poisson and interval probability, normal probability, the relationships existing between these probability laws, and Bayes' theorem. This treatment emphasizes the practical application of basic mathematical concepts to nuclear data research, and it includes numerous simple examples. 34 refs

Choice Probability Generating Functions

DEFF Research Database (Denmark)

Fosgerau, Mogens; McFadden, Daniel L; Bierlaire, Michel

This paper considers discrete choice, with choice probabilities coming from maximization of preferences from a random utility field perturbed by additive location shifters (ARUM). Any ARUM can be characterized by a choice-probability generating function (CPGF) whose gradient gives the choice...... probabilities, and every CPGF is consistent with an ARUM. We relate CPGF to multivariate extreme value distributions, and review and extend methods for constructing CPGF for applications....
Hydrological model calibration for derived flood frequency analysis using stochastic rainfall and probability distributions of peak flows

Science.gov (United States)

Haberlandt, U.; Radtke, I.

2014-01-01

Derived flood frequency analysis allows the estimation of design floods with hydrological modeling for poorly observed basins considering change and taking into account flood protection measures. There are several possible choices regarding precipitation input, discharge output and consequently the calibration of the model. The objective of this study is to compare different calibration strategies for a hydrological model considering various types of rainfall input and runoff output data sets and to propose the most suitable approach. Event based and continuous, observed hourly rainfall data as well as disaggregated daily rainfall and stochastically generated hourly rainfall data are used as input for the model. As output, short hourly and longer daily continuous flow time series as well as probability distributions of annual maximum peak flow series are employed. The performance of the strategies is evaluated using the obtained different model parameter sets for continuous simulation of discharge in an independent validation period and by comparing the model derived flood frequency distributions with the observed one. The investigations are carried out for three mesoscale catchments in northern Germany with the hydrological model HEC-HMS (Hydrologic Engineering Center's Hydrologic Modeling System). The results show that (I) the same type of precipitation input data should be used for calibration and application of the hydrological model, (II) a model calibrated using a small sample of extreme values works quite well for the simulation of continuous time series with moderate length but not vice versa, and (III) the best performance with small uncertainty is obtained when stochastic precipitation data and the observed probability distribution of peak flows are used for model calibration. This outcome suggests to calibrate a hydrological model directly on probability distributions of observed peak flows using stochastic rainfall as input if its purpose is the
Probability distribution of wave packet delay time for strong overlapping of resonance levels

International Nuclear Information System (INIS)

Lyuboshits, V.L.

1983-01-01

Time behaviour of nuclear reactions in the case of high level densities is investigated basing on the theory of overlapping resonances. In the framework of a model of n equivalent channels an analytical expression is obtained for the probability distribution function for wave packet delay time at the compound nucleus production. It is shown that at strong overlapping of the resonance levels the relative fluctuation of the delay time is small at the stage of compound nucleus production. A possible increase in the duration of nuclear reactions with the excitation energy rise is discussed
Probability distribution of machining center failures

International Nuclear Information System (INIS)

Jia Yazhou; Wang Molin; Jia Zhixin

1995-01-01

Through field tracing research for 24 Chinese cutter-changeable CNC machine tools (machining centers) over a period of one year, a database of operation and maintenance for machining centers was built, the failure data was fitted to the Weibull distribution and the exponential distribution, the effectiveness was tested, and the failure distribution pattern of machining centers was found. Finally, the reliability characterizations for machining centers are proposed
Combinatorial bounds on the α-divergence of univariate mixture models

KAUST Repository

Nielsen, Frank

2017-06-20

We derive lower- and upper-bounds of α-divergence between univariate mixture models with components in the exponential family. Three pairs of bounds are presented in order with increasing quality and increasing computational cost. They are verified empirically through simulated Gaussian mixture models. The presented methodology generalizes to other divergence families relying on Hellinger-type integrals.
Choice probability generating functions

DEFF Research Database (Denmark)

Fosgerau, Mogens; McFadden, Daniel; Bierlaire, Michel

2013-01-01

This paper considers discrete choice, with choice probabilities coming from maximization of preferences from a random utility field perturbed by additive location shifters (ARUM). Any ARUM can be characterized by a choice-probability generating function (CPGF) whose gradient gives the choice...... probabilities, and every CPGF is consistent with an ARUM. We relate CPGF to multivariate extreme value distributions, and review and extend methods for constructing CPGF for applications. The choice probabilities of any ARUM may be approximated by a cross-nested logit model. The results for ARUM are extended...
An innovative method for offshore wind farm site selection based on the interval number with probability distribution

Science.gov (United States)

Wu, Yunna; Chen, Kaifeng; Xu, Hu; Xu, Chuanbo; Zhang, Haobo; Yang, Meng

2017-12-01

There is insufficient research relating to offshore wind farm site selection in China. The current methods for site selection have some defects. First, information loss is caused by two aspects: the implicit assumption that the probability distribution on the interval number is uniform; and ignoring the value of decision makers' (DMs') common opinion on the criteria information evaluation. Secondly, the difference in DMs' utility function has failed to receive attention. An innovative method is proposed in this article to solve these drawbacks. First, a new form of interval number and its weighted operator are proposed to reflect the uncertainty and reduce information loss. Secondly, a new stochastic dominance degree is proposed to quantify the interval number with a probability distribution. Thirdly, a two-stage method integrating the weighted operator with stochastic dominance degree is proposed to evaluate the alternatives. Finally, a case from China proves the effectiveness of this method.
The quantum probability calculus

International Nuclear Information System (INIS)

Jauch, J.M.

1976-01-01

The Wigner anomaly (1932) for the joint distribution of noncompatible observables is an indication that the classical probability calculus is not applicable for quantum probabilities. It should, therefore, be replaced by another, more general calculus, which is specifically adapted to quantal systems. In this article this calculus is exhibited and its mathematical axioms and the definitions of the basic concepts such as probability field, random variable, and expectation values are given. (B.R.H)
Joint probabilities and quantum cognition

International Nuclear Information System (INIS)

Acacio de Barros, J.

2012-01-01

In this paper we discuss the existence of joint probability distributions for quantumlike response computations in the brain. We do so by focusing on a contextual neural-oscillator model shown to reproduce the main features of behavioral stimulus-response theory. We then exhibit a simple example of contextual random variables not having a joint probability distribution, and describe how such variables can be obtained from neural oscillators, but not from a quantum observable algebra.
Joint probabilities and quantum cognition

Energy Technology Data Exchange (ETDEWEB)

Acacio de Barros, J. [Liberal Studies, 1600 Holloway Ave., San Francisco State University, San Francisco, CA 94132 (United States)

2012-12-18

In this paper we discuss the existence of joint probability distributions for quantumlike response computations in the brain. We do so by focusing on a contextual neural-oscillator model shown to reproduce the main features of behavioral stimulus-response theory. We then exhibit a simple example of contextual random variables not having a joint probability distribution, and describe how such variables can be obtained from neural oscillators, but not from a quantum observable algebra.
Spatial distribution and occurrence probability of regional new particle formation events in eastern China

Directory of Open Access Journals (Sweden)

X. Shen

2018-01-01

Full Text Available In this work, the spatial extent of new particle formation (NPF events and the relative probability of observing particles originating from different spatial origins around three rural sites in eastern China were investigated using the NanoMap method, using particle number size distribution (PNSD data and air mass back trajectories. The length of the datasets used were 7, 1.5, and 3 years at rural sites Shangdianzi (SDZ in the North China Plain (NCP, Mt. Tai (TS in central eastern China, and Lin'an (LAN in the Yangtze River Delta region in eastern China, respectively. Regional NPF events were observed to occur with the horizontal extent larger than 500 km at SDZ and TS, favoured by the fast transport of northwesterly air masses. At LAN, however, the spatial footprint of NPF events was mostly observed around the site within 100–200 km. Difference in the horizontal spatial distribution of new particle source areas at different sites was connected to typical meteorological conditions at the sites. Consecutive large-scale regional NPF events were observed at SDZ and TS simultaneously and were associated with a high surface pressure system dominating over this area. Simultaneous NPF events at SDZ and LAN were seldom observed. At SDZ the polluted air masses arriving over the NCP were associated with higher particle growth rate (GR and new particle formation rate (J than air masses from Inner Mongolia (IM. At TS the same phenomenon was observed for J, but GR was somewhat lower in air masses arriving over the NCP compared to those arriving from IM. The capability of NanoMap to capture the NPF occurrence probability depends on the length of the dataset of PNSD measurement but also on topography around the measurement site and typical air mass advection speed during NPF events. Thus the long-term measurements of PNSD in the planetary boundary layer are necessary in the further study of spatial extent and the probability of NPF events. The spatial
Probability elements of the mathematical theory

CERN Document Server

Heathcote, C R

2000-01-01

Designed for students studying mathematical statistics and probability after completing a course in calculus and real variables, this text deals with basic notions of probability spaces, random variables, distribution functions and generating functions, as well as joint distributions and the convergence properties of sequences of random variables. Includes worked examples and over 250 exercises with solutions.
Risk Probabilities

DEFF Research Database (Denmark)

Rojas-Nandayapa, Leonardo

Tail probabilities of sums of heavy-tailed random variables are of a major importance in various branches of Applied Probability, such as Risk Theory, Queueing Theory, Financial Management, and are subject to intense research nowadays. To understand their relevance one just needs to think...... analytic expression for the distribution function of a sum of random variables. The presence of heavy-tailed random variables complicates the problem even more. The objective of this dissertation is to provide better approximations by means of sharp asymptotic expressions and Monte Carlo estimators...
Sampling Methods for Wallenius' and Fisher's Noncentral Hypergeometric Distributions

DEFF Research Database (Denmark)

Fog, Agner

2008-01-01

the mode, ratio-of-uniforms rejection method, and rejection by sampling in the tau domain. Methods for the multivariate distributions include: simulation of urn experiments, conditional method, Gibbs sampling, and Metropolis-Hastings sampling. These methods are useful for Monte Carlo simulation of models...... of biased sampling and models of evolution and for calculating moments and quantiles of the distributions.......Several methods for generating variates with univariate and multivariate Wallenius' and Fisher's noncentral hypergeometric distributions are developed. Methods for the univariate distributions include: simulation of urn experiments, inversion by binary search, inversion by chop-down search from...
Effect of optimum stratification on sampling with varying probabilities under proportional allocation

OpenAIRE

Syed Ejaz Husain Rizvi; Jaj P. Gupta; Manoj Bhargava

2007-01-01

The problem of optimum stratification on an auxiliary variable when the units from different strata are selected with probability proportional to the value of auxiliary variable (PPSWR) was considered by Singh (1975) for univariate case. In this paper we have extended the same problem, for proportional allocation, when two variates are under study. A cum. 3 R3(x) rule for obtaining approximately optimum strata boundaries has been provided. It has been shown theoretically as well as empiricall...
A statistical model for deriving probability distributions of contamination for accidental releases

International Nuclear Information System (INIS)

ApSimon, H.M.; Davison, A.C.

1986-01-01

Results generated from a detailed long-range transport model, MESOS, simulating dispersal of a large number of hypothetical releases of radionuclides in a variety of meteorological situations over Western Europe have been used to derive a simpler statistical model, MESOSTAT. This model may be used to generate probability distributions of different levels of contamination at a receptor point 100-1000 km or so from the source (for example, across a frontier in another country) without considering individual release and dispersal scenarios. The model is embodied in a series of equations involving parameters which are determined from such factors as distance between source and receptor, nuclide decay and deposition characteristics, release duration, and geostrophic windrose at the source. Suitable geostrophic windrose data have been derived for source locations covering Western Europe. Special attention has been paid to the relatively improbable extreme values of contamination at the top end of the distribution. The MESOSTAT model and its development are described, with illustrations of its use and comparison with the original more detailed modelling techniques. (author)
Probability distributions of placental morphological measurements and origins of variability of placental shapes.

Science.gov (United States)

Yampolsky, M; Salafia, C M; Shlakhter, O

2013-06-01

While the mean shape of human placenta is round with centrally inserted umbilical cord, significant deviations from this ideal are fairly common, and may be clinically meaningful. Traditionally, they are explained by trophotropism. We have proposed a hypothesis explaining typical variations in placental shape by randomly determined fluctuations in the growth process of the vascular tree. It has been recently reported that umbilical cord displacement in a birth cohort has a log-normal probability distribution, which indicates that the displacement between an initial point of origin and the centroid of the mature shape is a result of accumulation of random fluctuations of the dynamic growth of the placenta. To confirm this, we investigate statistical distributions of other features of placental morphology. In a cohort of 1023 births at term digital photographs of placentas were recorded at delivery. Excluding cases with velamentous cord insertion, or missing clinical data left 1001 (97.8%) for which placental surface morphology features were measured. Best-fit statistical distributions for them were obtained using EasyFit. The best-fit distributions of umbilical cord displacement, placental disk diameter, area, perimeter, and maximal radius calculated from the cord insertion point are of heavy-tailed type, similar in shape to log-normal distributions. This is consistent with a stochastic origin of deviations of placental shape from normal. Deviations of placental shape descriptors from average have heavy-tailed distributions similar in shape to log-normal. This evidence points away from trophotropism, and towards a spontaneous stochastic evolution of the variants of placental surface shape features. Copyright © 2013 Elsevier Ltd. All rights reserved.
Site-to-Source Finite Fault Distance Probability Distribution in Probabilistic Seismic Hazard and the Relationship Between Minimum Distances

Science.gov (United States)

Ortega, R.; Gutierrez, E.; Carciumaru, D. D.; Huesca-Perez, E.

2017-12-01

We present a method to compute the conditional and no-conditional probability density function (PDF) of the finite fault distance distribution (FFDD). Two cases are described: lines and areas. The case of lines has a simple analytical solution while, in the case of areas, the geometrical probability of a fault based on the strike, dip, and fault segment vertices is obtained using the projection of spheres in a piecewise rectangular surface. The cumulative distribution is computed by measuring the projection of a sphere of radius r in an effective area using an algorithm that estimates the area of a circle within a rectangle. In addition, we introduce the finite fault distance metrics. This distance is the distance where the maximum stress release occurs within the fault plane and generates a peak ground motion. Later, we can apply the appropriate ground motion prediction equations (GMPE) for PSHA. The conditional probability of distance given magnitude is also presented using different scaling laws. A simple model of constant distribution of the centroid at the geometrical mean is discussed, in this model hazard is reduced at the edges because the effective size is reduced. Nowadays there is a trend of using extended source distances in PSHA, however it is not possible to separate the fault geometry from the GMPE. With this new approach, it is possible to add fault rupture models separating geometrical and propagation effects.
Multivariate quantile mapping bias correction: an N-dimensional probability density function transform for climate model simulations of multiple variables

Science.gov (United States)

Cannon, Alex J.

2018-01-01

Most bias correction algorithms used in climatology, for example quantile mapping, are applied to univariate time series. They neglect the dependence between different variables. Those that are multivariate often correct only limited measures of joint dependence, such as Pearson or Spearman rank correlation. Here, an image processing technique designed to transfer colour information from one image to another—the N-dimensional probability density function transform—is adapted for use as a multivariate bias correction algorithm (MBCn) for climate model projections/predictions of multiple climate variables. MBCn is a multivariate generalization of quantile mapping that transfers all aspects of an observed continuous multivariate distribution to the corresponding multivariate distribution of variables from a climate model. When applied to climate model projections, changes in quantiles of each variable between the historical and projection period are also preserved. The MBCn algorithm is demonstrated on three case studies. First, the method is applied to an image processing example with characteristics that mimic a climate projection problem. Second, MBCn is used to correct a suite of 3-hourly surface meteorological variables from the Canadian Centre for Climate Modelling and Analysis Regional Climate Model (CanRCM4) across a North American domain. Components of the Canadian Forest Fire Weather Index (FWI) System, a complicated set of multivariate indices that characterizes the risk of wildfire, are then calculated and verified against observed values. Third, MBCn is used to correct biases in the spatial dependence structure of CanRCM4 precipitation fields. Results are compared against a univariate quantile mapping algorithm, which neglects the dependence between variables, and two multivariate bias correction algorithms, each of which corrects a different form of inter-variable correlation structure. MBCn outperforms these alternatives, often by a large margin
Introduction to probability with R

CERN Document Server

Baclawski, Kenneth

2008-01-01

FOREWORD PREFACE Sets, Events, and Probability The Algebra of Sets The Bernoulli Sample Space The Algebra of Multisets The Concept of Probability Properties of Probability Measures Independent Events The Bernoulli Process The R Language Finite Processes The Basic Models Counting Rules Computing Factorials The Second Rule of Counting Computing Probabilities Discrete Random Variables The Bernoulli Process: Tossing a Coin The Bernoulli Process: Random Walk Independence and Joint Distributions Expectations The Inclusion-Exclusion Principle General Random Variable

In favor of general probability distributions: lateral prefrontal and insular cortices respond to stimulus inherent, but irrelevant differences.

Science.gov (United States)

Mestres-Missé, Anna; Trampel, Robert; Turner, Robert; Kotz, Sonja A

2016-04-01

A key aspect of optimal behavior is the ability to predict what will come next. To achieve this, we must have a fairly good idea of the probability of occurrence of possible outcomes. This is based both on prior knowledge about a particular or similar situation and on immediately relevant new information. One question that arises is: when considering converging prior probability and external evidence, is the most probable outcome selected or does the brain represent degrees of uncertainty, even highly improbable ones? Using functional magnetic resonance imaging, the current study explored these possibilities by contrasting words that differ in their probability of occurrence, namely, unbalanced ambiguous words and unambiguous words. Unbalanced ambiguous words have a strong frequency-based bias towards one meaning, while unambiguous words have only one meaning. The current results reveal larger activation in lateral prefrontal and insular cortices in response to dominant ambiguous compared to unambiguous words even when prior and contextual information biases one interpretation only. These results suggest a probability distribution, whereby all outcomes and their associated probabilities of occurrence--even if very low--are represented and maintained.
Estimating species occurrence, abundance, and detection probability using zero-inflated distributions.

Science.gov (United States)

Wenger, Seth J; Freeman, Mary C

2008-10-01

Researchers have developed methods to account for imperfect detection of species with either occupancy (presence absence) or count data using replicated sampling. We show how these approaches can be combined to simultaneously estimate occurrence, abundance, and detection probability by specifying a zero-inflated distribution for abundance. This approach may be particularly appropriate when patterns of occurrence and abundance arise from distinct processes operating at differing spatial or temporal scales. We apply the model to two data sets: (1) previously published data for a species of duck, Anas platyrhynchos, and (2) data for a stream fish species, Etheostoma scotti. We show that in these cases, an incomplete-detection zero-inflated modeling approach yields a superior fit to the data than other models. We propose that zero-inflated abundance models accounting for incomplete detection be considered when replicate count data are available.
Probability distribution of distance in a uniform ellipsoid: Theory and applications to physics

International Nuclear Information System (INIS)

Parry, Michelle; Fischbach, Ephraim

2000-01-01

A number of authors have previously found the probability P n (r) that two points uniformly distributed in an n-dimensional sphere are separated by a distance r. This result greatly facilitates the calculation of self-energies of spherically symmetric matter distributions interacting by means of an arbitrary radially symmetric two-body potential. We present here the analogous results for P 2 (r;ε) and P 3 (r;ε) which respectively describe an ellipse and an ellipsoid whose major and minor axes are 2a and 2b. It is shown that for ε=(1-b 2 /a 2 ) 1/2 ≤1, P 2 (r;ε) and P 3 (r;ε) can be obtained as an expansion in powers of ε, and our results are valid through order ε 4 . As an application of these results we calculate the Coulomb energy of an ellipsoidal nucleus, and compare our result to an earlier result quoted in the literature. (c) 2000 American Institute of Physics
On probability-possibility transformations

Science.gov (United States)

Klir, George J.; Parviz, Behzad

1992-01-01

Several probability-possibility transformations are compared in terms of the closeness of preserving second-order properties. The comparison is based on experimental results obtained by computer simulation. Two second-order properties are involved in this study: noninteraction of two distributions and projections of a joint distribution.
Modeling the probability distribution of positional errors incurred by residential address geocoding

Directory of Open Access Journals (Sweden)

Mazumdar Soumya

2007-01-01

Full Text Available Abstract Background The assignment of a point-level geocode to subjects' residences is an important data assimilation component of many geographic public health studies. Often, these assignments are made by a method known as automated geocoding, which attempts to match each subject's address to an address-ranged street segment georeferenced within a streetline database and then interpolate the position of the address along that segment. Unfortunately, this process results in positional errors. Our study sought to model the probability distribution of positional errors associated with automated geocoding and E911 geocoding. Results Positional errors were determined for 1423 rural addresses in Carroll County, Iowa as the vector difference between each 100%-matched automated geocode and its true location as determined by orthophoto and parcel information. Errors were also determined for 1449 60%-matched geocodes and 2354 E911 geocodes. Huge (> 15 km outliers occurred among the 60%-matched geocoding errors; outliers occurred for the other two types of geocoding errors also but were much smaller. E911 geocoding was more accurate (median error length = 44 m than 100%-matched automated geocoding (median error length = 168 m. The empirical distributions of positional errors associated with 100%-matched automated geocoding and E911 geocoding exhibited a distinctive Greek-cross shape and had many other interesting features that were not capable of being fitted adequately by a single bivariate normal or t distribution. However, mixtures of t distributions with two or three components fit the errors very well. Conclusion Mixtures of bivariate t distributions with few components appear to be flexible enough to fit many positional error datasets associated with geocoding, yet parsimonious enough to be feasible for nascent applications of measurement-error methodology to spatial epidemiology.
CAN'T MISS--conquer any number task by making important statistics simple. Part 2. Probability, populations, samples, and normal distributions.

Science.gov (United States)

Hansen, John P

2003-01-01

Healthcare quality improvement professionals need to understand and use inferential statistics to interpret sample data from their organizations. In quality improvement and healthcare research studies all the data from a population often are not available, so investigators take samples and make inferences about the population by using inferential statistics. This three-part series will give readers an understanding of the concepts of inferential statistics as well as the specific tools for calculating confidence intervals for samples of data. This article, Part 2, describes probability, populations, and samples. The uses of descriptive and inferential statistics are outlined. The article also discusses the properties and probability of normal distributions, including the standard normal distribution.
Tools for Bramwell-Holdsworth-Pinton Probability Distribution

Directory of Open Access Journals (Sweden)

Mirela Danubianu

2009-01-01

Full Text Available This paper is a synthesis of a range of papers presentedat various conferences related to distribution Bramwell-Holdsworth-Pinton. S. T. Bramwell, P. C. W. Holdsworth, J. F.Pinton introduced a new non-parametric distribution (calledBHP after studying some magnetization problems in 2D. Probabilitydensity function of distribution can be aproximated as amodified GFT (Gumbel-Fisher-Tippitt distribution.
Predictable return distributions

DEFF Research Database (Denmark)

Pedersen, Thomas Quistgaard

trace out the entire distribution. A univariate quantile regression model is used to examine stock and bond return distributions individually, while a multivariate model is used to capture their joint distribution. An empirical analysis on US data shows that certain parts of the return distributions......-of-sample analyses show that the relative accuracy of the state variables in predicting future returns varies across the distribution. A portfolio study shows that an investor with power utility can obtain economic gains by applying the empirical return distribution in portfolio decisions instead of imposing...
A Review of Multivariate Distributions for Count Data Derived from the Poisson Distribution.

Science.gov (United States)

Inouye, David; Yang, Eunho; Allen, Genevera; Ravikumar, Pradeep

2017-01-01

The Poisson distribution has been widely studied and used for modeling univariate count-valued data. Multivariate generalizations of the Poisson distribution that permit dependencies, however, have been far less popular. Yet, real-world high-dimensional count-valued data found in word counts, genomics, and crime statistics, for example, exhibit rich dependencies, and motivate the need for multivariate distributions that can appropriately model this data. We review multivariate distributions derived from the univariate Poisson, categorizing these models into three main classes: 1) where the marginal distributions are Poisson, 2) where the joint distribution is a mixture of independent multivariate Poisson distributions, and 3) where the node-conditional distributions are derived from the Poisson. We discuss the development of multiple instances of these classes and compare the models in terms of interpretability and theory. Then, we empirically compare multiple models from each class on three real-world datasets that have varying data characteristics from different domains, namely traffic accident data, biological next generation sequencing data, and text data. These empirical experiments develop intuition about the comparative advantages and disadvantages of each class of multivariate distribution that was derived from the Poisson. Finally, we suggest new research directions as explored in the subsequent discussion section.
Constituent quarks as clusters in quark-gluon-parton model. [Total cross sections, probability distributions

Energy Technology Data Exchange (ETDEWEB)

Kanki, T [Osaka Univ., Toyonaka (Japan). Coll. of General Education

1976-12-01

We present a quark-gluon-parton model in which quark-partons and gluons make clusters corresponding to two or three constituent quarks (or anti-quarks) in the meson or in the baryon, respectively. We explicitly construct the constituent quark state (cluster), by employing the Kuti-Weisskopf theory and by requiring the scaling. The quark additivity of the hadronic total cross sections and the quark counting rules on the threshold powers of various distributions are satisfied. For small x (Feynman fraction), it is shown that the constituent quarks and quark-partons have quite different probability distributions. We apply our model to hadron-hadron inclusive reactions, and clarify that the fragmentation and the diffractive processes relate to the constituent quark distributions, while the processes in or near the central region are controlled by the quark-partons. Our model gives the reasonable interpretation for the experimental data and much improves the usual ''constituent interchange model'' result near and in the central region (x asymptotically equals x sub(T) asymptotically equals 0).
Concise method for evaluating the probability distribution of the marginal cost of power generation

International Nuclear Information System (INIS)

Zhang, S.H.; Li, Y.Z.

2000-01-01

In the developing electricity market, many questions on electricity pricing and the risk modelling of forward contracts require the evaluation of the expected value and probability distribution of the short-run marginal cost of power generation at any given time. A concise forecasting method is provided, which is consistent with the definitions of marginal costs and the techniques of probabilistic production costing. The method embodies clear physical concepts, so that it can be easily understood theoretically and computationally realised. A numerical example has been used to test the proposed method. (author)
Probability distribution and statistical properties of spherically compensated cosmic regions in ΛCDM cosmology

Science.gov (United States)

Alimi, Jean-Michel; de Fromont, Paul

2018-04-01

The statistical properties of cosmic structures are well known to be strong probes for cosmology. In particular, several studies tried to use the cosmic void counting number to obtain tight constrains on dark energy. In this paper, we model the statistical properties of these regions using the CoSphere formalism (de Fromont & Alimi) in both primordial and non-linearly evolved Universe in the standard Λ cold dark matter model. This formalism applies similarly for minima (voids) and maxima (such as DM haloes), which are here considered symmetrically. We first derive the full joint Gaussian distribution of CoSphere's parameters in the Gaussian random field. We recover the results of Bardeen et al. only in the limit where the compensation radius becomes very large, i.e. when the central extremum decouples from its cosmic environment. We compute the probability distribution of the compensation size in this primordial field. We show that this distribution is redshift independent and can be used to model cosmic voids size distribution. We also derive the statistical distribution of the peak parameters introduced by Bardeen et al. and discuss their correlation with the cosmic environment. We show that small central extrema with low density are associated with narrow compensation regions with deep compensation density, while higher central extrema are preferentially located in larger but smoother over/under massive regions.
Uncertainty Visualization Using Copula-Based Analysis in Mixed Distribution Models.

Science.gov (United States)

Hazarika, Subhashis; Biswas, Ayan; Shen, Han-Wei

2018-01-01

Distributions are often used to model uncertainty in many scientific datasets. To preserve the correlation among the spatially sampled grid locations in the dataset, various standard multivariate distribution models have been proposed in visualization literature. These models treat each grid location as a univariate random variable which models the uncertainty at that location. Standard multivariate distributions (both parametric and nonparametric) assume that all the univariate marginals are of the same type/family of distribution. But in reality, different grid locations show different statistical behavior which may not be modeled best by the same type of distribution. In this paper, we propose a new multivariate uncertainty modeling strategy to address the needs of uncertainty modeling in scientific datasets. Our proposed method is based on a statistically sound multivariate technique called Copula, which makes it possible to separate the process of estimating the univariate marginals and the process of modeling dependency, unlike the standard multivariate distributions. The modeling flexibility offered by our proposed method makes it possible to design distribution fields which can have different types of distribution (Gaussian, Histogram, KDE etc.) at the grid locations, while maintaining the correlation structure at the same time. Depending on the results of various standard statistical tests, we can choose an optimal distribution representation at each location, resulting in a more cost efficient modeling without significantly sacrificing on the analysis quality. To demonstrate the efficacy of our proposed modeling strategy, we extract and visualize uncertain features like isocontours and vortices in various real world datasets. We also study various modeling criterion to help users in the task of univariate model selection.
An experimental study of the surface elevation probability distribution and statistics of wind-generated waves

Science.gov (United States)

Huang, N. E.; Long, S. R.

1980-01-01

Laboratory experiments were performed to measure the surface elevation probability density function and associated statistical properties for a wind-generated wave field. The laboratory data along with some limited field data were compared. The statistical properties of the surface elevation were processed for comparison with the results derived from the Longuet-Higgins (1963) theory. It is found that, even for the highly non-Gaussian cases, the distribution function proposed by Longuet-Higgins still gives good approximations.
The correlation of defect distribution in collisional phase with measured cascade collapse probability

International Nuclear Information System (INIS)

Morishita, K.; Ishino, S.; Sekimura, N.

1995-01-01

The spatial distributions of atomic displacement at the end of the collisional phase of cascade damage processes were calculated using the computer simulation code MARLOWE, which is based on the binary collision approximation (BCA). The densities of the atomic displacement were evaluated in high dense regions (HDRs) of cascades in several pure metals (Fe, Ni, Cu, Ag, Au, Mo and W). They were compared with the measured cascade collapse probabilities reported in the literature where TEM observations were carried out using thin metal foils irradiated by low-dose ions at room temperature. We found that there exists the minimum or ''critical'' values of the atomic displacement densities for the HDR to collapse into TEM-visible vacancy clusters. The critical densities are generally independent of the cascade energy in the same metal. Furthermore, the material dependence of the critical densities can be explained by the difference in the vacancy mobility at the melting temperature of target materials. This critical density calibration, which is extracted from the ion-irradiation experiments and the BCA simulations, is applied to estimation of cascade collapse probabilities in the metals irradiated by fusion neutrons. (orig.)
Introduction to probability with statistical applications

CERN Document Server

Schay, Géza

2016-01-01

Now in its second edition, this textbook serves as an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The presentation covers the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. More classical examples such as Montmort's problem, the ballot problem, and Bertrand’s paradox are now included, along with applications such as the Maxwell-Boltzmann and Bose-Einstein distributions in physics. Key features in new edition: * 35 new exercises * Expanded section on the algebra of sets * Expanded chapters on probabilities to include more classical examples * New section on regression * Online instructors' manual containing solutions to all exercises
Eruption probabilities for the Lassen Volcanic Center and regional volcanism, northern California, and probabilities for large explosive eruptions in the Cascade Range

Science.gov (United States)

Nathenson, Manuel; Clynne, Michael A.; Muffler, L.J. Patrick

2012-01-01

Chronologies for eruptive activity of the Lassen Volcanic Center and for eruptions from the regional mafic vents in the surrounding area of the Lassen segment of the Cascade Range are here used to estimate probabilities of future eruptions. For the regional mafic volcanism, the ages of many vents are known only within broad ranges, and two models are developed that should bracket the actual eruptive ages. These chronologies are used with exponential, Weibull, and mixed-exponential probability distributions to match the data for time intervals between eruptions. For the Lassen Volcanic Center, the probability of an eruption in the next year is 1.4x10-4 for the exponential distribution and 2.3x10-4 for the mixed exponential distribution. For the regional mafic vents, the exponential distribution gives a probability of an eruption in the next year of 6.5x10-4, but the mixed exponential distribution indicates that the current probability, 12,000 years after the last event, could be significantly lower. For the exponential distribution, the highest probability is for an eruption from a regional mafic vent. Data on areas and volumes of lava flows and domes of the Lassen Volcanic Center and of eruptions from the regional mafic vents provide constraints on the probable sizes of future eruptions. Probabilities of lava-flow coverage are similar for the Lassen Volcanic Center and for regional mafic vents, whereas the probable eruptive volumes for the mafic vents are generally smaller. Data have been compiled for large explosive eruptions (>≈ 5 km3 in deposit volume) in the Cascade Range during the past 1.2 m.y. in order to estimate probabilities of eruption. For erupted volumes >≈5 km3, the rate of occurrence since 13.6 ka is much higher than for the entire period, and we use these data to calculate the annual probability of a large eruption at 4.6x10-4. For erupted volumes ≥10 km3, the rate of occurrence has been reasonably constant from 630 ka to the present, giving
Poisson Processes in Free Probability

OpenAIRE

An, Guimei; Gao, Mingchu

2015-01-01

We prove a multidimensional Poisson limit theorem in free probability, and define joint free Poisson distributions in a non-commutative probability space. We define (compound) free Poisson process explicitly, similar to the definitions of (compound) Poisson processes in classical probability. We proved that the sum of finitely many freely independent compound free Poisson processes is a compound free Poisson processes. We give a step by step procedure for constructing a (compound) free Poisso...
Bayesian Probability Theory

Science.gov (United States)

von der Linden, Wolfgang; Dose, Volker; von Toussaint, Udo

2014-06-01

Preface; Part I. Introduction: 1. The meaning of probability; 2. Basic definitions; 3. Bayesian inference; 4. Combinatrics; 5. Random walks; 6. Limit theorems; 7. Continuous distributions; 8. The central limit theorem; 9. Poisson processes and waiting times; Part II. Assigning Probabilities: 10. Transformation invariance; 11. Maximum entropy; 12. Qualified maximum entropy; 13. Global smoothness; Part III. Parameter Estimation: 14. Bayesian parameter estimation; 15. Frequentist parameter estimation; 16. The Cramer-Rao inequality; Part IV. Testing Hypotheses: 17. The Bayesian way; 18. The frequentist way; 19. Sampling distributions; 20. Bayesian vs frequentist hypothesis tests; Part V. Real World Applications: 21. Regression; 22. Inconsistent data; 23. Unrecognized signal contributions; 24. Change point problems; 25. Function estimation; 26. Integral equations; 27. Model selection; 28. Bayesian experimental design; Part VI. Probabilistic Numerical Techniques: 29. Numerical integration; 30. Monte Carlo methods; 31. Nested sampling; Appendixes; References; Index.
Normal probability plots with confidence.

Science.gov (United States)

Chantarangsi, Wanpen; Liu, Wei; Bretz, Frank; Kiatsupaibul, Seksan; Hayter, Anthony J; Wan, Fang

2015-01-01

Normal probability plots are widely used as a statistical tool for assessing whether an observed simple random sample is drawn from a normally distributed population. The users, however, have to judge subjectively, if no objective rule is provided, whether the plotted points fall close to a straight line. In this paper, we focus on how a normal probability plot can be augmented by intervals for all the points so that, if the population distribution is normal, then all the points should fall into the corresponding intervals simultaneously with probability 1-α. These simultaneous 1-α probability intervals provide therefore an objective mean to judge whether the plotted points fall close to the straight line: the plotted points fall close to the straight line if and only if all the points fall into the corresponding intervals. The powers of several normal probability plot based (graphical) tests and the most popular nongraphical Anderson-Darling and Shapiro-Wilk tests are compared by simulation. Based on this comparison, recommendations are given in Section 3 on which graphical tests should be used in what circumstances. An example is provided to illustrate the methods. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

The Multivariate Gaussian Probability Distribution

DEFF Research Database (Denmark)

Ahrendt, Peter

2005-01-01

This technical report intends to gather information about the multivariate gaussian distribution, that was previously not (at least to my knowledge) to be found in one place and written as a reference manual. Additionally, some useful tips and tricks are collected that may be useful in practical ...
Probability distribution function values in mobile phones;Valores de funciones de distribución de probabilidad en el teléfono móvil

Directory of Open Access Journals (Sweden)

Luis Vicente Chamorro Marcillllo

2013-06-01

Full Text Available Engineering, within its academic and application forms, as well as any formal research work requires the use of statistics and every inferential statistical analysis requires the use of values of probability distribution functions that are generally available in tables. Generally, management of those tables have physical problems (wasteful transport and wasteful consultation and operational (incomplete lists and limited accuracy. The study, “Probability distribution function values in mobile phones”, permitted determining – through a needs survey applied to students involved in statistics studies at Universidad de Nariño – that the best known and most used values correspond to Chi-Square, Binomial, Student’s t, and Standard Normal distributions. Similarly, it showed user’s interest in having the values in question within an alternative means to correct, at least in part, the problems presented by “the famous tables”. To try to contribute to the solution, we built software that allows immediately and dynamically obtaining the values of the probability distribution functions most commonly used by mobile phones.
Probability for statisticians

CERN Document Server

Shorack, Galen R

2017-01-01

This 2nd edition textbook offers a rigorous introduction to measure theoretic probability with particular attention to topics of interest to mathematical statisticians—a textbook for courses in probability for students in mathematical statistics. It is recommended to anyone interested in the probability underlying modern statistics, providing a solid grounding in the probabilistic tools and techniques necessary to do theoretical research in statistics. For the teaching of probability theory to post graduate statistics students, this is one of the most attractive books available. Of particular interest is a presentation of the major central limit theorems via Stein's method either prior to or alternative to a characteristic function presentation. Additionally, there is considerable emphasis placed on the quantile function as well as the distribution function. The bootstrap and trimming are both presented. Martingale coverage includes coverage of censored data martingales. The text includes measure theoretic...
Estimation of Extreme Response and Failure Probability of Wind Turbines under Normal Operation using Probability Density Evolution Method

DEFF Research Database (Denmark)

Sichani, Mahdi Teimouri; Nielsen, Søren R.K.; Liu, W. F.

2013-01-01

Estimation of extreme response and failure probability of structures subjected to ultimate design loads is essential for structural design of wind turbines according to the new standard IEC61400-1. This task is focused on in the present paper in virtue of probability density evolution method (PDEM......), which underlies the schemes of random vibration analysis and structural reliability assessment. The short-term rare failure probability of 5-mega-watt wind turbines, for illustrative purposes, in case of given mean wind speeds and turbulence levels is investigated through the scheme of extreme value...... distribution instead of any other approximate schemes of fitted distribution currently used in statistical extrapolation techniques. Besides, the comparative studies against the classical fitted distributions and the standard Monte Carlo techniques are carried out. Numerical results indicate that PDEM exhibits...
Which DTW Method Applied to Marine Univariate Time Series Imputation

OpenAIRE

Phan , Thi-Thu-Hong; Caillault , Émilie; Lefebvre , Alain; Bigand , André

2017-01-01

International audience; Missing data are ubiquitous in any domains of applied sciences. Processing datasets containing missing values can lead to a loss of efficiency and unreliable results, especially for large missing sub-sequence(s). Therefore, the aim of this paper is to build a framework for filling missing values in univariate time series and to perform a comparison of different similarity metrics used for the imputation task. This allows to suggest the most suitable methods for the imp...
In situ calibration using univariate analyses based on the onboard ChemCam targets: first prediction of Martian rock and soil compositions

International Nuclear Information System (INIS)

Fabre, C.; Cousin, A.; Wiens, R.C.; Ollila, A.; Gasnault, O.; Maurice, S.; Sautter, V.; Forni, O.; Lasue, J.; Tokar, R.; Vaniman, D.; Melikechi, N.

2014-01-01

Curiosity rover landed on August 6th, 2012 in Gale Crater, Mars and it possesses unique analytical capabilities to investigate the chemistry and mineralogy of the Martian soil. In particular, the LIBS technique is being used for the first time on another planet with the ChemCam instrument, and more than 75,000 spectra have been returned in the first year on Mars. Curiosity carries body-mounted calibration targets specially designed for the ChemCam instrument, some of which are homgeneous glasses and others that are fine-grained glass-ceramics. We present direct calibrations, using these onboard standards to infer elements and element ratios by ratioing relative peak areas. As the laser spot size is around 300 μm, the LIBS technique provides measurements of the silicate glass compositions representing homogeneous material and measurements of the ceramic targets that are comparable to fine-grained rock or soil. The laser energy and the auto-focus are controlled for all sequences used for calibration. The univariate calibration curves present relatively to very good correlation coefficients with low RSDs for major and ratio calibrations. Trace element calibration curves (Li, Sr, and Mn), down to several ppm, can be used as a rapid tool to draw attention to remarkable rocks and soils along the traverse. First comparisons to alpha-particle X-ray spectroscopy (APXS) data, on selected targets, show good agreement for most elements and for Mg# and Al/Si estimates. SiO 2 estimates using univariate cannot be yet used. Na 2 O and K 2 O estimates are relevant for high alkali contents, but probably under estimated due to the CCCT initial compositions. Very good results for CaO and Al 2 O 3 estimates and satisfactory results for FeO are obtained. - Highlights: • In situ LIBS univariate calibrations are done using the Curiosity onboard standards. • Major and minor element contents can be rapidly obtained. • Trace element contents can be used as a rapid tool along the
The pathways for intelligible speech: multivariate and univariate perspectives.

Science.gov (United States)

Evans, S; Kyong, J S; Rosen, S; Golestani, N; Warren, J E; McGettigan, C; Mourão-Miranda, J; Wise, R J S; Scott, S K

2014-09-01

An anterior pathway, concerned with extracting meaning from sound, has been identified in nonhuman primates. An analogous pathway has been suggested in humans, but controversy exists concerning the degree of lateralization and the precise location where responses to intelligible speech emerge. We have demonstrated that the left anterior superior temporal sulcus (STS) responds preferentially to intelligible speech (Scott SK, Blank CC, Rosen S, Wise RJS. 2000. Identification of a pathway for intelligible speech in the left temporal lobe. Brain. 123:2400-2406.). A functional magnetic resonance imaging study in Cerebral Cortex used equivalent stimuli and univariate and multivariate analyses to argue for the greater importance of bilateral posterior when compared with the left anterior STS in responding to intelligible speech (Okada K, Rong F, Venezia J, Matchin W, Hsieh IH, Saberi K, Serences JT,Hickok G. 2010. Hierarchical organization of human auditory cortex: evidence from acoustic invariance in the response to intelligible speech. 20: 2486-2495.). Here, we also replicate our original study, demonstrating that the left anterior STS exhibits the strongest univariate response and, in decoding using the bilateral temporal cortex, contains the most informative voxels showing an increased response to intelligible speech. In contrast, in classifications using local "searchlights" and a whole brain analysis, we find greater classification accuracy in posterior rather than anterior temporal regions. Thus, we show that the precise nature of the multivariate analysis used will emphasize different response profiles associated with complex sound to speech processing. © The Author 2013. Published by Oxford University Press.
Probability of Failure in Random Vibration

DEFF Research Database (Denmark)

Nielsen, Søren R.K.; Sørensen, John Dalsgaard

1988-01-01

Close approximations to the first-passage probability of failure in random vibration can be obtained by integral equation methods. A simple relation exists between the first-passage probability density function and the distribution function for the time interval spent below a barrier before out......-crossing. An integral equation for the probability density function of the time interval is formulated, and adequate approximations for the kernel are suggested. The kernel approximation results in approximate solutions for the probability density function of the time interval and thus for the first-passage probability...
Approximation of ruin probabilities via Erlangized scale mixtures

DEFF Research Database (Denmark)

Peralta, Oscar; Rojas-Nandayapa, Leonardo; Xie, Wangyue

2018-01-01

In this paper, we extend an existing scheme for numerically calculating the probability of ruin of a classical Cramér–Lundbergreserve process having absolutely continuous but otherwise general claim size distributions. We employ a dense class of distributions that we denominate Erlangized scale...... a simple methodology for constructing a sequence of distributions having the form Π⋆G with the purpose of approximating the integrated tail distribution of the claim sizes. Then we adapt a recent result which delivers an explicit expression for the probability of ruin in the case that the claim size...... distribution is modeled as an Erlangized scale mixture. We provide simplified expressions for the approximation of the probability of ruin and construct explicit bounds for the error of approximation. We complement our results with a classical example where the claim sizes are heavy-tailed....
A comparison of bivariate and univariate QTL mapping in livestock populations

Directory of Open Access Journals (Sweden)

Sorensen Daniel

2003-11-01

Full Text Available Abstract This study presents a multivariate, variance component-based QTL mapping model implemented via restricted maximum likelihood (REML. The method was applied to investigate bivariate and univariate QTL mapping analyses, using simulated data. Specifically, we report results on the statistical power to detect a QTL and on the precision of parameter estimates using univariate and bivariate approaches. The model and methodology were also applied to study the effectiveness of partitioning the overall genetic correlation between two traits into a component due to many genes of small effect, and one due to the QTL. It is shown that when the QTL has a pleiotropic effect on two traits, a bivariate analysis leads to a higher statistical power of detecting the QTL and to a more precise estimate of the QTL's map position, in particular in the case when the QTL has a small effect on the trait. The increase in power is most marked in cases where the contributions of the QTL and of the polygenic components to the genetic correlation have opposite signs. The bivariate REML analysis can successfully partition the two components contributing to the genetic correlation between traits.
The probability distribution of side-chain conformations in [Leu] and [Met]enkephalin determines the potency and selectivity to mu and delta opiate receptors

DEFF Research Database (Denmark)

Nielsen, Bjørn Gilbert; Jensen, Morten Østergaard; Bohr, Henrik

2003-01-01

The structure of enkephalin, a small neuropeptide with five amino acids, has been simulated on computers using molecular dynamics. Such simulations exhibit a few stable conformations, which also have been identified experimentally. The simulations provide the possibility to perform cluster analysis...... in the space defined by potentially pharmacophoric measures such as dihedral angles, side-chain orientation, etc. By analyzing the statistics of the resulting clusters, the probability distribution of the side-chain conformations may be determined. These probabilities allow us to predict the selectivity...... of [Leu]enkephalin and [Met]enkephalin to the known mu- and delta-type opiate receptors to which they bind as agonists. Other plausible consequences of these probability distributions are discussed in relation to the way in which they may influence the dynamics of the synapse....
The probability representation as a new formulation of quantum mechanics

International Nuclear Information System (INIS)

Man'ko, Margarita A; Man'ko, Vladimir I

2012-01-01

We present a new formulation of conventional quantum mechanics, in which the notion of a quantum state is identified via a fair probability distribution of the position measured in a reference frame of the phase space with rotated axes. In this formulation, the quantum evolution equation as well as the equation for finding energy levels are expressed as linear equations for the probability distributions that determine the quantum states. We also give the integral transforms relating the probability distribution (called the tomographic-probability distribution or the state tomogram) to the density matrix and the Wigner function and discuss their connection with the Radon transform. Qudit states are considered and the invertible map of the state density operators onto the probability vectors is discussed. The tomographic entropies and entropic uncertainty relations are reviewed. We demonstrate the uncertainty relations for the position and momentum and the entropic uncertainty relations in the tomographic-probability representation, which is suitable for an experimental check of the uncertainty relations.
Scoring Rules for Subjective Probability Distributions

DEFF Research Database (Denmark)

Harrison, Glenn W.; Martínez-Correa, Jimmy; Swarthout, J. Todd

2017-01-01

significantly due to risk aversion. We characterize an approach for eliciting the entire subjective belief distribution that is minimally biased due to risk aversion. We offer simulated examples to demonstrate the intuition of our approach. We also provide theory to formally characterize our framework. And we...... provide experimental evidence which corroborates our theoretical results. We conclude that for empirically plausible levels of risk aversion, one can reliably elicit most important features of the latent subjective belief distribution without undertaking calibration for risk attitudes providing one...
Influence of nucleon density distribution in nucleon emission probability

International Nuclear Information System (INIS)

Paul, Sabyasachi; Nandy, Maitreyee; Mohanty, A.K.; Sarkar, P.K.; Gambhir, Y.K.

2014-01-01

Different decay modes are observed in heavy ion reactions at low to intermediate energies. It is interesting to study total neutron emission in these reactions which may be contributed by all/many of these decay modes. In an attempt to understand the importance of mean field and the entrance channel angular momentum, we study their influence on the emission probability of nucleons in heavy ion reactions in this work. This study owes its significance to the fact that once population of different states are determined, emission probability governs the double differential neutron yield
Probability densities and Lévy densities

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole Eiler

For positive Lévy processes (i.e. subordinators) formulae are derived that express the probability density or the distribution function in terms of power series in time t. The applicability of the results to finance and to turbulence is briefly indicated.......For positive Lévy processes (i.e. subordinators) formulae are derived that express the probability density or the distribution function in terms of power series in time t. The applicability of the results to finance and to turbulence is briefly indicated....
Probability an introduction

CERN Document Server

Grimmett, Geoffrey

2014-01-01

Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains. A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit th...
Probability theory and mathematical statistics for engineers

CERN Document Server

Pugachev, V S

1984-01-01

Probability Theory and Mathematical Statistics for Engineers focuses on the concepts of probability theory and mathematical statistics for finite-dimensional random variables.The publication first underscores the probabilities of events, random variables, and numerical characteristics of random variables. Discussions focus on canonical expansions of random vectors, second-order moments of random vectors, generalization of the density concept, entropy of a distribution, direct evaluation of probabilities, and conditional probabilities. The text then examines projections of random vector
Validated univariate and multivariate spectrophotometric methods for the determination of pharmaceuticals mixture in complex wastewater

Science.gov (United States)

Riad, Safaa M.; Salem, Hesham; Elbalkiny, Heba T.; Khattab, Fatma I.

2015-04-01

Five, accurate, precise, and sensitive univariate and multivariate spectrophotometric methods were developed for the simultaneous determination of a ternary mixture containing Trimethoprim (TMP), Sulphamethoxazole (SMZ) and Oxytetracycline (OTC) in waste water samples collected from different cites either production wastewater or livestock wastewater after their solid phase extraction using OASIS HLB cartridges. In univariate methods OTC was determined at its λmax 355.7 nm (0D), while (TMP) and (SMZ) were determined by three different univariate methods. Method (A) is based on successive spectrophotometric resolution technique (SSRT). The technique starts with the ratio subtraction method followed by ratio difference method for determination of TMP and SMZ. Method (B) is successive derivative ratio technique (SDR). Method (C) is mean centering of the ratio spectra (MCR). The developed multivariate methods are principle component regression (PCR) and partial least squares (PLS). The specificity of the developed methods is investigated by analyzing laboratory prepared mixtures containing different ratios of the three drugs. The obtained results are statistically compared with those obtained by the official methods, showing no significant difference with respect to accuracy and precision at p = 0.05.
VIBRATION ISOLATION SYSTEM PROBABILITY ANALYSIS

Directory of Open Access Journals (Sweden)

Smirnov Vladimir Alexandrovich

2012-10-01

Full Text Available The article deals with the probability analysis for a vibration isolation system of high-precision equipment, which is extremely sensitive to low-frequency oscillations even of submicron amplitude. The external sources of low-frequency vibrations may include the natural city background or internal low-frequency sources inside buildings (pedestrian activity, HVAC. Taking Gauss distribution into account, the author estimates the probability of the relative displacement of the isolated mass being still lower than the vibration criteria. This problem is being solved in the three dimensional space, evolved by the system parameters, including damping and natural frequency. According to this probability distribution, the chance of exceeding the vibration criteria for a vibration isolation system is evaluated. Optimal system parameters - damping and natural frequency - are being developed, thus the possibility of exceeding vibration criteria VC-E and VC-D is assumed to be less than 0.04.
Probability Distributions for Cyclone Key Parameters and Cyclonic Wind Speed for the East Coast of Indian Region

Directory of Open Access Journals (Sweden)

Pradeep K. Goyal

2011-09-01

Full Text Available This paper presents a study conducted on the probabilistic distribution of key cyclone parameters and the cyclonic wind speed by analyzing the cyclone track records obtained from India meteorological department for east coast region of India. The dataset of historical landfalling storm tracks in India from 1975–2007 with latitude /longitude and landfall locations are used to map the cyclone tracks in a region of study. The statistical tests were performed to find a best fit distribution to the track data for each cyclone parameter. These parameters include central pressure difference, the radius of maximum wind speed, the translation velocity, track angle with site and are used to generate digital simulated cyclones using wind field simulation techniques. For this, different sets of values for all the cyclone key parameters are generated randomly from their probability distributions. Using these simulated values of the cyclone key parameters, the distribution of wind velocity at a particular site is obtained. The same distribution of wind velocity at the site is also obtained from actual track records and using the distributions of the cyclone key parameters as published in the literature. The simulated distribution is compared with the wind speed distributions obtained from actual track records. The findings are useful in cyclone disaster mitigation.

Spatial probability aids visual stimulus discrimination

Directory of Open Access Journals (Sweden)

Michael Druker

2010-08-01

Full Text Available We investigated whether the statistical predictability of a target's location would influence how quickly and accurately it was classified. Recent results have suggested that spatial probability can be a cue for the allocation of attention in visual search. One explanation for probability cuing is spatial repetition priming. In our two experiments we used probability distributions that were continuous across the display rather than relying on a few arbitrary screen locations. This produced fewer spatial repeats and allowed us to dissociate the effect of a high probability location from that of short-term spatial repetition. The task required participants to quickly judge the color of a single dot presented on a computer screen. In Experiment 1, targets were more probable in an off-center hotspot of high probability that gradually declined to a background rate. Targets garnered faster responses if they were near earlier target locations (priming and if they were near the high probability hotspot (probability cuing. In Experiment 2, target locations were chosen on three concentric circles around fixation. One circle contained 80% of targets. The value of this ring distribution is that it allowed for a spatially restricted high probability zone in which sequentially repeated trials were not likely to be physically close. Participant performance was sensitive to the high-probability circle in addition to the expected effects of eccentricity and the distance to recent targets. These two experiments suggest that inhomogeneities in spatial probability can be learned and used by participants on-line and without prompting as an aid for visual stimulus discrimination and that spatial repetition priming is not a sufficient explanation for this effect. Future models of attention should consider explicitly incorporating the probabilities of targets locations and features.
Wigner function and the probability representation of quantum states

Directory of Open Access Journals (Sweden)

Man’ko Margarita A.

2014-01-01

Full Text Available The relation of theWigner function with the fair probability distribution called tomographic distribution or quantum tomogram associated with the quantum state is reviewed. The connection of the tomographic picture of quantum mechanics with the integral Radon transform of the Wigner quasidistribution is discussed. The Wigner–Moyal equation for the Wigner function is presented in the form of kinetic equation for the tomographic probability distribution both in quantum mechanics and in the classical limit of the Liouville equation. The calculation of moments of physical observables in terms of integrals with the state tomographic probability distributions is constructed having a standard form of averaging in the probability theory. New uncertainty relations for the position and momentum are written in terms of optical tomograms suitable for directexperimental check. Some recent experiments on checking the uncertainty relations including the entropic uncertainty relations are discussed.
Benchmarking PARTISN with Analog Monte Carlo: Moments of the Neutron Number and the Cumulative Fission Number Probability Distributions

Energy Technology Data Exchange (ETDEWEB)

O' Rourke, Patrick Francis [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2016-10-27

The purpose of this report is to provide the reader with an understanding of how a Monte Carlo neutron transport code was written, developed, and evolved to calculate the probability distribution functions (PDFs) and their moments for the neutron number at a final time as well as the cumulative fission number, along with introducing several basic Monte Carlo concepts.
A probability distribution model of tooth pits for evaluating time-varying mesh stiffness of pitting gears

Science.gov (United States)

Lei, Yaguo; Liu, Zongyao; Wang, Delong; Yang, Xiao; Liu, Huan; Lin, Jing

2018-06-01

Tooth damage often causes a reduction in gear mesh stiffness. Thus time-varying mesh stiffness (TVMS) can be treated as an indication of gear health conditions. This study is devoted to investigating the mesh stiffness variations of a pair of external spur gears with tooth pitting, and proposes a new model for describing tooth pitting based on probability distribution. In the model, considering the appearance and development process of tooth pitting, we model the pitting on the surface of spur gear teeth as a series of pits with a uniform distribution in the direction of tooth width and a normal distribution in the direction of tooth height, respectively. In addition, four pitting degrees, from no pitting to severe pitting, are modeled. Finally, influences of tooth pitting on TVMS are analyzed in details and the proposed model is validated by comparing with a finite element model. The comparison results show that the proposed model is effective for the TVMS evaluations of pitting gears.
Uncertainty about probability: a decision analysis perspective

International Nuclear Information System (INIS)

Howard, R.A.

1988-01-01

The issue of how to think about uncertainty about probability is framed and analyzed from the viewpoint of a decision analyst. The failure of nuclear power plants is used as an example. The key idea is to think of probability as describing a state of information on an uncertain event, and to pose the issue of uncertainty in this quantity as uncertainty about a number that would be definitive: it has the property that you would assign it as the probability if you knew it. Logical consistency requires that the probability to assign to a single occurrence in the absence of further information be the mean of the distribution of this definitive number, not the medium as is sometimes suggested. Any decision that must be made without the benefit of further information must also be made using the mean of the definitive number's distribution. With this formulation, they find further that the probability of r occurrences in n exchangeable trials will depend on the first n moments of the definitive number's distribution. In making decisions, the expected value of clairvoyance on the occurrence of the event must be at least as great as that on the definitive number. If one of the events in question occurs, then the increase in probability of another such event is readily computed. This means, in terms of coin tossing, that unless one is absolutely sure of the fairness of a coin, seeing a head must increase the probability of heads, in distinction to usual thought. A numerical example for nuclear power shows that the failure of one plant of a group with a low probability of failure can significantly increase the probability that must be assigned to failure of a second plant in the group
Probability distribution functions for ELM bursts in a series of JET tokamak discharges

International Nuclear Information System (INIS)

Greenhough, J; Chapman, S C; Dendy, R O; Ward, D J

2003-01-01

A novel statistical treatment of the full raw edge localized mode (ELM) signal from a series of previously studied JET plasmas is tested. The approach involves constructing probability distribution functions (PDFs) for ELM amplitudes and time separations, and quantifying the fit between the measured PDFs and model distributions (Gaussian, inverse exponential) and Poisson processes. Uncertainties inherent in the discreteness of the raw signal require the application of statistically rigorous techniques to distinguish ELM data points from background, and to extrapolate peak amplitudes. The accuracy of PDF construction is further constrained by the relatively small number of ELM bursts (several hundred) in each sample. In consequence the statistical technique is found to be difficult to apply to low frequency (typically Type I) ELMs, so the focus is narrowed to four JET plasmas with high frequency (typically Type III) ELMs. The results suggest that there may be several fundamentally different kinds of Type III ELMing process at work. It is concluded that this novel statistical treatment can be made to work, may have wider applications to ELM data, and has immediate practical value as an additional quantitative discriminant between classes of ELMing behaviour
Cellulose I crystallinity determination using FT-Raman spectroscopy : univariate and multivariate methods

Science.gov (United States)

Umesh P. Agarwal; Richard S. Reiner; Sally A. Ralph

2010-01-01

Two new methods based on FTâRaman spectroscopy, one simple, based on band intensity ratio, and the other using a partial least squares (PLS) regression model, are proposed to determine cellulose I crystallinity. In the simple method, crystallinity in cellulose I samples was determined based on univariate regression that was first developed using the Raman band...
Calculating the Prior Probability Distribution for a Causal Network Using Maximum Entropy: Alternative Approaches

Directory of Open Access Journals (Sweden)

Michael J. Markham

2011-07-01

Full Text Available Some problems occurring in Expert Systems can be resolved by employing a causal (Bayesian network and methodologies exist for this purpose. These require data in a specific form and make assumptions about the independence relationships involved. Methodologies using Maximum Entropy (ME are free from these conditions and have the potential to be used in a wider context including systems consisting of given sets of linear and independence constraints, subject to consistency and convergence. ME can also be used to validate results from the causal network methodologies. Three ME methods for determining the prior probability distribution of causal network systems are considered. The first method is Sequential Maximum Entropy in which the computation of a progression of local distributions leads to the over-all distribution. This is followed by development of the Method of Tribus. The development takes the form of an algorithm that includes the handling of explicit independence constraints. These fall into two groups those relating parents of vertices, and those deduced from triangulation of the remaining graph. The third method involves a variation in the part of that algorithm which handles independence constraints. Evidence is presented that this adaptation only requires the linear constraints and the parental independence constraints to emulate the second method in a substantial class of examples.
Collision Probability Analysis

DEFF Research Database (Denmark)

Hansen, Peter Friis; Pedersen, Preben Terndrup

1998-01-01

It is the purpose of this report to apply a rational model for prediction of ship-ship collision probabilities as function of the ship and the crew characteristics and the navigational environment for MS Dextra sailing on a route between Cadiz and the Canary Islands.The most important ship and crew...... characteristics are: ship speed, ship manoeuvrability, the layout of the navigational bridge, the radar system, the number and the training of navigators, the presence of a look out etc. The main parameters affecting the navigational environment are ship traffic density, probability distributions of wind speeds...... probability, i.e. a study of the navigator's role in resolving critical situations, a causation factor is derived as a second step.The report documents the first step in a probabilistic collision damage analysis. Future work will inlcude calculation of energy released for crushing of structures giving...
Assignment of probability distributions for parameters in the 1996 performance assessment for the Waste Isolation Pilot Plant. Part 1: description of process

International Nuclear Information System (INIS)

Rechard, Rob P.; Tierney, Martin S.

2005-01-01

A managed process was used to consistently and traceably develop probability distributions for parameters representing epistemic uncertainty in four preliminary and the final 1996 performance assessment (PA) for the Waste Isolation Pilot Plant (WIPP). The key to the success of the process was the use of a three-member team consisting of a Parameter Task Leader, PA Analyst, and Subject Matter Expert. This team, in turn, relied upon a series of guidelines for selecting distribution types. The primary function of the guidelines was not to constrain the actual process of developing a parameter distribution but rather to establish a series of well-defined steps where recognized methods would be consistently applied to all parameters. An important guideline was to use a small set of distributions satisfying the maximum entropy formalism. Another important guideline was the consistent use of the log transform for parameters with large ranges (i.e. maximum/minimum>10 3 ). A parameter development team assigned 67 probability density functions (PDFs) in the 1989 PA and 236 PDFs in the 1996 PA using these and other guidelines described
Concepts of probability theory

CERN Document Server

Pfeiffer, Paul E

1979-01-01

Using the Kolmogorov model, this intermediate-level text discusses random variables, probability distributions, mathematical expectation, random processes, more. For advanced undergraduates students of science, engineering, or math. Includes problems with answers and six appendixes. 1965 edition.
Univaried models in the series of temperature of the air

International Nuclear Information System (INIS)

Leon Aristizabal Gloria esperanza

2000-01-01

The theoretical framework for the study of the air's temperature time series is the theory of stochastic processes, particularly those known as ARIMA, that make it possible to carry out a univaried analysis. ARIMA models are built in order to explain the structure of the monthly temperatures corresponding to the mean, the absolute maximum, absolute minimum, maximum mean and minimum mean temperatures, for four stations in Colombia. By means of those models, the possible evolution of the latter variables is estimated with predictive aims in mind. The application and utility of the models is discussed
Handbook of univariate and multivariate data analysis with IBM SPSS

CERN Document Server

Ho, Robert

2013-01-01

Using the same accessible, hands-on approach as its best-selling predecessor, the Handbook of Univariate and Multivariate Data Analysis with IBM SPSS, Second Edition explains how to apply statistical tests to experimental findings, identify the assumptions underlying the tests, and interpret the findings. This second edition now covers more topics and has been updated with the SPSS statistical package for Windows.New to the Second EditionThree new chapters on multiple discriminant analysis, logistic regression, and canonical correlationNew section on how to deal with missing dataCoverage of te
Choice probability generating functions

DEFF Research Database (Denmark)

Fosgerau, Mogens; McFadden, Daniel; Bierlaire, Michel

2010-01-01

This paper establishes that every random utility discrete choice model (RUM) has a representation that can be characterized by a choice-probability generating function (CPGF) with specific properties, and that every function with these specific properties is consistent with a RUM. The choice...... probabilities from the RUM are obtained from the gradient of the CPGF. Mixtures of RUM are characterized by logarithmic mixtures of their associated CPGF. The paper relates CPGF to multivariate extreme value distributions, and reviews and extends methods for constructing generating functions for applications....... The choice probabilities of any ARUM may be approximated by a cross-nested logit model. The results for ARUM are extended to competing risk survival models....
Pattern recognition in spaces of probability distributions for the analysis of edge-localized modes in tokamak plasmas

Energy Technology Data Exchange (ETDEWEB)

Shabbir, Aqsa

2016-07-07

In this doctoral work, pattern recognition techniques are developed and applied to data from tokamak plasmas, in order to contribute to a systematic analysis of edge-localized modes (ELMs). We employ probabilistic models for a quantitative data description geared towards an enhanced systematization of ELM phenomenology. Hence, we start from the point of view that the fundamental object resulting from the observation of a system is a probability distribution, with every single measurement providing a sample from this distribution. In exploring the patterns emerging from the various ELM regimes and relations, we need methods that can handle the intrinsic probabilistic nature of the data. The original contributions of this work are twofold. First, several novel pattern recognition methods in non-Euclidean spaces of probability distribution functions (PDFs) are developed and validated. The second main contribution lies in the application of these and other techniques to a systematic analysis of ELMs in tokamak plasmas. In regard to the methodological aims of the work, we employ the framework of information geometry to develop pattern visualization and classification methods in spaces of probability distributions. In information geometry, a family of probability distributions is considered as a Riemannian manifold. Every point on the manifold represents a single PDF and the distribution parameters provide local coordinates on the manifold. The Fisher information plays the role of a Riemannian metric tensor, enabling calculation of geodesic curves on the surface. The length of such curves yields the geodesic distance (GD) on probabilistic manifolds, which is a natural similarity (distance) measure between PDFs. Equipped with a suitable distance measure, we extrapolate several distance-based pattern recognition methods to the manifold setting. This includes k-nearest neighbor (kNN) and conformal predictor (CP) methods for classification, as well as multidimensional
Pattern recognition in spaces of probability distributions for the analysis of edge-localized modes in tokamak plasmas

International Nuclear Information System (INIS)

Shabbir, Aqsa

2016-01-01

In this doctoral work, pattern recognition techniques are developed and applied to data from tokamak plasmas, in order to contribute to a systematic analysis of edge-localized modes (ELMs). We employ probabilistic models for a quantitative data description geared towards an enhanced systematization of ELM phenomenology. Hence, we start from the point of view that the fundamental object resulting from the observation of a system is a probability distribution, with every single measurement providing a sample from this distribution. In exploring the patterns emerging from the various ELM regimes and relations, we need methods that can handle the intrinsic probabilistic nature of the data. The original contributions of this work are twofold. First, several novel pattern recognition methods in non-Euclidean spaces of probability distribution functions (PDFs) are developed and validated. The second main contribution lies in the application of these and other techniques to a systematic analysis of ELMs in tokamak plasmas. In regard to the methodological aims of the work, we employ the framework of information geometry to develop pattern visualization and classification methods in spaces of probability distributions. In information geometry, a family of probability distributions is considered as a Riemannian manifold. Every point on the manifold represents a single PDF and the distribution parameters provide local coordinates on the manifold. The Fisher information plays the role of a Riemannian metric tensor, enabling calculation of geodesic curves on the surface. The length of such curves yields the geodesic distance (GD) on probabilistic manifolds, which is a natural similarity (distance) measure between PDFs. Equipped with a suitable distance measure, we extrapolate several distance-based pattern recognition methods to the manifold setting. This includes k-nearest neighbor (kNN) and conformal predictor (CP) methods for classification, as well as multidimensional
Investigation of Probability Distributions Using Dice Rolling Simulation

Science.gov (United States)

Lukac, Stanislav; Engel, Radovan

2010-01-01

Dice are considered one of the oldest gambling devices and thus many mathematicians have been interested in various dice gambling games in the past. Dice have been used to teach probability, and dice rolls can be effectively simulated using technology. The National Council of Teachers of Mathematics (NCTM) recommends that teachers use simulations…
Performance Probability Distributions for Sediment Control Best Management Practices

Science.gov (United States)

Ferrell, L.; Beighley, R.; Walsh, K.

2007-12-01

Controlling soil erosion and sediment transport can be a significant challenge during the construction process due to the extent and conditions of bare, disturbed soils. Best Management Practices (BMPs) are used as the framework for the design of sediment discharge prevention systems in stormwater pollution prevention plans which are typically required for construction sites. This research focuses on commonly-used BMP systems for perimeter control of sediment export: silt fences and fiber rolls. Although these systems are widely used, the physical and engineering parameters describing their performance are not well understood. Performance expectations are based on manufacturer results, but due to the dynamic conditions that exist on a construction site performance expectations are not always achievable in the field. Based on experimental results product performance is shown to be highly variable. Experiments using the same installation procedures show inconsistent sediment removal performances ranging from (>)85 percent to zero. The goal of this research is to improve the determination of off-site sediment yield based on probabilistic performance results of perimeter control BMPs. BMPs are evaluated in the Soil Erosion Research Laboratory (SERL) in the Civil and Environmental Engineering department at San Diego State University. SERL experiments are performed on a 3-m by 10-m tilting soil bed with a soil depth of 0.5 meters and a slope of 33 percent. The simulated storm event consists of 17 mm/hr for 20 minutes followed by 51 mm/hr for 30 minutes. The storm event is based on an ASTM design storm intended to simulate BMP failures. BMP performance is assessed based on experiments where BMPs are installed per manufacture specifications, less than optimal installations, and no treatment conditions. Preliminary results from 30 experiments are presented and used to develop probability distributions for BMP sediment removal efficiencies. The results are then combined with
A discussion on the origin of quantum probabilities

International Nuclear Information System (INIS)

Holik, Federico; Sáenz, Manuel; Plastino, Angel

2014-01-01

We study the origin of quantum probabilities as arising from non-Boolean propositional-operational structures. We apply the method developed by Cox to non distributive lattices and develop an alternative formulation of non-Kolmogorovian probability measures for quantum mechanics. By generalizing the method presented in previous works, we outline a general framework for the deduction of probabilities in general propositional structures represented by lattices (including the non-distributive case). -- Highlights: •Several recent works use a derivation similar to that of R.T. Cox to obtain quantum probabilities. •We apply Cox’s method to the lattice of subspaces of the Hilbert space. •We obtain a derivation of quantum probabilities which includes mixed states. •The method presented in this work is susceptible to generalization. •It includes quantum mechanics and classical mechanics as particular cases
Wave functions and two-electron probability distributions of the Hooke's-law atom and helium

International Nuclear Information System (INIS)

O'Neill, Darragh P.; Gill, Peter M. W.

2003-01-01

The Hooke's-law atom (hookium) provides an exactly soluble model for a two-electron atom in which the nuclear-electron Coulombic attraction has been replaced by a harmonic one. Starting from the known exact position-space wave function for the ground state of hookium, we present the momentum-space wave function. We also look at the intracules, two-electron probability distributions, for hookium in position, momentum, and phase space. These are compared with the Hartree-Fock results and the Coulomb holes (the difference between the exact and Hartree-Fock intracules) in position, momentum, and phase space are examined. We then compare these results with analogous results for the ground state of helium using a simple, explicitly correlated wave function

Subjective Probabilities for State-Dependent Continuous Utility

NARCIS (Netherlands)

P.P. Wakker (Peter)

1987-01-01

textabstractFor the expected utility model with state dependent utilities, Karni, Schmeidler and Vind (1983) have shown how to recover uniquely the involved subjective probabilities if the preferences, contingent on a hypothetical probability distribution over the state space, are known. This they
In situ calibration using univariate analyses based on the onboard ChemCam targets: first prediction of Martian rock and soil compositions

Energy Technology Data Exchange (ETDEWEB)

Fabre, C. [GeoRessources lab, Université de Lorraine, Nancy (France); Cousin, A.; Wiens, R.C. [Los Alamos National Laboratory, Los Alamos, NM (United States); Ollila, A. [University of NM, Albuquerque (United States); Gasnault, O.; Maurice, S. [IRAP, Toulouse (France); Sautter, V. [Museum National d' Histoire Naturelle, Paris (France); Forni, O.; Lasue, J. [IRAP, Toulouse (France); Tokar, R.; Vaniman, D. [Planetary Science Institute, Tucson, AZ (United States); Melikechi, N. [Delaware State University (United States)

2014-09-01

Curiosity rover landed on August 6th, 2012 in Gale Crater, Mars and it possesses unique analytical capabilities to investigate the chemistry and mineralogy of the Martian soil. In particular, the LIBS technique is being used for the first time on another planet with the ChemCam instrument, and more than 75,000 spectra have been returned in the first year on Mars. Curiosity carries body-mounted calibration targets specially designed for the ChemCam instrument, some of which are homgeneous glasses and others that are fine-grained glass-ceramics. We present direct calibrations, using these onboard standards to infer elements and element ratios by ratioing relative peak areas. As the laser spot size is around 300 μm, the LIBS technique provides measurements of the silicate glass compositions representing homogeneous material and measurements of the ceramic targets that are comparable to fine-grained rock or soil. The laser energy and the auto-focus are controlled for all sequences used for calibration. The univariate calibration curves present relatively to very good correlation coefficients with low RSDs for major and ratio calibrations. Trace element calibration curves (Li, Sr, and Mn), down to several ppm, can be used as a rapid tool to draw attention to remarkable rocks and soils along the traverse. First comparisons to alpha-particle X-ray spectroscopy (APXS) data, on selected targets, show good agreement for most elements and for Mg# and Al/Si estimates. SiO{sub 2} estimates using univariate cannot be yet used. Na{sub 2}O and K{sub 2}O estimates are relevant for high alkali contents, but probably under estimated due to the CCCT initial compositions. Very good results for CaO and Al{sub 2}O{sub 3} estimates and satisfactory results for FeO are obtained. - Highlights: • In situ LIBS univariate calibrations are done using the Curiosity onboard standards. • Major and minor element contents can be rapidly obtained. • Trace element contents can be used as a
Extinction probabilities and stationary distributions of mobile genetic elements in prokaryotes: The birth-death-diversification model.

Science.gov (United States)

Drakos, Nicole E; Wahl, Lindi M

2015-12-01

Theoretical approaches are essential to our understanding of the complex dynamics of mobile genetic elements (MGEs) within genomes. Recently, the birth-death-diversification model was developed to describe the dynamics of mobile promoters (MPs), a particular class of MGEs in prokaryotes. A unique feature of this model is that genetic diversification of elements was included. To explore the implications of diversification on the longterm fate of MGE lineages, in this contribution we analyze the extinction probabilities, extinction times and equilibrium solutions of the birth-death-diversification model. We find that diversification increases both the survival and growth rate of MGE families, but the strength of this effect depends on the rate of horizontal gene transfer (HGT). We also find that the distribution of MGE families per genome is not necessarily monotonically decreasing, as observed for MPs, but may have a peak in the distribution that is related to the HGT rate. For MPs specifically, we find that new families have a high extinction probability, and predict that the number of MPs is increasing, albeit at a very slow rate. Additionally, we develop an extension of the birth-death-diversification model which allows MGEs in different regions of the genome, for example coding and non-coding, to be described by different rates. This extension may offer a potential explanation as to why the majority of MPs are located in non-promoter regions of the genome. Copyright © 2015 Elsevier Inc. All rights reserved.
Optimal design of unit hydrographs using probability distribution and ...

Indian Academy of Sciences (India)

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

optimization formulation is solved using binary-coded genetic algorithms. The number of variables to ... Unit hydrograph; rainfall-runoff; hydrology; genetic algorithms; optimization; probability ..... Application of the model. Data derived from the ...
The Bayesian count rate probability distribution in measurement of ionizing radiation by use of a ratemeter

Energy Technology Data Exchange (ETDEWEB)

Weise, K.

2004-06-01

Recent metrological developments concerning measurement uncertainty, founded on Bayesian statistics, give rise to a revision of several parts of the DIN 25482 and ISO 11929 standard series. These series stipulate detection limits and decision thresholds for ionizing-radiation measurements. Part 3 and, respectively, part 4 of them deal with measurements by use of linear-scale analogue ratemeters. A normal frequency distribution of the momentary ratemeter indication for a fixed count rate value is assumed. The actual distribution, which is first calculated numerically by solving an integral equation, differs, however, considerably from the normal distribution although this one represents an approximation of it for sufficiently large values of the count rate to be measured. As is shown, this similarly holds true for the Bayesian probability distribution of the count rate for sufficiently large given measured values indicated by the ratemeter. This distribution follows from the first one mentioned by means of the Bayes theorem. Its expectation value and variance are needed for the standards to be revised on the basis of Bayesian statistics. Simple expressions are given by the present standards for estimating these parameters and for calculating the detection limit and the decision threshold. As is also shown, the same expressions can similarly be used as sufficient approximations by the revised standards if, roughly, the present indicated value exceeds the reciprocal ratemeter relaxation time constant. (orig.)
Path probabilities of continuous time random walks

International Nuclear Information System (INIS)

Eule, Stephan; Friedrich, Rudolf

2014-01-01

Employing the path integral formulation of a broad class of anomalous diffusion processes, we derive the exact relations for the path probability densities of these processes. In particular, we obtain a closed analytical solution for the path probability distribution of a Continuous Time Random Walk (CTRW) process. This solution is given in terms of its waiting time distribution and short time propagator of the corresponding random walk as a solution of a Dyson equation. Applying our analytical solution we derive generalized Feynman–Kac formulae. (paper)
Bivariate Rainfall and Runoff Analysis Using Shannon Entropy Theory

Science.gov (United States)

Rahimi, A.; Zhang, L.

2012-12-01

Rainfall-Runoff analysis is the key component for many hydrological and hydraulic designs in which the dependence of rainfall and runoff needs to be studied. It is known that the convenient bivariate distribution are often unable to model the rainfall-runoff variables due to that they either have constraints on the range of the dependence or fixed form for the marginal distributions. Thus, this paper presents an approach to derive the entropy-based joint rainfall-runoff distribution using Shannon entropy theory. The distribution derived can model the full range of dependence and allow different specified marginals. The modeling and estimation can be proceeded as: (i) univariate analysis of marginal distributions which includes two steps, (a) using the nonparametric statistics approach to detect modes and underlying probability density, and (b) fitting the appropriate parametric probability density functions; (ii) define the constraints based on the univariate analysis and the dependence structure; (iii) derive and validate the entropy-based joint distribution. As to validate the method, the rainfall-runoff data are collected from the small agricultural experimental watersheds located in semi-arid region near Riesel (Waco), Texas, maintained by the USDA. The results of unviariate analysis show that the rainfall variables follow the gamma distribution, whereas the runoff variables have mixed structure and follow the mixed-gamma distribution. With this information, the entropy-based joint distribution is derived using the first moments, the first moments of logarithm transformed rainfall and runoff, and the covariance between rainfall and runoff. The results of entropy-based joint distribution indicate: (1) the joint distribution derived successfully preserves the dependence between rainfall and runoff, and (2) the K-S goodness of fit statistical tests confirm the marginal distributions re-derived reveal the underlying univariate probability densities which further
The mean distance to the nth neighbour in a uniform distribution of random points: an application of probability theory

International Nuclear Information System (INIS)

Bhattacharyya, Pratip; Chakrabarti, Bikas K

2008-01-01

We study different ways of determining the mean distance (r n ) between a reference point and its nth neighbour among random points distributed with uniform density in a D-dimensional Euclidean space. First, we present a heuristic method; though this method provides only a crude mathematical result, it shows a simple way of estimating (r n ). Next, we describe two alternative means of deriving the exact expression of (r n ): we review the method using absolute probability and develop an alternative method using conditional probability. Finally, we obtain an approximation to (r n ) from the mean volume between the reference point and its nth neighbour and compare it with the heuristic and exact results
Characteristic functions of scale mixtures of multivariate skew-normal distributions

KAUST Repository

Kim, Hyoung-Moon; Genton, Marc G.

2011-01-01

We obtain the characteristic function of scale mixtures of skew-normal distributions both in the univariate and multivariate cases. The derivation uses the simple stochastic relationship between skew-normal distributions and scale mixtures of skew
Probability distributions of bed load particle velocities, accelerations, hop distances, and travel times informed by Jaynes's principle of maximum entropy

Science.gov (United States)

Furbish, David; Schmeeckle, Mark; Schumer, Rina; Fathel, Siobhan

2016-01-01

We describe the most likely forms of the probability distributions of bed load particle velocities, accelerations, hop distances, and travel times, in a manner that formally appeals to inferential statistics while honoring mechanical and kinematic constraints imposed by equilibrium transport conditions. The analysis is based on E. Jaynes's elaboration of the implications of the similarity between the Gibbs entropy in statistical mechanics and the Shannon entropy in information theory. By maximizing the information entropy of a distribution subject to known constraints on its moments, our choice of the form of the distribution is unbiased. The analysis suggests that particle velocities and travel times are exponentially distributed and that particle accelerations follow a Laplace distribution with zero mean. Particle hop distances, viewed alone, ought to be distributed exponentially. However, the covariance between hop distances and travel times precludes this result. Instead, the covariance structure suggests that hop distances follow a Weibull distribution. These distributions are consistent with high-resolution measurements obtained from high-speed imaging of bed load particle motions. The analysis brings us closer to choosing distributions based on our mechanical insight.
Analysis of Observation Data of Earth-Rockfill Dam Based on Cloud Probability Distribution Density Algorithm

Directory of Open Access Journals (Sweden)

Han Liwei

2014-07-01

Full Text Available Monitoring data on an earth-rockfill dam constitutes a form of spatial data. Such data include much uncertainty owing to the limitation of measurement information, material parameters, load, geometry size, initial conditions, boundary conditions and the calculation model. So the cloud probability density of the monitoring data must be addressed. In this paper, the cloud theory model was used to address the uncertainty transition between the qualitative concept and the quantitative description. Then an improved algorithm of cloud probability distribution density based on a backward cloud generator was proposed. This was used to effectively convert certain parcels of accurate data into concepts which can be described by proper qualitative linguistic values. Such qualitative description was addressed as cloud numerical characteristics-- {Ex, En, He}, which could represent the characteristics of all cloud drops. The algorithm was then applied to analyze the observation data of a piezometric tube in an earth-rockfill dam. And experiment results proved that the proposed algorithm was feasible, through which, we could reveal the changing regularity of piezometric tube’s water level. And the damage of the seepage in the body was able to be found out.
Univariate graduation of mortality by local polynomial regression

NARCIS (Netherlands)

Tomas, J.

2012-01-01

Life tables are used to describe the one-year probability of death within a well defined population as a function of attained age. These probabilities play an important role in the determination of premium rates and reserves in life insurance. The crude estimates on which life tables are based might
Constructing inverse probability weights for continuous exposures: a comparison of methods.

Science.gov (United States)

Naimi, Ashley I; Moodie, Erica E M; Auger, Nathalie; Kaufman, Jay S

2014-03-01

Inverse probability-weighted marginal structural models with binary exposures are common in epidemiology. Constructing inverse probability weights for a continuous exposure can be complicated by the presence of outliers, and the need to identify a parametric form for the exposure and account for nonconstant exposure variance. We explored the performance of various methods to construct inverse probability weights for continuous exposures using Monte Carlo simulation. We generated two continuous exposures and binary outcomes using data sampled from a large empirical cohort. The first exposure followed a normal distribution with homoscedastic variance. The second exposure followed a contaminated Poisson distribution, with heteroscedastic variance equal to the conditional mean. We assessed six methods to construct inverse probability weights using: a normal distribution, a normal distribution with heteroscedastic variance, a truncated normal distribution with heteroscedastic variance, a gamma distribution, a t distribution (1, 3, and 5 degrees of freedom), and a quantile binning approach (based on 10, 15, and 20 exposure categories). We estimated the marginal odds ratio for a single-unit increase in each simulated exposure in a regression model weighted by the inverse probability weights constructed using each approach, and then computed the bias and mean squared error for each method. For the homoscedastic exposure, the standard normal, gamma, and quantile binning approaches performed best. For the heteroscedastic exposure, the quantile binning, gamma, and heteroscedastic normal approaches performed best. Our results suggest that the quantile binning approach is a simple and versatile way to construct inverse probability weights for continuous exposures.
Finding upper bounds for software failure probabilities - experiments and results

International Nuclear Information System (INIS)

Kristiansen, Monica; Winther, Rune

2005-09-01

This report looks into some aspects of using Bayesian hypothesis testing to find upper bounds for software failure probabilities. In the first part, the report evaluates the Bayesian hypothesis testing approach for finding upper bounds for failure probabilities of single software components. The report shows how different choices of prior probability distributions for a software component's failure probability influence the number of tests required to obtain adequate confidence in a software component. In the evaluation, both the effect of the shape of the prior distribution as well as one's prior confidence in the software component were investigated. In addition, different choices of prior probability distributions are discussed based on their relevance in a software context. In the second part, ideas on how the Bayesian hypothesis testing approach can be extended to assess systems consisting of multiple software components are given. One of the main challenges when assessing systems consisting of multiple software components is to include dependency aspects in the software reliability models. However, different types of failure dependencies between software components must be modelled differently. Identifying different types of failure dependencies are therefore an important condition for choosing a prior probability distribution, which correctly reflects one's prior belief in the probability for software components failing dependently. In this report, software components include both general in-house software components, as well as pre-developed software components (e.g. COTS, SOUP, etc). (Author)
The effects of radiotherapy treatment uncertainties on the delivered dose distribution and tumour control probability

International Nuclear Information System (INIS)

Booth, J.T.; Zavgorodni, S.F.; Royal Adelaide Hospital, SA

2001-01-01

Uncertainty in the precise quantity of radiation dose delivered to tumours in external beam radiotherapy is present due to many factors, and can result in either spatially uniform (Gaussian) or spatially non-uniform dose errors. These dose errors are incorporated into the calculation of tumour control probability (TCP) and produce a distribution of possible TCP values over a population. We also study the effect of inter-patient cell sensitivity heterogeneity on the population distribution of patient TCPs. This study aims to investigate the relative importance of these three uncertainties (spatially uniform dose uncertainty, spatially non-uniform dose uncertainty, and inter-patient cell sensitivity heterogeneity) on the delivered dose and TCP distribution following a typical course of fractionated external beam radiotherapy. The dose distributions used for patient treatments are modelled in one dimension. Geometric positioning uncertainties during and before treatment are considered as shifts of a pre-calculated dose distribution. Following the simulation of a population of patients, distributions of dose across the patient population are used to calculate mean treatment dose, standard deviation in mean treatment dose, mean TCP, standard deviation in TCP, and TCP mode. These parameters are calculated with each of the three uncertainties included separately. The calculations show that the dose errors in the tumour volume are dominated by the spatially uniform component of dose uncertainty. This could be related to machine specific parameters, such as linear accelerator calibration. TCP calculation is affected dramatically by inter-patient variation in the cell sensitivity and to a lesser extent by the spatially uniform dose errors. The positioning errors with the 1.5 cm margins used cause dose uncertainty outside the tumour volume and have a small effect on mean treatment dose (in the tumour volume) and tumour control. Copyright (2001) Australasian College of
Irreversibility and conditional probability

International Nuclear Information System (INIS)

Stuart, C.I.J.M.

1989-01-01

The mathematical entropy - unlike physical entropy - is simply a measure of uniformity for probability distributions in general. So understood, conditional entropies have the same logical structure as conditional probabilities. If, as is sometimes supposed, conditional probabilities are time-reversible, then so are conditional entropies and, paradoxically, both then share this symmetry with physical equations of motion. The paradox is, of course that probabilities yield a direction to time both in statistical mechanics and quantum mechanics, while the equations of motion do not. The supposed time-reversibility of both conditionals seems also to involve a form of retrocausality that is related to, but possibly not the same as, that described by Costa de Beaurgard. The retrocausality is paradoxically at odds with the generally presumed irreversibility of the quantum mechanical measurement process. Further paradox emerges if the supposed time-reversibility of the conditionals is linked with the idea that the thermodynamic entropy is the same thing as 'missing information' since this confounds the thermodynamic and mathematical entropies. However, it is shown that irreversibility is a formal consequence of conditional entropies and, hence, of conditional probabilities also. 8 refs. (Author)
Influence of random setup error on dose distribution

International Nuclear Information System (INIS)

Zhai Zhenyu

2008-01-01

Objective: To investigate the influence of random setup error on dose distribution in radiotherapy and determine the margin from ITV to PTV. Methods: A random sample approach was used to simulate the fields position in target coordinate system. Cumulative effect of random setup error was the sum of dose distributions of all individual treatment fractions. Study of 100 cumulative effects might get shift sizes of 90% dose point position. Margins from ITV to PTV caused by random setup error were chosen by 95% probability. Spearman's correlation was used to analyze the influence of each factor. Results: The average shift sizes of 90% dose point position was 0.62, 1.84, 3.13, 4.78, 6.34 and 8.03 mm if random setup error was 1,2,3,4,5 and 6 mm,respectively. Univariate analysis showed the size of margin was associated only by the size of random setup error. Conclusions: Margin of ITV to PTV is 1.2 times random setup error for head-and-neck cancer and 1.5 times for thoracic and abdominal cancer. Field size, energy and target depth, unlike random setup error, have no relation with the size of the margin. (authors)
Introduction to probability and statistics for science, engineering, and finance

CERN Document Server

Rosenkrantz, Walter A

2008-01-01

Data Analysis Orientation The Role and Scope of Statistics in Science and Engineering Types of Data: Examples from Engineering, Public Health, and Finance The Frequency Distribution of a Variable Defined on a Population Quantiles of a Distribution Measures of Location (Central Value) and Variability Covariance, Correlation, and Regression: Computing a Stock's Beta Mathematical Details and Derivations Large Data Sets Probability Theory Orientation Sample Space, Events, Axioms of Probability Theory Mathematical Models of Random Sampling Conditional Probability and Baye
Optimum parameters in a model for tumour control probability, including interpatient heterogeneity: evaluation of the log-normal distribution

International Nuclear Information System (INIS)

Keall, P J; Webb, S

2007-01-01

The heterogeneity of human tumour radiation response is well known. Researchers have used the normal distribution to describe interpatient tumour radiosensitivity. However, many natural phenomena show a log-normal distribution. Log-normal distributions are common when mean values are low, variances are large and values cannot be negative. These conditions apply to radiosensitivity. The aim of this work was to evaluate the log-normal distribution to predict clinical tumour control probability (TCP) data and to compare the results with the homogeneous (δ-function with single α-value) and normal distributions. The clinically derived TCP data for four tumour types-melanoma, breast, squamous cell carcinoma and nodes-were used to fit the TCP models. Three forms of interpatient tumour radiosensitivity were considered: the log-normal, normal and δ-function. The free parameters in the models were the radiosensitivity mean, standard deviation and clonogenic cell density. The evaluation metric was the deviance of the maximum likelihood estimation of the fit of the TCP calculated using the predicted parameters to the clinical data. We conclude that (1) the log-normal and normal distributions of interpatient tumour radiosensitivity heterogeneity more closely describe clinical TCP data than a single radiosensitivity value and (2) the log-normal distribution has some theoretical and practical advantages over the normal distribution. Further work is needed to test these models on higher quality clinical outcome datasets
Light Scattering of Rough Orthogonal Anisotropic Surfaces with Secondary Most Probable Slope Distributions

International Nuclear Information System (INIS)

Li Hai-Xia; Cheng Chuan-Fu

2011-01-01

We study the light scattering of an orthogonal anisotropic rough surface with secondary most probable slope distribution. It is found that the scattered intensity profiles have obvious secondary maxima, and in the direction perpendicular to the plane of incidence, the secondary maxima are oriented in a curve on the observation plane, which is called the orientation curve. By numerical calculation of the scattering wave fields with the height data of the sample, it is validated that the secondary maxima are induced by the side face element, which constitutes the prismoid structure of the anisotropic surface. We derive the equation of the quadratic orientation curve. Experimentally, we construct the system for light scattering measurement using a CCD. The scattered intensity profiles are extracted from the images at different angles of incidence along the orientation curves. The experimental results conform to the theory. (fundamental areas of phenomenology(including applications))

Classical probabilities for Majorana and Weyl spinors

International Nuclear Information System (INIS)

Wetterich, C.

2011-01-01

Highlights: → Map of classical statistical Ising model to fermionic quantum field theory. → Lattice-regularized real Grassmann functional integral for single Weyl spinor. → Emerging complex structure characteristic for quantum physics. → A classical statistical ensemble describes a quantum theory. - Abstract: We construct a map between the quantum field theory of free Weyl or Majorana fermions and the probability distribution of a classical statistical ensemble for Ising spins or discrete bits. More precisely, a Grassmann functional integral based on a real Grassmann algebra specifies the time evolution of the real wave function q τ (t) for the Ising states τ. The time dependent probability distribution of a generalized Ising model obtains as p τ (t)=q τ 2 (t). The functional integral employs a lattice regularization for single Weyl or Majorana spinors. We further introduce the complex structure characteristic for quantum mechanics. Probability distributions of the Ising model which correspond to one or many propagating fermions are discussed explicitly. Expectation values of observables can be computed equivalently in the classical statistical Ising model or in the quantum field theory for fermions.
What do differences between multi-voxel and univariate analysis mean? How subject-, voxel-, and trial-level variance impact fMRI analysis.

Science.gov (United States)

Davis, Tyler; LaRocque, Karen F; Mumford, Jeanette A; Norman, Kenneth A; Wagner, Anthony D; Poldrack, Russell A

2014-08-15

Multi-voxel pattern analysis (MVPA) has led to major changes in how fMRI data are analyzed and interpreted. Many studies now report both MVPA results and results from standard univariate voxel-wise analysis, often with the goal of drawing different conclusions from each. Because MVPA results can be sensitive to latent multidimensional representations and processes whereas univariate voxel-wise analysis cannot, one conclusion that is often drawn when MVPA and univariate results differ is that the activation patterns underlying MVPA results contain a multidimensional code. In the current study, we conducted simulations to formally test this assumption. Our findings reveal that MVPA tests are sensitive to the magnitude of voxel-level variability in the effect of a condition within subjects, even when the same linear relationship is coded in all voxels. We also find that MVPA is insensitive to subject-level variability in mean activation across an ROI, which is the primary variance component of interest in many standard univariate tests. Together, these results illustrate that differences between MVPA and univariate tests do not afford conclusions about the nature or dimensionality of the neural code. Instead, targeted tests of the informational content and/or dimensionality of activation patterns are critical for drawing strong conclusions about the representational codes that are indicated by significant MVPA results. Copyright © 2014 Elsevier Inc. All rights reserved.
Characterizing the Lyα forest flux probability distribution function using Legendre polynomials

Energy Technology Data Exchange (ETDEWEB)

Cieplak, Agnieszka M.; Slosar, Anže, E-mail: acieplak@bnl.gov, E-mail: anze@bnl.gov [Brookhaven National Laboratory, Bldg 510, Upton, NY, 11973 (United States)

2017-10-01

The Lyman-α forest is a highly non-linear field with considerable information available in the data beyond the power spectrum. The flux probability distribution function (PDF) has been used as a successful probe of small-scale physics. In this paper we argue that measuring coefficients of the Legendre polynomial expansion of the PDF offers several advantages over measuring the binned values as is commonly done. In particular, the n -th Legendre coefficient can be expressed as a linear combination of the first n moments, allowing these coefficients to be measured in the presence of noise and allowing a clear route for marginalisation over mean flux. Moreover, in the presence of noise, our numerical work shows that a finite number of coefficients are well measured with a very sharp transition into noise dominance. This compresses the available information into a small number of well-measured quantities. We find that the amount of recoverable information is a very non-linear function of spectral noise that strongly favors fewer quasars measured at better signal to noise.
Characterizing the Lyα forest flux probability distribution function using Legendre polynomials

Science.gov (United States)

Cieplak, Agnieszka M.; Slosar, Anže

2017-10-01

The Lyman-α forest is a highly non-linear field with considerable information available in the data beyond the power spectrum. The flux probability distribution function (PDF) has been used as a successful probe of small-scale physics. In this paper we argue that measuring coefficients of the Legendre polynomial expansion of the PDF offers several advantages over measuring the binned values as is commonly done. In particular, the n-th Legendre coefficient can be expressed as a linear combination of the first n moments, allowing these coefficients to be measured in the presence of noise and allowing a clear route for marginalisation over mean flux. Moreover, in the presence of noise, our numerical work shows that a finite number of coefficients are well measured with a very sharp transition into noise dominance. This compresses the available information into a small number of well-measured quantities. We find that the amount of recoverable information is a very non-linear function of spectral noise that strongly favors fewer quasars measured at better signal to noise.
The probability distribution of the delay time of a wave packet in strong overlap of resonance levels

International Nuclear Information System (INIS)

Lyuboshitz, V.L.

1982-01-01

The time development of nuclear reactions at a large density of levels is investigated using the theory of overlapping resonances. The analytical expression for the function describing the time delay probability distribution of a wave packet is obtained in the framework of the model of n equi - valent channels. It is shown that a relative fluctuation of the time delay at the stage of the compound nucleus is snall. The possibility is discussed of increasing the duration of nuclear raactions with rising excitation energy
Computing Confidence Bounds for Power and Sample Size of the General Linear Univariate Model

OpenAIRE

Taylor, Douglas J.; Muller, Keith E.

1995-01-01

The power of a test, the probability of rejecting the null hypothesis in favor of an alternative, may be computed using estimates of one or more distributional parameters. Statisticians frequently fix mean values and calculate power or sample size using a variance estimate from an existing study. Hence computed power becomes a random variable for a fixed sample size. Likewise, the sample size necessary to achieve a fixed power varies randomly. Standard statistical practice requires reporting ...
Spectral analysis of growing graphs a quantum probability point of view

CERN Document Server

Obata, Nobuaki

2017-01-01

This book is designed as a concise introduction to the recent achievements on spectral analysis of graphs or networks from the point of view of quantum (or non-commutative) probability theory. The main topics are spectral distributions of the adjacency matrices of finite or infinite graphs and their limit distributions for growing graphs. The main vehicle is quantum probability, an algebraic extension of the traditional probability theory, which provides a new framework for the analysis of adjacency matrices revealing their non-commutative nature. For example, the method of quantum decomposition makes it possible to study spectral distributions by means of interacting Fock spaces or equivalently by orthogonal polynomials. Various concepts of independence in quantum probability and corresponding central limit theorems are used for the asymptotic study of spectral distributions for product graphs. This book is written for researchers, teachers, and students interested in graph spectra, their (asymptotic) spectr...
Characteristic functions of scale mixtures of multivariate skew-normal distributions

KAUST Repository

Kim, Hyoung-Moon

2011-08-01

We obtain the characteristic function of scale mixtures of skew-normal distributions both in the univariate and multivariate cases. The derivation uses the simple stochastic relationship between skew-normal distributions and scale mixtures of skew-normal distributions. In particular, we describe the characteristic function of skew-normal, skew-t, and other related distributions. © 2011 Elsevier Inc.
Exploration of probability distribution of velocities of saltating sand particles based on the stochastic particle-bed collisions

International Nuclear Information System (INIS)

Zheng Xiaojing; Xie Li; Zhou Youhe

2005-01-01

The wind-blown sand saltating movement is mainly categorized into two mechanical processes, that is, the interaction between the moving sand particles and the wind in the saltation layer, and the collisions of incident particles with sand bed, and the latter produces a lift-off velocity of a sand particle moving into saltation. In this Letter a methodology of phenomenological analysis is presented to get probability density (distribution) function (pdf) of the lift-off velocity of sand particles from sand bed based on the stochastic particle-bed collision. After the sand particles are dealt with by uniform circular disks and a 2D collision between an incident particle and the granular bed is employed, we get the analytical formulas of lift-off velocity of ejected and rebound particles in saltation, which are functions of some random parameters such as angle and magnitude of incident velocity of the impacting particles, impact and contact angles between the collision particles, and creeping velocity of sand particles, etc. By introducing the probability density functions (pdf's) of these parameters in communion with all possible patterns of sand bed and all possible particle-bed collisions, and using the essential arithmetic of multi-dimension random variables' pdf, the pdf's of lift-off velocities are deduced out and expressed by the pdf's of the random parameters in the collisions. The numerical results of the distributions of lift-off velocities display that they agree well with experimental ones
On the Hitting Probability of Max-Stable Processes

OpenAIRE

Hofmann, Martin

2012-01-01

The probability that a max-stable process {\\eta} in C[0, 1] with identical marginal distribution function F hits x \\in R with 0 < F (x) < 1 is the hitting probability of x. We show that the hitting probability is always positive, unless the components of {\\eta} are completely dependent. Moreover, we consider the event that the paths of standard MSP hit some x \\in R twice and we give a sufficient condition for a positive probability of this event.
Univariate/multivariate genome-wide association scans using data from families and unrelated samples.

Directory of Open Access Journals (Sweden)

Lei Zhang

2009-08-01

Full Text Available As genome-wide association studies (GWAS are becoming more popular, two approaches, among others, could be considered in order to improve statistical power for identifying genes contributing subtle to moderate effects to human diseases. The first approach is to increase sample size, which could be achieved by combining both unrelated and familial subjects together. The second approach is to jointly analyze multiple correlated traits. In this study, by extending generalized estimating equations (GEEs, we propose a simple approach for performing univariate or multivariate association tests for the combined data of unrelated subjects and nuclear families. In particular, we correct for population stratification by integrating principal component analysis and transmission disequilibrium test strategies. The proposed method allows for multiple siblings as well as missing parental information. Simulation studies show that the proposed test has improved power compared to two popular methods, EIGENSTRAT and FBAT, by analyzing the combined data, while correcting for population stratification. In addition, joint analysis of bivariate traits has improved power over univariate analysis when pleiotropic effects are present. Application to the Genetic Analysis Workshop 16 (GAW16 data sets attests to the feasibility and applicability of the proposed method.
Wind Speed Prediction Using a Univariate ARIMA Model and a Multivariate NARX Model

Directory of Open Access Journals (Sweden)

Erasmo Cadenas

2016-02-01

Full Text Available Two on step ahead wind speed forecasting models were compared. A univariate model was developed using a linear autoregressive integrated moving average (ARIMA. This method’s performance is well studied for a large number of prediction problems. The other is a multivariate model developed using a nonlinear autoregressive exogenous artificial neural network (NARX. This uses the variables: barometric pressure, air temperature, wind direction and solar radiation or relative humidity, as well as delayed wind speed. Both models were developed from two databases from two sites: an hourly average measurements database from La Mata, Oaxaca, Mexico, and a ten minute average measurements database from Metepec, Hidalgo, Mexico. The main objective was to compare the impact of the various meteorological variables on the performance of the multivariate model of wind speed prediction with respect to the high performance univariate linear model. The NARX model gave better results with improvements on the ARIMA model of between 5.5% and 10. 6% for the hourly database and of between 2.3% and 12.8% for the ten minute database for mean absolute error and mean squared error, respectively.
R package imputeTestbench to compare imputations methods for univariate time series

OpenAIRE

Bokde, Neeraj; Kulat, Kishore; Beck, Marcus W; Asencio-Cortés, Gualberto

2016-01-01

This paper describes the R package imputeTestbench that provides a testbench for comparing imputation methods for missing data in univariate time series. The imputeTestbench package can be used to simulate the amount and type of missing data in a complete dataset and compare filled data using different imputation methods. The user has the option to simulate missing data by removing observations completely at random or in blocks of different sizes. Several default imputation methods are includ...
Exact valence bond entanglement entropy and probability distribution in the XXX spin chain and the potts model.

Science.gov (United States)

Jacobsen, J L; Saleur, H

2008-02-29

We determine exactly the probability distribution of the number N_(c) of valence bonds connecting a subsystem of length L>1 to the rest of the system in the ground state of the XXX antiferromagnetic spin chain. This provides, in particular, the asymptotic behavior of the valence-bond entanglement entropy S_(VB)=N_(c)ln2=4ln2/pi(2)lnL disproving a recent conjecture that this should be related with the von Neumann entropy, and thus equal to 1/3lnL. Our results generalize to the Q-state Potts model.
Oil spill contamination probability in the southeastern Levantine basin.

Science.gov (United States)

Goldman, Ron; Biton, Eli; Brokovich, Eran; Kark, Salit; Levin, Noam

2015-02-15

Recent gas discoveries in the eastern Mediterranean Sea led to multiple operations with substantial economic interest, and with them there is a risk of oil spills and their potential environmental impacts. To examine the potential spatial distribution of this threat, we created seasonal maps of the probability of oil spill pollution reaching an area in the Israeli coastal and exclusive economic zones, given knowledge of its initial sources. We performed simulations of virtual oil spills using realistic atmospheric and oceanic conditions. The resulting maps show dominance of the alongshore northerly current, which causes the high probability areas to be stretched parallel to the coast, increasing contamination probability downstream of source points. The seasonal westerly wind forcing determines how wide the high probability areas are, and may also restrict these to a small coastal region near source points. Seasonal variability in probability distribution, oil state, and pollution time is also discussed. Copyright © 2014 Elsevier Ltd. All rights reserved.
Supervised learning of probability distributions by neural networks

Science.gov (United States)

Baum, Eric B.; Wilczek, Frank

1988-01-01

Supervised learning algorithms for feedforward neural networks are investigated analytically. The back-propagation algorithm described by Werbos (1974), Parker (1985), and Rumelhart et al. (1986) is generalized by redefining the values of the input and output neurons as probabilities. The synaptic weights are then varied to follow gradients in the logarithm of likelihood rather than in the error. This modification is shown to provide a more rigorous theoretical basis for the algorithm and to permit more accurate predictions. A typical application involving a medical-diagnosis expert system is discussed.
Regression Is a Univariate General Linear Model Subsuming Other Parametric Methods as Special Cases.

Science.gov (United States)

Vidal, Sherry

Although the concept of the general linear model (GLM) has existed since the 1960s, other univariate analyses such as the t-test and the analysis of variance models have remained popular. The GLM produces an equation that minimizes the mean differences of independent variables as they are related to a dependent variable. From a computer printout…
Encounter Probability of Individual Wave Height

DEFF Research Database (Denmark)

Liu, Z.; Burcharth, H. F.

1998-01-01

wave height corresponding to a certain exceedence probability within a structure lifetime (encounter probability), based on the statistical analysis of long-term extreme significant wave height. Then the design individual wave height is calculated as the expected maximum individual wave height...... associated with the design significant wave height, with the assumption that the individual wave heights follow the Rayleigh distribution. However, the exceedence probability of such a design individual wave height within the structure lifetime is unknown. The paper presents a method for the determination...... of the design individual wave height corresponding to an exceedence probability within the structure lifetime, given the long-term extreme significant wave height. The method can also be applied for estimation of the number of relatively large waves for fatigue analysis of constructions....
Conditional probability of the tornado missile impact given a tornado occurrence

International Nuclear Information System (INIS)

Goodman, J.; Koch, J.E.

1982-01-01

Using an approach based on statistical mechanics, an expression for the probability of the first missile strike is developed. The expression depends on two generic parameters (injection probability eta(F) and height distribution psi(Z,F)), which are developed in this study, and one plant specific parameter (number of potential missiles N/sub p/). The expression for the joint probability of simultaneous impact of muitiple targets is also developed. This espression is applicable to calculation of the probability of common cause failure due to tornado missiles. It is shown that the probability of the first missile strike can be determined using a uniform missile distribution model. It is also shown that the conditional probability of the second strike, given the first, is underestimated by the uniform model. The probability of the second strike is greatly increased if the missiles are in clusters large enough to cover both targets
Characterizing the Lyman-alpha forest flux probability distribution function using Legendre polynomials

Science.gov (United States)

Cieplak, Agnieszka; Slosar, Anze

2018-01-01

The Lyman-alpha forest has become a powerful cosmological probe at intermediate redshift. It is a highly non-linear field with much information present beyond the power spectrum. The flux probability flux distribution (PDF) in particular has been a successful probe of small scale physics. However, it is also sensitive to pixel noise, spectrum resolution, and continuum fitting, all of which lead to possible biased estimators. Here we argue that measuring the coefficients of the Legendre polynomial expansion of the PDF offers several advantages over measuring the binned values as is commonly done. Since the n-th Legendre coefficient can be expressed as a linear combination of the first n moments of the field, this allows for the coefficients to be measured in the presence of noise and allows for a clear route towards marginalization over the mean flux. Additionally, in the presence of noise, a finite number of these coefficients are well measured with a very sharp transition into noise dominance. This compresses the information into a small amount of well-measured quantities. Finally, we find that measuring fewer quasars with high signal-to-noise produces a higher amount of recoverable information.

Convergence of Transition Probability Matrix in CLVMarkov Models

Science.gov (United States)

Permana, D.; Pasaribu, U. S.; Indratno, S. W.; Suprayogi, S.

2018-04-01

A transition probability matrix is an arrangement of transition probability from one states to another in a Markov chain model (MCM). One of interesting study on the MCM is its behavior for a long time in the future. The behavior is derived from one property of transition probabilty matrix for n steps. This term is called the convergence of the n-step transition matrix for n move to infinity. Mathematically, the convergence of the transition probability matrix is finding the limit of the transition matrix which is powered by n where n moves to infinity. The convergence form of the transition probability matrix is very interesting as it will bring the matrix to its stationary form. This form is useful for predicting the probability of transitions between states in the future. The method usually used to find the convergence of transition probability matrix is through the process of limiting the distribution. In this paper, the convergence of the transition probability matrix is searched using a simple concept of linear algebra that is by diagonalizing the matrix.This method has a higher level of complexity because it has to perform the process of diagonalization in its matrix. But this way has the advantage of obtaining a common form of power n of the transition probability matrix. This form is useful to see transition matrix before stationary. For example cases are taken from CLV model using MCM called Model of CLV-Markov. There are several models taken by its transition probability matrix to find its convergence form. The result is that the convergence of the matrix of transition probability through diagonalization has similarity with convergence with commonly used distribution of probability limiting method.
Models for probability and statistical inference theory and applications

CERN Document Server

Stapleton, James H

2007-01-01

This concise, yet thorough, book is enhanced with simulations and graphs to build the intuition of readersModels for Probability and Statistical Inference was written over a five-year period and serves as a comprehensive treatment of the fundamentals of probability and statistical inference. With detailed theoretical coverage found throughout the book, readers acquire the fundamentals needed to advance to more specialized topics, such as sampling, linear models, design of experiments, statistical computing, survival analysis, and bootstrapping.Ideal as a textbook for a two-semester sequence on probability and statistical inference, early chapters provide coverage on probability and include discussions of: discrete models and random variables; discrete distributions including binomial, hypergeometric, geometric, and Poisson; continuous, normal, gamma, and conditional distributions; and limit theory. Since limit theory is usually the most difficult topic for readers to master, the author thoroughly discusses mo...
Imprecise Probability Methods for Weapons UQ

Energy Technology Data Exchange (ETDEWEB)

Picard, Richard Roy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Vander Wiel, Scott Alan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2016-05-13

Building on recent work in uncertainty quanti cation, we examine the use of imprecise probability methods to better characterize expert knowledge and to improve on misleading aspects of Bayesian analysis with informative prior distributions. Quantitative approaches to incorporate uncertainties in weapons certi cation are subject to rigorous external peer review, and in this regard, certain imprecise probability methods are well established in the literature and attractive. These methods are illustrated using experimental data from LANL detonator impact testing.
Eliciting Subjective Probability Distributions with Binary Lotteries

DEFF Research Database (Denmark)

Harrison, Glenn W.; Martínez-Correa, Jimmy; Swarthout, J. Todd

2015-01-01

We test in a laboratory experiment the theoretical prediction that risk attitudes have a surprisingly small role in distorting reports from true belief distributions. We find evidence consistent with theory in our experiment....
QRS complex detection based on continuous density hidden Markov models using univariate observations

Science.gov (United States)

Sotelo, S.; Arenas, W.; Altuve, M.

2018-04-01

In the electrocardiogram (ECG), the detection of QRS complexes is a fundamental step in the ECG signal processing chain since it allows the determination of other characteristics waves of the ECG and provides information about heart rate variability. In this work, an automatic QRS complex detector based on continuous density hidden Markov models (HMM) is proposed. HMM were trained using univariate observation sequences taken either from QRS complexes or their derivatives. The detection approach is based on the log-likelihood comparison of the observation sequence with a fixed threshold. A sliding window was used to obtain the observation sequence to be evaluated by the model. The threshold was optimized by receiver operating characteristic curves. Sensitivity (Sen), specificity (Spc) and F1 score were used to evaluate the detection performance. The approach was validated using ECG recordings from the MIT-BIH Arrhythmia database. A 6-fold cross-validation shows that the best detection performance was achieved with 2 states HMM trained with QRS complexes sequences (Sen = 0.668, Spc = 0.360 and F1 = 0.309). We concluded that these univariate sequences provide enough information to characterize the QRS complex dynamics from HMM. Future works are directed to the use of multivariate observations to increase the detection performance.
Objective Bayesian Analysis of Skew- t Distributions

KAUST Repository

BRANCO, MARCIA D'ELIA; GENTON, MARC G.; LISEO, BRUNERO

2012-01-01

We study the Jeffreys prior and its properties for the shape parameter of univariate skew-t distributions with linear and nonlinear Student's t skewing functions. In both cases, we show that the resulting priors for the shape parameter are symmetric
The Visualization of the Space Probability Distribution for a Particle Moving in a Double Ring-Shaped Coulomb Potential

Directory of Open Access Journals (Sweden)

Yuan You

2018-01-01

Full Text Available The analytical solutions to a double ring-shaped Coulomb potential (RSCP are presented. The visualizations of the space probability distribution (SPD are illustrated for the two- (contour and three-dimensional (isosurface cases. The quantum numbers (n,l,m are mainly relevant for those quasi-quantum numbers (n′,l′,m′ via the double RSCP parameter c. The SPDs are of circular ring shape in spherical coordinates. The properties for the relative probability values (RPVs P are also discussed. For example, when we consider the special case (n,l,m=(6,5,0, the SPD moves towards two poles of z-axis when P increases. Finally, we discuss the different cases for the potential parameter b, which is taken as negative and positive values for c>0. Compared with the particular case b=0, the SPDs are shrunk for b=-0.5, while they are spread out for b=0.5.
The perception of probability.

Science.gov (United States)

Gallistel, C R; Krishan, Monika; Liu, Ye; Miller, Reilly; Latham, Peter E

2014-01-01

We present a computational model to explain the results from experiments in which subjects estimate the hidden probability parameter of a stepwise nonstationary Bernoulli process outcome by outcome. The model captures the following results qualitatively and quantitatively, with only 2 free parameters: (a) Subjects do not update their estimate after each outcome; they step from one estimate to another at irregular intervals. (b) The joint distribution of step widths and heights cannot be explained on the assumption that a threshold amount of change must be exceeded in order for them to indicate a change in their perception. (c) The mapping of observed probability to the median perceived probability is the identity function over the full range of probabilities. (d) Precision (how close estimates are to the best possible estimate) is good and constant over the full range. (e) Subjects quickly detect substantial changes in the hidden probability parameter. (f) The perceived probability sometimes changes dramatically from one observation to the next. (g) Subjects sometimes have second thoughts about a previous change perception, after observing further outcomes. (h) The frequency with which they perceive changes moves in the direction of the true frequency over sessions. (Explaining this finding requires 2 additional parametric assumptions.) The model treats the perception of the current probability as a by-product of the construction of a compact encoding of the experienced sequence in terms of its change points. It illustrates the why and the how of intermittent Bayesian belief updating and retrospective revision in simple perception. It suggests a reinterpretation of findings in the recent literature on the neurobiology of decision making. (PsycINFO Database Record (c) 2014 APA, all rights reserved).
Probability Distribution of Long-run Indiscriminate Felling of Trees in ...

African Journals Online (AJOL)

Bright

conditionally independent of every prior state given the current state (Obodos, ... of events or experiments in which the probability of occurrence for an event ... represent the exhaustive and mutually exclusive outcomes (states) of a system at.
Towards a Categorical Account of Conditional Probability

Directory of Open Access Journals (Sweden)

Robert Furber

2015-11-01

Full Text Available This paper presents a categorical account of conditional probability, covering both the classical and the quantum case. Classical conditional probabilities are expressed as a certain "triangle-fill-in" condition, connecting marginal and joint probabilities, in the Kleisli category of the distribution monad. The conditional probabilities are induced by a map together with a predicate (the condition. The latter is a predicate in the logic of effect modules on this Kleisli category. This same approach can be transferred to the category of C*-algebras (with positive unital maps, whose predicate logic is also expressed in terms of effect modules. Conditional probabilities can again be expressed via a triangle-fill-in property. In the literature, there are several proposals for what quantum conditional probability should be, and also there are extra difficulties not present in the classical case. At this stage, we only describe quantum systems with classical parametrization.
Distributional Inference

NARCIS (Netherlands)

Kroese, A.H.; van der Meulen, E.A.; Poortema, Klaas; Schaafsma, W.

1995-01-01

The making of statistical inferences in distributional form is conceptionally complicated because the epistemic 'probabilities' assigned are mixtures of fact and fiction. In this respect they are essentially different from 'physical' or 'frequency-theoretic' probabilities. The distributional form is
Path probability of stochastic motion: A functional approach

Science.gov (United States)

Hattori, Masayuki; Abe, Sumiyoshi

2016-06-01

The path probability of a particle undergoing stochastic motion is studied by the use of functional technique, and the general formula is derived for the path probability distribution functional. The probability of finding paths inside a tube/band, the center of which is stipulated by a given path, is analytically evaluated in a way analogous to continuous measurements in quantum mechanics. Then, the formalism developed here is applied to the stochastic dynamics of stock price in finance.
EDF: Computing electron number probability distribution functions in real space from molecular wave functions

Science.gov (United States)

Francisco, E.; Pendás, A. Martín; Blanco, M. A.

2008-04-01

Given an N-electron molecule and an exhaustive partition of the real space ( R) into m arbitrary regions Ω,Ω,…,Ω ( ⋃i=1mΩ=R), the edf program computes all the probabilities P(n,n,…,n) of having exactly n electrons in Ω, n electrons in Ω,…, and n electrons ( n+n+⋯+n=N) in Ω. Each Ω may correspond to a single basin (atomic domain) or several such basins (functional group). In the later case, each atomic domain must belong to a single Ω. The program can manage both single- and multi-determinant wave functions which are read in from an aimpac-like wave function description ( .wfn) file (T.A. Keith et al., The AIMPAC95 programs, http://www.chemistry.mcmaster.ca/aimpac, 1995). For multi-determinantal wave functions a generalization of the original .wfn file has been introduced. The new format is completely backwards compatible, adding to the previous structure a description of the configuration interaction (CI) coefficients and the determinants of correlated wave functions. Besides the .wfn file, edf only needs the overlap integrals over all the atomic domains between the molecular orbitals (MO). After the P(n,n,…,n) probabilities are computed, edf obtains from them several magnitudes relevant to chemical bonding theory, such as average electronic populations and localization/delocalization indices. Regarding spin, edf may be used in two ways: with or without a splitting of the P(n,n,…,n) probabilities into α and β spin components. Program summaryProgram title: edf Catalogue identifier: AEAJ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAJ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5387 No. of bytes in distributed program, including test data, etc.: 52 381 Distribution format: tar.gz Programming language: Fortran 77 Computer
A stochastic-bayesian model for the fracture probability of PWR pressure vessels

Energy Technology Data Exchange (ETDEWEB)

Francisco, Alexandre S.; Duran, Jorge Alberto R., E-mail: afrancisco@metal.eeimvr.uff.br, E-mail: duran@metal.eeimvr.uff.br [Universidade Federal Fluminense (UFF), Volta Redonda, RJ (Brazil). Dept. de Engenharia Mecanica

2013-07-01

Fracture probability of pressure vessels containing cracks can be obtained by methodologies of easy understanding, which require a deterministic treatment, complemented by statistical methods. However, more accurate results are required, methodologies need to be better formulated. This paper presents a new methodology to address this problem. First, a more rigorous methodology is obtained by means of the relationship of probability distributions that model crack incidence and nondestructive inspection efficiency using the Bayes' theorem. The result is an updated crack incidence distribution. Further, the accuracy of the methodology is improved by using a stochastic model for the crack growth. The stochastic model incorporates the statistical variability of the crack growth process, combining the stochastic theory with experimental data. Stochastic differential equations are derived by the randomization of empirical equations. From the solution of this equation, a distribution function related to the crack growth is derived. The fracture probability using both probability distribution functions is in agreement with theory, and presents realistic value for pressure vessels. (author)
A stochastic-bayesian model for the fracture probability of PWR pressure vessels

International Nuclear Information System (INIS)

Francisco, Alexandre S.; Duran, Jorge Alberto R.

2013-01-01

Fracture probability of pressure vessels containing cracks can be obtained by methodologies of easy understanding, which require a deterministic treatment, complemented by statistical methods. However, more accurate results are required, methodologies need to be better formulated. This paper presents a new methodology to address this problem. First, a more rigorous methodology is obtained by means of the relationship of probability distributions that model crack incidence and nondestructive inspection efficiency using the Bayes' theorem. The result is an updated crack incidence distribution. Further, the accuracy of the methodology is improved by using a stochastic model for the crack growth. The stochastic model incorporates the statistical variability of the crack growth process, combining the stochastic theory with experimental data. Stochastic differential equations are derived by the randomization of empirical equations. From the solution of this equation, a distribution function related to the crack growth is derived. The fracture probability using both probability distribution functions is in agreement with theory, and presents realistic value for pressure vessels. (author)
A Guideline to Univariate Statistical Analysis for LC/MS-Based Untargeted Metabolomics-Derived Data

Directory of Open Access Journals (Sweden)

Maria Vinaixa

2012-10-01

Full Text Available Several metabolomic software programs provide methods for peak picking, retention time alignment and quantification of metabolite features in LC/MS-based metabolomics. Statistical analysis, however, is needed in order to discover those features significantly altered between samples. By comparing the retention time and MS/MS data of a model compound to that from the altered feature of interest in the research sample, metabolites can be then unequivocally identified. This paper reports on a comprehensive overview of a workflow for statistical analysis to rank relevant metabolite features that will be selected for further MS/MS experiments. We focus on univariate data analysis applied in parallel on all detected features. Characteristics and challenges of this analysis are discussed and illustrated using four different real LC/MS untargeted metabolomic datasets. We demonstrate the influence of considering or violating mathematical assumptions on which univariate statistical test rely, using high-dimensional LC/MS datasets. Issues in data analysis such as determination of sample size, analytical variation, assumption of normality and homocedasticity, or correction for multiple testing are discussed and illustrated in the context of our four untargeted LC/MS working examples.
Probability of crack-initiation and application to NDE

Energy Technology Data Exchange (ETDEWEB)

Prantl, G [Nuclear Safety Inspectorate HSK, (Switzerland)

1988-12-31

Fracture toughness is a property with a certain variability. When a statistical distribution is assumed, the probability of crack initiation may be calculated for a given problem defined by its geometry and the applied stress. Experiments have shown, that cracks which experience a certain small amount of ductile growth can reliably be detected by acoustic emission measurements. The probability of crack detection by AE-techniques may be estimated using this experimental finding and the calculated probability of crack initiation. (author).
Comparing linear probability model coefficients across groups

DEFF Research Database (Denmark)

Holm, Anders; Ejrnæs, Mette; Karlson, Kristian Bernt

2015-01-01

of the following three components: outcome truncation, scale parameters and distributional shape of the predictor variable. These results point to limitations in using linear probability model coefficients for group comparisons. We also provide Monte Carlo simulations and real examples to illustrate......This article offers a formal identification analysis of the problem in comparing coefficients from linear probability models between groups. We show that differences in coefficients from these models can result not only from genuine differences in effects, but also from differences in one or more...... these limitations, and we suggest a restricted approach to using linear probability model coefficients in group comparisons....
On misclassication probabilities of linear and quadratic classiers ...

African Journals Online (AJOL)

We study the theoretical misclassication probability of linear and quadratic classiers and examine the performance of these classiers under distributional variations in theory and using simulation. We derive expression for Bayes errors for some competing distributions from the same family under location shift. Keywords: ...
An exercise in model validation: Comparing univariate statistics and Monte Carlo-based multivariate statistics

International Nuclear Information System (INIS)

Weathers, J.B.; Luck, R.; Weathers, J.W.

2009-01-01

The complexity of mathematical models used by practicing engineers is increasing due to the growing availability of sophisticated mathematical modeling tools and ever-improving computational power. For this reason, the need to define a well-structured process for validating these models against experimental results has become a pressing issue in the engineering community. This validation process is partially characterized by the uncertainties associated with the modeling effort as well as the experimental results. The net impact of the uncertainties on the validation effort is assessed through the 'noise level of the validation procedure', which can be defined as an estimate of the 95% confidence uncertainty bounds for the comparison error between actual experimental results and model-based predictions of the same quantities of interest. Although general descriptions associated with the construction of the noise level using multivariate statistics exists in the literature, a detailed procedure outlining how to account for the systematic and random uncertainties is not available. In this paper, the methodology used to derive the covariance matrix associated with the multivariate normal pdf based on random and systematic uncertainties is examined, and a procedure used to estimate this covariance matrix using Monte Carlo analysis is presented. The covariance matrices are then used to construct approximate 95% confidence constant probability contours associated with comparison error results for a practical example. In addition, the example is used to show the drawbacks of using a first-order sensitivity analysis when nonlinear local sensitivity coefficients exist. Finally, the example is used to show the connection between the noise level of the validation exercise calculated using multivariate and univariate statistics.

An exercise in model validation: Comparing univariate statistics and Monte Carlo-based multivariate statistics

Energy Technology Data Exchange (ETDEWEB)

Weathers, J.B. [Shock, Noise, and Vibration Group, Northrop Grumman Shipbuilding, P.O. Box 149, Pascagoula, MS 39568 (United States)], E-mail: James.Weathers@ngc.com; Luck, R. [Department of Mechanical Engineering, Mississippi State University, 210 Carpenter Engineering Building, P.O. Box ME, Mississippi State, MS 39762-5925 (United States)], E-mail: Luck@me.msstate.edu; Weathers, J.W. [Structural Analysis Group, Northrop Grumman Shipbuilding, P.O. Box 149, Pascagoula, MS 39568 (United States)], E-mail: Jeffrey.Weathers@ngc.com

2009-11-15

The complexity of mathematical models used by practicing engineers is increasing due to the growing availability of sophisticated mathematical modeling tools and ever-improving computational power. For this reason, the need to define a well-structured process for validating these models against experimental results has become a pressing issue in the engineering community. This validation process is partially characterized by the uncertainties associated with the modeling effort as well as the experimental results. The net impact of the uncertainties on the validation effort is assessed through the 'noise level of the validation procedure', which can be defined as an estimate of the 95% confidence uncertainty bounds for the comparison error between actual experimental results and model-based predictions of the same quantities of interest. Although general descriptions associated with the construction of the noise level using multivariate statistics exists in the literature, a detailed procedure outlining how to account for the systematic and random uncertainties is not available. In this paper, the methodology used to derive the covariance matrix associated with the multivariate normal pdf based on random and systematic uncertainties is examined, and a procedure used to estimate this covariance matrix using Monte Carlo analysis is presented. The covariance matrices are then used to construct approximate 95% confidence constant probability contours associated with comparison error results for a practical example. In addition, the example is used to show the drawbacks of using a first-order sensitivity analysis when nonlinear local sensitivity coefficients exist. Finally, the example is used to show the connection between the noise level of the validation exercise calculated using multivariate and univariate statistics.
Extreme value distribution of earthquake magnitude

Science.gov (United States)

Zi, Jun Gan; Tung, C. C.

1983-07-01

Probability distribution of maximum earthquake magnitude is first derived for an unspecified probability distribution of earthquake magnitude. A model for energy release of large earthquakes, similar to that of Adler-Lomnitz and Lomnitz, is introduced from which the probability distribution of earthquake magnitude is obtained. An extensive set of world data for shallow earthquakes, covering the period from 1904 to 1980, is used to determine the parameters of the probability distribution of maximum earthquake magnitude. Because of the special form of probability distribution of earthquake magnitude, a simple iterative scheme is devised to facilitate the estimation of these parameters by the method of least-squares. The agreement between the empirical and derived probability distributions of maximum earthquake magnitude is excellent.
Probability intervals for the top event unavailability of fault trees

International Nuclear Information System (INIS)

Lee, Y.T.; Apostolakis, G.E.

1976-06-01

The evaluation of probabilities of rare events is of major importance in the quantitative assessment of the risk from large technological systems. In particular, for nuclear power plants the complexity of the systems, their high reliability and the lack of significant statistical records have led to the extensive use of logic diagrams in the estimation of low probabilities. The estimation of probability intervals for the probability of existence of the top event of a fault tree is examined. Given the uncertainties of the primary input data, a method is described for the evaluation of the first four moments of the top event occurrence probability. These moments are then used to estimate confidence bounds by several approaches which are based on standard inequalities (e.g., Tchebycheff, Cantelli, etc.) or on empirical distributions (the Johnson family). Several examples indicate that the Johnson family of distributions yields results which are in good agreement with those produced by Monte Carlo simulation
Linear and nonlinear optical signals in probability and phase-space representations

International Nuclear Information System (INIS)

Man'ko, Margarita A

2006-01-01

Review of different representations of signals including the phase-space representations and tomographic representations is presented. The signals under consideration are either linear or nonlinear ones. The linear signals satisfy linear quantumlike Schroedinger and von Neumann equations. Nonlinear signals satisfy nonlinear Schroedinger equations as well as Gross-Pitaevskii equation describing solitons in Bose-Einstein condensate. The Ville-Wigner distributions for solitons are considered in comparison with tomographic-probability densities describing solitons completely. different kinds of tomographies - symplectic tomography, optical tomography and Fresnel tomography are reviewed. New kind of map of the signals onto probability distributions of discrete photon number-like variable is discussed. Mutual relations between different transformations of signal functions are established in explicit form. Such characteristics of the signal-probability distribution as entropy is discussed
Numerical modelling of local deposition patients, activity distributions and cellular hit probabilities of inhaled radon progenies in human airways

International Nuclear Information System (INIS)

Farkas, A.; Balashazy, I.; Szoeke, I.

2003-01-01

The general objective of our research is modelling the biophysical processes of the effects of inhaled radon progenies. This effort is related to the rejection or support of the linear no threshold (LNT) dose-effect hypothesis, which seems to be one of the most challenging tasks of current radiation protection. Our approximation and results may also serve as a useful tool for lung cancer models. In this study, deposition patterns, activity distributions and alpha-hit probabilities of inhaled radon progenies in the large airways of the human tracheobronchial tree are computed. The airflow fields and related particle deposition patterns strongly depend on the shape of airway geometry and breathing pattern. Computed deposition patterns of attached an unattached radon progenies are strongly inhomogeneous creating hot spots at the carinal regions and downstream of the inner sides of the daughter airways. The results suggest that in the vicinity of the carinal regions the multiple hit probabilities are quite high even at low average doses and increase exponentially in the low-dose range. Thus, even the so-called low doses may present high doses for large clusters of cells. The cell transformation probabilities are much higher in these regions and this phenomenon cannot be modeled with average burdens. (authors)
Classroom Research: Assessment of Student Understanding of Sampling Distributions of Means and the Central Limit Theorem in Post-Calculus Probability and Statistics Classes

Science.gov (United States)

Lunsford, M. Leigh; Rowell, Ginger Holmes; Goodson-Espy, Tracy

2006-01-01

We applied a classroom research model to investigate student understanding of sampling distributions of sample means and the Central Limit Theorem in post-calculus introductory probability and statistics courses. Using a quantitative assessment tool developed by previous researchers and a qualitative assessment tool developed by the authors, we…
Theory of overdispersion in counting statistics caused by fluctuating probabilities

International Nuclear Information System (INIS)

Semkow, Thomas M.

1999-01-01

It is shown that the random Lexis fluctuations of probabilities such as probability of decay or detection cause the counting statistics to be overdispersed with respect to the classical binomial, Poisson, or Gaussian distributions. The generating and the distribution functions for the overdispersed counting statistics are derived. Applications to radioactive decay with detection and more complex experiments are given, as well as distinguishing between the source and background, in the presence of overdispersion. Monte-Carlo verifications are provided
Finite-size scaling of survival probability in branching processes

OpenAIRE

Garcia-Millan, Rosalba; Font-Clos, Francesc; Corral, Alvaro

2014-01-01

Branching processes pervade many models in statistical physics. We investigate the survival probability of a Galton-Watson branching process after a finite number of generations. We reveal the finite-size scaling law of the survival probability for a given branching process ruled by a probability distribution of the number of offspring per element whose standard deviation is finite, obtaining the exact scaling function as well as the critical exponents. Our findings prove the universal behavi...
Computational statistics handbook with Matlab

CERN Document Server

Martinez, Wendy L

2007-01-01

Prefaces Introduction What Is Computational Statistics? An Overview of the Book Probability Concepts Introduction Probability Conditional Probability and Independence Expectation Common Distributions Sampling Concepts Introduction Sampling Terminology and Concepts Sampling Distributions Parameter Estimation Empirical Distribution Function Generating Random Variables Introduction General Techniques for Generating Random Variables Generating Continuous Random Variables Generating Discrete Random Variables Exploratory Data Analysis Introduction Exploring Univariate Data Exploring Bivariate and Trivariate Data Exploring Multidimensional Data Finding Structure Introduction Projecting Data Principal Component Analysis Projection Pursuit EDA Independent Component Analysis Grand Tour Nonlinear Dimensionality Reduction Monte Carlo Methods for Inferential Statistics Introduction Classical Inferential Statistics Monte Carlo Methods for Inferential Statist...
Failure probability analysis of optical grid

Science.gov (United States)

Zhong, Yaoquan; Guo, Wei; Sun, Weiqiang; Jin, Yaohui; Hu, Weisheng

2008-11-01

Optical grid, the integrated computing environment based on optical network, is expected to be an efficient infrastructure to support advanced data-intensive grid applications. In optical grid, the faults of both computational and network resources are inevitable due to the large scale and high complexity of the system. With the optical network based distributed computing systems extensive applied in the processing of data, the requirement of the application failure probability have been an important indicator of the quality of application and an important aspect the operators consider. This paper will present a task-based analysis method of the application failure probability in optical grid. Then the failure probability of the entire application can be quantified, and the performance of reducing application failure probability in different backup strategies can be compared, so that the different requirements of different clients can be satisfied according to the application failure probability respectively. In optical grid, when the application based DAG (directed acyclic graph) is executed in different backup strategies, the application failure probability and the application complete time is different. This paper will propose new multi-objective differentiated services algorithm (MDSA). New application scheduling algorithm can guarantee the requirement of the failure probability and improve the network resource utilization, realize a compromise between the network operator and the application submission. Then differentiated services can be achieved in optical grid.
Estimating the Probability of Wind Ramping Events: A Data-driven Approach

OpenAIRE

Wang, Cheng; Wei, Wei; Wang, Jianhui; Qiu, Feng

2016-01-01

This letter proposes a data-driven method for estimating the probability of wind ramping events without exploiting the exact probability distribution function (PDF) of wind power. Actual wind data validates the proposed method.
Probability of success for phase III after exploratory biomarker analysis in phase II.

Science.gov (United States)

Götte, Heiko; Kirchner, Marietta; Sailer, Martin Oliver

2017-05-01

The probability of success or average power describes the potential of a future trial by weighting the power with a probability distribution of the treatment effect. The treatment effect estimate from a previous trial can be used to define such a distribution. During the development of targeted therapies, it is common practice to look for predictive biomarkers. The consequence is that the trial population for phase III is often selected on the basis of the most extreme result from phase II biomarker subgroup analyses. In such a case, there is a tendency to overestimate the treatment effect. We investigate whether the overestimation of the treatment effect estimate from phase II is transformed into a positive bias for the probability of success for phase III. We simulate a phase II/III development program for targeted therapies. This simulation allows to investigate selection probabilities and allows to compare the estimated with the true probability of success. We consider the estimated probability of success with and without subgroup selection. Depending on the true treatment effects, there is a negative bias without selection because of the weighting by the phase II distribution. In comparison, selection increases the estimated probability of success. Thus, selection does not lead to a bias in probability of success if underestimation due to the phase II distribution and overestimation due to selection cancel each other out. We recommend to perform similar simulations in practice to get the necessary information about the risk and chances associated with such subgroup selection designs. Copyright © 2017 John Wiley & Sons, Ltd.
The influence of initial beliefs on judgments of probability.

Science.gov (United States)

Yu, Erica C; Lagnado, David A

2012-01-01

This study aims to investigate whether experimentally induced prior beliefs affect processing of evidence including the updating of beliefs under uncertainty about the unknown probabilities of outcomes and the structural, outcome-generating nature of the environment. Participants played a gambling task in the form of computer-simulated slot machines and were given information about the slot machines' possible outcomes without their associated probabilities. One group was induced with a prior belief about the outcome space that matched the space of actual outcomes to be sampled; the other group was induced with a skewed prior belief that included the actual outcomes and also fictional higher outcomes. In reality, however, all participants sampled evidence from the same underlying outcome distribution, regardless of priors given. Before and during sampling, participants expressed their beliefs about the outcome distribution (values and probabilities). Evaluation of those subjective probability distributions suggests that all participants' judgments converged toward the observed outcome distribution. However, despite observing no supporting evidence for fictional outcomes, a significant proportion of participants in the skewed priors condition expected them in the future. A probe of the participants' understanding of the underlying outcome-generating processes indicated that participants' judgments were based on the information given in the induced priors and consequently, a significant proportion of participants in the skewed condition believed the slot machines were not games of chance while participants in the control condition believed the machines generated outcomes at random. Beyond Bayesian or heuristic belief updating, priors not only contribute to belief revision but also affect one's deeper understanding of the environment.
Optimizing Probability of Detection Point Estimate Demonstration

Science.gov (United States)

Koshti, Ajay M.

2017-01-01

Probability of detection (POD) analysis is used in assessing reliably detectable flaw size in nondestructive evaluation (NDE). MIL-HDBK-18231and associated mh18232POD software gives most common methods of POD analysis. Real flaws such as cracks and crack-like flaws are desired to be detected using these NDE methods. A reliably detectable crack size is required for safe life analysis of fracture critical parts. The paper provides discussion on optimizing probability of detection (POD) demonstration experiments using Point Estimate Method. POD Point estimate method is used by NASA for qualifying special NDE procedures. The point estimate method uses binomial distribution for probability density. Normally, a set of 29 flaws of same size within some tolerance are used in the demonstration. The optimization is performed to provide acceptable value for probability of passing demonstration (PPD) and achieving acceptable value for probability of false (POF) calls while keeping the flaw sizes in the set as small as possible.
The maximum entropy method of moments and Bayesian probability theory

Science.gov (United States)

Bretthorst, G. Larry

2013-08-01

The problem of density estimation occurs in many disciplines. For example, in MRI it is often necessary to classify the types of tissues in an image. To perform this classification one must first identify the characteristics of the tissues to be classified. These characteristics might be the intensity of a T1 weighted image and in MRI many other types of characteristic weightings (classifiers) may be generated. In a given tissue type there is no single intensity that characterizes the tissue, rather there is a distribution of intensities. Often this distributions can be characterized by a Gaussian, but just as often it is much more complicated. Either way, estimating the distribution of intensities is an inference problem. In the case of a Gaussian distribution, one must estimate the mean and standard deviation. However, in the Non-Gaussian case the shape of the density function itself must be inferred. Three common techniques for estimating density functions are binned histograms [1, 2], kernel density estimation [3, 4], and the maximum entropy method of moments [5, 6]. In the introduction, the maximum entropy method of moments will be reviewed. Some of its problems and conditions under which it fails will be discussed. Then in later sections, the functional form of the maximum entropy method of moments probability distribution will be incorporated into Bayesian probability theory. It will be shown that Bayesian probability theory solves all of the problems with the maximum entropy method of moments. One gets posterior probabilities for the Lagrange multipliers, and, finally, one can put error bars on the resulting estimated density function.
Probabilistic Cloning of Three Real States with Optimal Success Probabilities

Science.gov (United States)

Rui, Pin-shu

2017-06-01

We investigate the probabilistic quantum cloning (PQC) of three real states with average probability distribution. To get the analytic forms of the optimal success probabilities we assume that the three states have only two pairwise inner products. Based on the optimal success probabilities, we derive the explicit form of 1 →2 PQC for cloning three real states. The unitary operation needed in the PQC process is worked out too. The optimal success probabilities are also generalized to the M→ N PQC case.
Binomial probability distribution model-based protein identification algorithm for tandem mass spectrometry utilizing peak intensity information.

Science.gov (United States)

Xiao, Chuan-Le; Chen, Xiao-Zhou; Du, Yang-Li; Sun, Xuesong; Zhang, Gong; He, Qing-Yu

2013-01-04

Mass spectrometry has become one of the most important technologies in proteomic analysis. Tandem mass spectrometry (LC-MS/MS) is a major tool for the analysis of peptide mixtures from protein samples. The key step of MS data processing is the identification of peptides from experimental spectra by searching public sequence databases. Although a number of algorithms to identify peptides from MS/MS data have been already proposed, e.g. Sequest, OMSSA, X!Tandem, Mascot, etc., they are mainly based on statistical models considering only peak-matches between experimental and theoretical spectra, but not peak intensity information. Moreover, different algorithms gave different results from the same MS data, implying their probable incompleteness and questionable reproducibility. We developed a novel peptide identification algorithm, ProVerB, based on a binomial probability distribution model of protein tandem mass spectrometry combined with a new scoring function, making full use of peak intensity information and, thus, enhancing the ability of identification. Compared with Mascot, Sequest, and SQID, ProVerB identified significantly more peptides from LC-MS/MS data sets than the current algorithms at 1% False Discovery Rate (FDR) and provided more confident peptide identifications. ProVerB is also compatible with various platforms and experimental data sets, showing its robustness and versatility. The open-source program ProVerB is available at http://bioinformatics.jnu.edu.cn/software/proverb/ .
The transition probability and the probability for the left-most particle's position of the q-totally asymmetric zero range process

Energy Technology Data Exchange (ETDEWEB)

Korhonen, Marko [Department of Mathematics and Statistics, University of Helsinki, FIN-00014 (Finland); Lee, Eunghyun [Centre de Recherches Mathématiques (CRM), Université de Montréal, Quebec H3C 3J7 (Canada)

2014-01-15

We treat the N-particle zero range process whose jumping rates satisfy a certain condition. This condition is required to use the Bethe ansatz and the resulting model is the q-boson model by Sasamoto and Wadati [“Exact results for one-dimensional totally asymmetric diffusion models,” J. Phys. A 31, 6057–6071 (1998)] or the q-totally asymmetric zero range process (TAZRP) by Borodin and Corwin [“Macdonald processes,” Probab. Theory Relat. Fields (to be published)]. We find the explicit formula of the transition probability of the q-TAZRP via the Bethe ansatz. By using the transition probability we find the probability distribution of the left-most particle's position at time t. To find the probability for the left-most particle's position we find a new identity corresponding to identity for the asymmetric simple exclusion process by Tracy and Widom [“Integral formulas for the asymmetric simple exclusion process,” Commun. Math. Phys. 279, 815–844 (2008)]. For the initial state that all particles occupy a single site, the probability distribution of the left-most particle's position at time t is represented by the contour integral of a determinant.
Probability theory a foundational course

CERN Document Server

Pakshirajan, R P

2013-01-01

This book shares the dictum of J. L. Doob in treating Probability Theory as a branch of Measure Theory and establishes this relation early. Probability measures in product spaces are introduced right at the start by way of laying the ground work to later claim the existence of stochastic processes with prescribed finite dimensional distributions. Other topics analysed in the book include supports of probability measures, zero-one laws in product measure spaces, Erdos-Kac invariance principle, functional central limit theorem and functional law of the iterated logarithm for independent variables, Skorohod embedding, and the use of analytic functions of a complex variable in the study of geometric ergodicity in Markov chains. This book is offered as a text book for students pursuing graduate programs in Mathematics and or Statistics. The book aims to help the teacher present the theory with ease, and to help the student sustain his interest and joy in learning the subject.
Modified Stieltjes Transform and Generalized Convolutions of Probability Distributions

Directory of Open Access Journals (Sweden)

Lev B. Klebanov

2018-01-01

Full Text Available The classical Stieltjes transform is modified in such a way as to generalize both Stieltjes and Fourier transforms. This transform allows the introduction of new classes of commutative and non-commutative generalized convolutions. A particular case of such a convolution for degenerate distributions appears to be the Wigner semicircle distribution.

Representing Uncertainty by Probability and Possibility

DEFF Research Database (Denmark)

of uncertain parameters. Monte Carlo simulation is readily used for practical calculations. However, an alternative approach is offered by possibility theory making use of possibility distributions such as intervals and fuzzy intervals. This approach is well suited to represent lack of knowledge or imprecision......Uncertain parameters in modeling are usually represented by probability distributions reflecting either the objective uncertainty of the parameters or the subjective belief held by the model builder. This approach is particularly suited for representing the statistical nature or variance...
Percentile estimation using the normal and lognormal probability distribution

International Nuclear Information System (INIS)

Bement, T.R.

1980-01-01

Implicitly or explicitly percentile estimation is an important aspect of the analysis of aerial radiometric survey data. Standard deviation maps are produced for quadrangles which are surveyed as part of the National Uranium Resource Evaluation. These maps show where variables differ from their mean values by more than one, two or three standard deviations. Data may or may not be log-transformed prior to analysis. These maps have specific percentile interpretations only when proper distributional assumptions are met. Monte Carlo results are presented in this paper which show the consequences of estimating percentiles by: (1) assuming normality when the data are really from a lognormal distribution; and (2) assuming lognormality when the data are really from a normal distribution
Effect of optimum stratification on sampling with varying probabilities under proportional allocation

Directory of Open Access Journals (Sweden)

Syed Ejaz Husain Rizvi

2007-10-01

Full Text Available The problem of optimum stratification on an auxiliary variable when the units from different strata are selected with probability proportional to the value of auxiliary variable (PPSWR was considered by Singh (1975 for univariate case. In this paper we have extended the same problem, for proportional allocation, when two variates are under study. A cum. 3 R3(x rule for obtaining approximately optimum strata boundaries has been provided. It has been shown theoretically as well as empirically that the use of stratification has inverse effect on the relative efficiency of PPSWR as compared to unstratified PPSWR method when proportional method of allocation is envisaged. Further comparison showed that with increase in number of strata the stratified simple random sampling is equally efficient as PPSWR.
Bayesian estimation of core-melt probability

International Nuclear Information System (INIS)

Lewis, H.W.

1984-01-01

A very simple application of the canonical Bayesian algorithm is made to the problem of estimation of the probability of core melt in a commercial power reactor. An approximation to the results of the Rasmussen study on reactor safety is used as the prior distribution, and the observation that there has been no core melt yet is used as the single experiment. The result is a substantial decrease in the mean probability of core melt--factors of 2 to 4 for reasonable choices of parameters. The purpose is to illustrate the procedure, not to argue for the decrease
Generalized Probability-Probability Plots

NARCIS (Netherlands)

Mushkudiani, N.A.; Einmahl, J.H.J.

2004-01-01

We introduce generalized Probability-Probability (P-P) plots in order to study the one-sample goodness-of-fit problem and the two-sample problem, for real valued data.These plots, that are constructed by indexing with the class of closed intervals, globally preserve the properties of classical P-P
Quantum Probabilities as Behavioral Probabilities

Directory of Open Access Journals (Sweden)

Vyacheslav I. Yukalov

2017-03-01

Full Text Available We demonstrate that behavioral probabilities of human decision makers share many common features with quantum probabilities. This does not imply that humans are some quantum objects, but just shows that the mathematics of quantum theory is applicable to the description of human decision making. The applicability of quantum rules for describing decision making is connected with the nontrivial process of making decisions in the case of composite prospects under uncertainty. Such a process involves deliberations of a decision maker when making a choice. In addition to the evaluation of the utilities of considered prospects, real decision makers also appreciate their respective attractiveness. Therefore, human choice is not based solely on the utility of prospects, but includes the necessity of resolving the utility-attraction duality. In order to justify that human consciousness really functions similarly to the rules of quantum theory, we develop an approach defining human behavioral probabilities as the probabilities determined by quantum rules. We show that quantum behavioral probabilities of humans do not merely explain qualitatively how human decisions are made, but they predict quantitative values of the behavioral probabilities. Analyzing a large set of empirical data, we find good quantitative agreement between theoretical predictions and observed experimental data.
Contributions to quantum probability

International Nuclear Information System (INIS)

Fritz, Tobias

2010-01-01

Chapter 1: On the existence of quantum representations for two dichotomic measurements. Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum system with trivial dynamics. The solution uses methods from the theory of operator algebras and the theory of moment problems. The ensuing conditions reveal surprisingly simple relations between certain quantum-mechanical probabilities. It also shown that generally, none of these relations holds in general probabilistic models. This result might facilitate further experimental discrimination between quantum mechanics and other general probabilistic theories. Chapter 2: Possibilistic Physics. I try to outline a framework for fundamental physics where the concept of probability gets replaced by the concept of possibility. Whereas a probabilistic theory assigns a state-dependent probability value to each outcome of each measurement, a possibilistic theory merely assigns one of the state-dependent labels ''possible to occur'' or ''impossible to occur'' to each outcome of each measurement. It is argued that Spekkens' combinatorial toy theory of quantum mechanics is inconsistent in a probabilistic framework, but can be regarded as possibilistic. Then, I introduce the concept of possibilistic local hidden variable models and derive a class of possibilistic Bell inequalities which are violated for the possibilistic Popescu-Rohrlich boxes. The chapter ends with a philosophical discussion on possibilistic vs. probabilistic. It can be argued that, due to better falsifiability properties, a possibilistic theory has higher predictive power than a probabilistic one. Chapter 3: The quantum region for von Neumann measurements with postselection. It is determined under which conditions a probability distribution on a finite set can occur as the outcome
The probability of a tornado missile hitting a target

International Nuclear Information System (INIS)

Goodman, J.; Koch, J.E.

1983-01-01

It is shown that tornado missile transportation is a diffusion Markovian process. Therefore, the Green's function method is applied for the estimation of the probability of hitting a unit target area. This propability is expressed through a joint density of tornado intensity and path area, a probability of tornado missile injection and a tornado missile height distribution. (orig.)
Reliability Implications in Wood Systems of a Bivariate Gaussian-Weibull Distribution and the Associated Univariate Pseudo-truncated Weibull

Science.gov (United States)

Steve P. Verrill; James W. Evans; David E. Kretschmann; Cherilyn A. Hatfield

2014-01-01

Two important wood properties are the modulus of elasticity (MOE) and the modulus of rupture (MOR). In the past, the statistical distribution of the MOE has often been modeled as Gaussian, and that of the MOR as lognormal or as a two- or three-parameter Weibull distribution. It is well known that MOE and MOR are positively correlated. To model the simultaneous behavior...
Probability Aggregates in Probability Answer Set Programming

OpenAIRE

Saad, Emad

2013-01-01

Probability answer set programming is a declarative programming that has been shown effective for representing and reasoning about a variety of probability reasoning tasks. However, the lack of probability aggregates, e.g. {\\em expected values}, in the language of disjunctive hybrid probability logic programs (DHPP) disallows the natural and concise representation of many interesting problems. In this paper, we extend DHPP to allow arbitrary probability aggregates. We introduce two types of p...
Clan structure analysis and rapidity gap probability

International Nuclear Information System (INIS)

Lupia, S.; Giovannini, A.; Ugoccioni, R.

1995-01-01

Clan structure analysis in rapidity intervals is generalized from negative binomial multiplicity distribution to the wide class of compound Poisson distributions. The link of generalized clan structure analysis with correlation functions is also established. These theoretical results are then applied to minimum bias events and evidentiate new interesting features, which can be inspiring and useful in order to discuss data on rapidity gap probability at TEVATRON and HERA. (orig.)
Clan structure analysis and rapidity gap probability

Energy Technology Data Exchange (ETDEWEB)

Lupia, S. [Turin Univ. (Italy). Ist. di Fisica Teorica]|[Istituto Nazionale di Fisica Nucleare, Turin (Italy); Giovannini, A. [Turin Univ. (Italy). Ist. di Fisica Teorica]|[Istituto Nazionale di Fisica Nucleare, Turin (Italy); Ugoccioni, R. [Turin Univ. (Italy). Ist. di Fisica Teorica]|[Istituto Nazionale di Fisica Nucleare, Turin (Italy)

1995-03-01

Clan structure analysis in rapidity intervals is generalized from negative binomial multiplicity distribution to the wide class of compound Poisson distributions. The link of generalized clan structure analysis with correlation functions is also established. These theoretical results are then applied to minimum bias events and evidentiate new interesting features, which can be inspiring and useful in order to discuss data on rapidity gap probability at TEVATRON and HERA. (orig.)
A bioinformatic survey of distribution, conservation, and probable functions of LuxR solo regulators in bacteria

Science.gov (United States)

Subramoni, Sujatha; Florez Salcedo, Diana Vanessa; Suarez-Moreno, Zulma R.

2015-01-01

LuxR solo transcriptional regulators contain both an autoinducer binding domain (ABD; N-terminal) and a DNA binding Helix-Turn-Helix domain (HTH; C-terminal), but are not associated with a cognate N-acyl homoserine lactone (AHL) synthase coding gene in the same genome. Although a few LuxR solos have been characterized, their distributions as well as their role in bacterial signal perception and other processes are poorly understood. In this study we have carried out a systematic survey of distribution of all ABD containing LuxR transcriptional regulators (QS domain LuxRs) available in the InterPro database (IPR005143), and identified those lacking a cognate AHL synthase. These LuxR solos were then analyzed regarding their taxonomical distribution, predicted functions of neighboring genes and the presence of complete AHL-QS systems in the genomes that carry them. Our analyses reveal the presence of one or multiple predicted LuxR solos in many proteobacterial genomes carrying QS domain LuxRs, some of them harboring genes for one or more AHL-QS circuits. The presence of LuxR solos in bacteria occupying diverse environments suggests potential ecological functions for these proteins beyond AHL and interkingdom signaling. Based on gene context and the conservation levels of invariant amino acids of ABD, we have classified LuxR solos into functionally meaningful groups or putative orthologs. Surprisingly, putative LuxR solos were also found in a few non-proteobacterial genomes which are not known to carry AHL-QS systems. Multiple predicted LuxR solos in the same genome appeared to have different levels of conservation of invariant amino acid residues of ABD questioning their binding to AHLs. In summary, this study provides a detailed overview of distribution of LuxR solos and their probable roles in bacteria with genome sequence information. PMID:25759807
A bioinformatic survey of distribution, conservation, and probable functions of LuxR solo regulators in bacteria.

Science.gov (United States)

Subramoni, Sujatha; Florez Salcedo, Diana Vanessa; Suarez-Moreno, Zulma R

2015-01-01

LuxR solo transcriptional regulators contain both an autoinducer binding domain (ABD; N-terminal) and a DNA binding Helix-Turn-Helix domain (HTH; C-terminal), but are not associated with a cognate N-acyl homoserine lactone (AHL) synthase coding gene in the same genome. Although a few LuxR solos have been characterized, their distributions as well as their role in bacterial signal perception and other processes are poorly understood. In this study we have carried out a systematic survey of distribution of all ABD containing LuxR transcriptional regulators (QS domain LuxRs) available in the InterPro database (IPR005143), and identified those lacking a cognate AHL synthase. These LuxR solos were then analyzed regarding their taxonomical distribution, predicted functions of neighboring genes and the presence of complete AHL-QS systems in the genomes that carry them. Our analyses reveal the presence of one or multiple predicted LuxR solos in many proteobacterial genomes carrying QS domain LuxRs, some of them harboring genes for one or more AHL-QS circuits. The presence of LuxR solos in bacteria occupying diverse environments suggests potential ecological functions for these proteins beyond AHL and interkingdom signaling. Based on gene context and the conservation levels of invariant amino acids of ABD, we have classified LuxR solos into functionally meaningful groups or putative orthologs. Surprisingly, putative LuxR solos were also found in a few non-proteobacterial genomes which are not known to carry AHL-QS systems. Multiple predicted LuxR solos in the same genome appeared to have different levels of conservation of invariant amino acid residues of ABD questioning their binding to AHLs. In summary, this study provides a detailed overview of distribution of LuxR solos and their probable roles in bacteria with genome sequence information.
A bioinformatic survey of distribution, conservation and probable functions of LuxR solo regulators in bacteria

Directory of Open Access Journals (Sweden)

Sujatha eSubramoni

2015-02-01

Full Text Available LuxR solo transcriptional regulators contain both an autoinducer binding domain (ABD; N-terminal and a DNA binding Helix-Turn-Helix domain (HTH; C-terminal, but are not associated with a cognate N-acyl homoserine lactone (AHL synthase coding gene in the same genome. Although a few LuxR solos have been characterized, their distributions as well as their role in bacterial signal perception and other processes are poorly understood. In this study we have carried out a systematic survey of distribution of all ABD containing LuxR transcriptional regulators (QS domain LuxRs available in the InterPro database (IPR005143, and identified those lacking a cognate AHL synthase. These LuxR solos were then analyzed regarding their taxonomical distribution, predicted functions of neighboring genes and the presence of complete AHL-QS systems in the genomes that carry them. Our analyses reveal the presence of one or multiple predicted LuxR solos in many proteobacterial genomes carrying QS domain LuxRs, some of them harboring genes for one or more AHL-QS circuits. The presence of LuxR solos in bacteria occupying diverse environments suggests potential ecological functions for these proteins beyond AHL and interkingdom signaling. Based on gene context and the conservation levels of invariant amino acids of ABD, we have classified LuxR solos into functionally meaningful groups or putative orthologs. Surprisingly, putative LuxR solos were also found in a few non-proteobacterial genomes which are not known to carry AHL-QS systems. Multiple predicted LuxR solos in the same genome appeared to have different levels of conservation of invariant amino acid residues of ABD questioning their binding to AHLs. In summary, this study provides a detailed overview of distribution of LuxR solos and their probable roles in bacteria with genome sequence information.
Some explicit expressions for the probability distribution of force ...

Indian Academy of Sciences (India)

96: Art. No. 098001. Tighe B P, Socolar J E S, Schaeffer D G, Mitchener W G, Huber M L 2005 Force distributions in a triangular lattice of rigid bars. Phys. Rev. E 72: Art. No. 031306. Vargas W L, Murcia J C, Palacio L E, Dominguez D M 2003 Fractional diffusion model for force distribution in static granular media. Phys. Rev.
Trend and forecasting rate of cancer deaths at a public university hospital using univariate modeling

Science.gov (United States)

Ismail, A.; Hassan, Noor I.

2013-09-01

Cancer is one of the principal causes of death in Malaysia. This study was performed to determine the pattern of rate of cancer deaths at a public hospital in Malaysia over an 11 year period from year 2001 to 2011, to determine the best fitted model of forecasting the rate of cancer deaths using Univariate Modeling and to forecast the rates for the next two years (2012 to 2013). The medical records of the death of patients with cancer admitted at this Hospital over 11 year's period were reviewed, with a total of 663 cases. The cancers were classified according to 10th Revision International Classification of Diseases (ICD-10). Data collected include socio-demographic background of patients such as registration number, age, gender, ethnicity, ward and diagnosis. Data entry and analysis was accomplished using SPSS 19.0 and Minitab 16.0. The five Univariate Models used were Naïve with Trend Model, Average Percent Change Model (ACPM), Single Exponential Smoothing, Double Exponential Smoothing and Holt's Method. The overall 11 years rate of cancer deaths showed that at this hospital, Malay patients have the highest percentage (88.10%) compared to other ethnic groups with males (51.30%) higher than females. Lung and breast cancer have the most number of cancer deaths among gender. About 29.60% of the patients who died due to cancer were aged 61 years old and above. The best Univariate Model used for forecasting the rate of cancer deaths is Single Exponential Smoothing Technique with alpha of 0.10. The forecast for the rate of cancer deaths shows a horizontally or flat value. The forecasted mortality trend remains at 6.84% from January 2012 to December 2013. All the government and private sectors and non-governmental organizations need to highlight issues on cancer especially lung and breast cancers to the public through campaigns using mass media, media electronics, posters and pamphlets in the attempt to decrease the rate of cancer deaths in Malaysia.
Probability distributions in risk management operations

CERN Document Server

Artikis, Constantinos

2015-01-01

This book is about the formulations, theoretical investigations, and practical applications of new stochastic models for fundamental concepts and operations of the discipline of risk management. It also examines how these models can be useful in the descriptions, measurements, evaluations, and treatments of risks threatening various modern organizations. Moreover, the book makes clear that such stochastic models constitute very strong analytical tools which substantially facilitate strategic thinking and strategic decision making in many significant areas of risk management. In particular the incorporation of fundamental probabilistic concepts such as the sum, minimum, and maximum of a random number of continuous, positive, independent, and identically distributed random variables in the mathematical structure of stochastic models significantly supports the suitability of these models in the developments, investigations, selections, and implementations of proactive and reactive risk management operations. The...
Probability shapes perceptual precision: A study in orientation estimation.

Science.gov (United States)

Jabar, Syaheed B; Anderson, Britt

2015-12-01

Probability is known to affect perceptual estimations, but an understanding of mechanisms is lacking. Moving beyond binary classification tasks, we had naive participants report the orientation of briefly viewed gratings where we systematically manipulated contingent probability. Participants rapidly developed faster and more precise estimations for high-probability tilts. The shapes of their error distributions, as indexed by a kurtosis measure, also showed a distortion from Gaussian. This kurtosis metric was robust, capturing probability effects that were graded, contextual, and varying as a function of stimulus orientation. Our data can be understood as a probability-induced reduction in the variability or "shape" of estimation errors, as would be expected if probability affects the perceptual representations. As probability manipulations are an implicit component of many endogenous cuing paradigms, changes at the perceptual level could account for changes in performance that might have traditionally been ascribed to "attention." (c) 2015 APA, all rights reserved).
On the Efficient Simulation of the Distribution of the Sum of Gamma-Gamma Variates with Application to the Outage Probability Evaluation Over Fading Channels

KAUST Repository

Ben Issaid, Chaouki

2016-06-01

The Gamma-Gamma distribution has recently emerged in a number of applications ranging from modeling scattering and reverbation in sonar and radar systems to modeling atmospheric turbulence in wireless optical channels. In this respect, assessing the outage probability achieved by some diversity techniques over this kind of channels is of major practical importance. In many circumstances, this is intimately related to the difficult question of analyzing the statistics of a sum of Gamma-Gamma random variables. Answering this question is not a simple matter. This is essentially because outage probabilities encountered in practice are often very small, and hence the use of classical Monte Carlo methods is not a reasonable choice. This lies behind the main motivation of the present work. In particular, this paper proposes a new approach to estimate the left tail of the sum of Gamma-Gamma variates. More specifically, we propose a mean-shift importance sampling scheme that efficiently evaluates the outage probability of L-branch maximum ratio combining diversity receivers over Gamma-Gamma fading channels. The proposed estimator satisfies the well-known bounded relative error criterion, a well-desired property characterizing the robustness of importance sampling schemes, for both identically and non-identically independent distributed cases. We show the accuracy and the efficiency of our approach compared to naive Monte Carlo via some selected numerical simulations.

On the Efficient Simulation of the Distribution of the Sum of Gamma-Gamma Variates with Application to the Outage Probability Evaluation Over Fading Channels

KAUST Repository

Ben Issaid, Chaouki; Ben Rached, Nadhir; Kammoun, Abla; Alouini, Mohamed-Slim; Tempone, Raul

2016-01-01

The Gamma-Gamma distribution has recently emerged in a number of applications ranging from modeling scattering and reverbation in sonar and radar systems to modeling atmospheric turbulence in wireless optical channels. In this respect, assessing the outage probability achieved by some diversity techniques over this kind of channels is of major practical importance. In many circumstances, this is intimately related to the difficult question of analyzing the statistics of a sum of Gamma-Gamma random variables. Answering this question is not a simple matter. This is essentially because outage probabilities encountered in practice are often very small, and hence the use of classical Monte Carlo methods is not a reasonable choice. This lies behind the main motivation of the present work. In particular, this paper proposes a new approach to estimate the left tail of the sum of Gamma-Gamma variates. More specifically, we propose a mean-shift importance sampling scheme that efficiently evaluates the outage probability of L-branch maximum ratio combining diversity receivers over Gamma-Gamma fading channels. The proposed estimator satisfies the well-known bounded relative error criterion, a well-desired property characterizing the robustness of importance sampling schemes, for both identically and non-identically independent distributed cases. We show the accuracy and the efficiency of our approach compared to naive Monte Carlo via some selected numerical simulations.
A hydroclimatological approach to predicting regional landslide probability using Landlab

Directory of Open Access Journals (Sweden)

R. Strauch

2018-02-01

Full Text Available We develop a hydroclimatological approach to the modeling of regional shallow landslide initiation that integrates spatial and temporal dimensions of parameter uncertainty to estimate an annual probability of landslide initiation based on Monte Carlo simulations. The physically based model couples the infinite-slope stability model with a steady-state subsurface flow representation and operates in a digital elevation model. Spatially distributed gridded data for soil properties and vegetation classification are used for parameter estimation of probability distributions that characterize model input uncertainty. Hydrologic forcing to the model is through annual maximum daily recharge to subsurface flow obtained from a macroscale hydrologic model. We demonstrate the model in a steep mountainous region in northern Washington, USA, over 2700 km2. The influence of soil depth on the probability of landslide initiation is investigated through comparisons among model output produced using three different soil depth scenarios reflecting the uncertainty of soil depth and its potential long-term variability. We found elevation-dependent patterns in probability of landslide initiation that showed the stabilizing effects of forests at low elevations, an increased landslide probability with forest decline at mid-elevations (1400 to 2400 m, and soil limitation and steep topographic controls at high alpine elevations and in post-glacial landscapes. These dominant controls manifest themselves in a bimodal distribution of spatial annual landslide probability. Model testing with limited observations revealed similarly moderate model confidence for the three hazard maps, suggesting suitable use as relative hazard products. The model is available as a component in Landlab, an open-source, Python-based landscape earth systems modeling environment, and is designed to be easily reproduced utilizing HydroShare cyberinfrastructure.
A hydroclimatological approach to predicting regional landslide probability using Landlab

Science.gov (United States)

Strauch, Ronda; Istanbulluoglu, Erkan; Nudurupati, Sai Siddhartha; Bandaragoda, Christina; Gasparini, Nicole M.; Tucker, Gregory E.

2018-02-01

We develop a hydroclimatological approach to the modeling of regional shallow landslide initiation that integrates spatial and temporal dimensions of parameter uncertainty to estimate an annual probability of landslide initiation based on Monte Carlo simulations. The physically based model couples the infinite-slope stability model with a steady-state subsurface flow representation and operates in a digital elevation model. Spatially distributed gridded data for soil properties and vegetation classification are used for parameter estimation of probability distributions that characterize model input uncertainty. Hydrologic forcing to the model is through annual maximum daily recharge to subsurface flow obtained from a macroscale hydrologic model. We demonstrate the model in a steep mountainous region in northern Washington, USA, over 2700 km2. The influence of soil depth on the probability of landslide initiation is investigated through comparisons among model output produced using three different soil depth scenarios reflecting the uncertainty of soil depth and its potential long-term variability. We found elevation-dependent patterns in probability of landslide initiation that showed the stabilizing effects of forests at low elevations, an increased landslide probability with forest decline at mid-elevations (1400 to 2400 m), and soil limitation and steep topographic controls at high alpine elevations and in post-glacial landscapes. These dominant controls manifest themselves in a bimodal distribution of spatial annual landslide probability. Model testing with limited observations revealed similarly moderate model confidence for the three hazard maps, suggesting suitable use as relative hazard products. The model is available as a component in Landlab, an open-source, Python-based landscape earth systems modeling environment, and is designed to be easily reproduced utilizing HydroShare cyberinfrastructure.
Predicting binary choices from probability phrase meanings.

Science.gov (United States)

Wallsten, Thomas S; Jang, Yoonhee

2008-08-01

The issues of how individuals decide which of two events is more likely and of how they understand probability phrases both involve judging relative likelihoods. In this study, we investigated whether derived scales representing probability phrase meanings could be used within a choice model to predict independently observed binary choices. If they can, this simultaneously provides support for our model and suggests that the phrase meanings are measured meaningfully. The model assumes that, when deciding which of two events is more likely, judges take a single sample from memory regarding each event and respond accordingly. The model predicts choice probabilities by using the scaled meanings of individually selected probability phrases as proxies for confidence distributions associated with sampling from memory. Predictions are sustained for 34 of 41 participants but, nevertheless, are biased slightly low. Sequential sampling models improve the fit. The results have both theoretical and applied implications.
The effect of fog on the probability density distribution of the ranging data of imaging laser radar

Directory of Open Access Journals (Sweden)

Wenhua Song

2018-02-01

Full Text Available This paper outlines theoretically investigations of the probability density distribution (PDD of ranging data for the imaging laser radar (ILR system operating at a wavelength of 905 nm under the fog condition. Based on the physical model of the reflected laser pulses from a standard Lambertian target, a theoretical approximate model of PDD of the ranging data is developed under different fog concentrations, which offer improved precision target ranging and imaging. An experimental test bed for the ILR system is developed and its performance is evaluated using a dedicated indoor atmospheric chamber under homogeneously controlled fog conditions. We show that the measured results are in good agreement with both the accurate and approximate models within a given margin of error of less than 1%.
The effect of fog on the probability density distribution of the ranging data of imaging laser radar

Science.gov (United States)

Song, Wenhua; Lai, JianCheng; Ghassemlooy, Zabih; Gu, Zhiyong; Yan, Wei; Wang, Chunyong; Li, Zhenhua

2018-02-01

This paper outlines theoretically investigations of the probability density distribution (PDD) of ranging data for the imaging laser radar (ILR) system operating at a wavelength of 905 nm under the fog condition. Based on the physical model of the reflected laser pulses from a standard Lambertian target, a theoretical approximate model of PDD of the ranging data is developed under different fog concentrations, which offer improved precision target ranging and imaging. An experimental test bed for the ILR system is developed and its performance is evaluated using a dedicated indoor atmospheric chamber under homogeneously controlled fog conditions. We show that the measured results are in good agreement with both the accurate and approximate models within a given margin of error of less than 1%.
An analytic approach to probability tables for the unresolved resonance region

Science.gov (United States)

Brown, David; Kawano, Toshihiko

2017-09-01

The Unresolved Resonance Region (URR) connects the fast neutron region with the Resolved Resonance Region (RRR). The URR is problematic since resonances are not resolvable experimentally yet the fluctuations in the neutron cross sections play a discernible and technologically important role: the URR in a typical nucleus is in the 100 keV - 2 MeV window where the typical fission spectrum peaks. The URR also represents the transition between R-matrix theory used to described isolated resonances and Hauser-Feshbach theory which accurately describes the average cross sections. In practice, only average or systematic features of the resonances in the URR are known and are tabulated in evaluations in a nuclear data library such as ENDF/B-VII.1. Codes such as AMPX and NJOY can compute the probability distribution of the cross section in the URR under some assumptions using Monte Carlo realizations of sets of resonances. These probability distributions are stored in the so-called PURR tables. In our work, we begin to develop a scheme for computing the covariance of the cross section probability distribution analytically. Our approach offers the possibility of defining the limits of applicability of Hauser-Feshbach theory and suggests a way to calculate PURR tables directly from systematics for nuclei whose RRR is unknown, provided one makes appropriate assumptions about the shape of the cross section probability distribution.
Dynamic SEP event probability forecasts

Science.gov (United States)

Kahler, S. W.; Ling, A.

2015-10-01

The forecasting of solar energetic particle (SEP) event probabilities at Earth has been based primarily on the estimates of magnetic free energy in active regions and on the observations of peak fluxes and fluences of large (≥ M2) solar X-ray flares. These forecasts are typically issued for the next 24 h or with no definite expiration time, which can be deficient for time-critical operations when no SEP event appears following a large X-ray flare. It is therefore important to decrease the event probability forecast with time as a SEP event fails to appear. We use the NOAA listing of major (≥10 pfu) SEP events from 1976 to 2014 to plot the delay times from X-ray peaks to SEP threshold onsets as a function of solar source longitude. An algorithm is derived to decrease the SEP event probabilities with time when no event is observed to reach the 10 pfu threshold. In addition, we use known SEP event size distributions to modify probability forecasts when SEP intensity increases occur below the 10 pfu event threshold. An algorithm to provide a dynamic SEP event forecast, Pd, for both situations of SEP intensities following a large flare is derived.
Maximum likelihood estimation of phase-type distributions

DEFF Research Database (Denmark)

Esparza, Luz Judith R

for both univariate and multivariate cases. Methods like the EM algorithm and Markov chain Monte Carlo are applied for this purpose. Furthermore, this thesis provides explicit formulae for computing the Fisher information matrix for discrete and continuous phase-type distributions, which is needed to find......This work is concerned with the statistical inference of phase-type distributions and the analysis of distributions with rational Laplace transform, known as matrix-exponential distributions. The thesis is focused on the estimation of the maximum likelihood parameters of phase-type distributions...... confidence regions for their estimated parameters. Finally, a new general class of distributions, called bilateral matrix-exponential distributions, is defined. These distributions have the entire real line as domain and can be used, for instance, for modelling. In addition, this class of distributions...
Single Trial Probability Applications: Can Subjectivity Evade Frequency Limitations?

Directory of Open Access Journals (Sweden)

David Howden

2009-10-01

Full Text Available Frequency probability theorists define an event’s probability distribution as the limit of a repeated set of trials belonging to a homogeneous collective. The subsets of this collective are events which we have deficient knowledge about on an individual level, although for the larger collective we have knowledge its aggregate behavior. Hence, probabilities can only be achieved through repeated trials of these subsets arriving at the established frequencies that define the probabilities. Crovelli (2009 argues that this is a mistaken approach, and that a subjective assessment of individual trials should be used instead. Bifurcating between the two concepts of risk and uncertainty, Crovelli first asserts that probability is the tool used to manage uncertain situations, and then attempts to rebuild a definition of probability theory with this in mind. We show that such an attempt has little to gain, and results in an indeterminate application of entrepreneurial forecasting to uncertain decisions—a process far-removed from any application of probability theory.
A Case Series of the Probability Density and Cumulative Distribution of Laryngeal Disease in a Tertiary Care Voice Center.

Science.gov (United States)

de la Fuente, Jaime; Garrett, C Gaelyn; Ossoff, Robert; Vinson, Kim; Francis, David O; Gelbard, Alexander

2017-11-01

To examine the distribution of clinic and operative pathology in a tertiary care laryngology practice. Probability density and cumulative distribution analyses (Pareto analysis) was used to rank order laryngeal conditions seen in an outpatient tertiary care laryngology practice and those requiring surgical intervention during a 3-year period. Among 3783 new clinic consultations and 1380 operative procedures, voice disorders were the most common primary diagnostic category seen in clinic (n = 3223), followed by airway (n = 374) and swallowing (n = 186) disorders. Within the voice strata, the most common primary ICD-9 code used was dysphonia (41%), followed by unilateral vocal fold paralysis (UVFP) (9%) and cough (7%). Among new voice patients, 45% were found to have a structural abnormality. The most common surgical indications were laryngotracheal stenosis (37%), followed by recurrent respiratory papillomatosis (18%) and UVFP (17%). Nearly 55% of patients presenting to a tertiary referral laryngology practice did not have an identifiable structural abnormality in the larynx on direct or indirect examination. The distribution of ICD-9 codes requiring surgical intervention was disparate from that seen in clinic. Application of the Pareto principle may improve resource allocation in laryngology, but these initial results require confirmation across multiple institutions.
The distribution of two medically and agriculturally important cryptic ...

African Journals Online (AJOL)

Univariate and multivariate analyses showed statistically significant differences between eco geographic characteristics of collecting localities associated with each of the two species in South Africa. The derived distributions indicate previously reported cases of plague in South Africa, to some extent, coincide with the ...
A short walk in quantum probability

Science.gov (United States)

Hudson, Robin

2018-04-01

This is a personal survey of aspects of quantum probability related to the Heisenberg commutation relation for canonical pairs. Using the failure, in general, of non-negativity of the Wigner distribution for canonical pairs to motivate a more satisfactory quantum notion of joint distribution, we visit a central limit theorem for such pairs and a resulting family of quantum planar Brownian motions which deform the classical planar Brownian motion, together with a corresponding family of quantum stochastic areas. This article is part of the themed issue `Hilbert's sixth problem'.
A short walk in quantum probability.

Science.gov (United States)

Hudson, Robin

2018-04-28

This is a personal survey of aspects of quantum probability related to the Heisenberg commutation relation for canonical pairs. Using the failure, in general, of non-negativity of the Wigner distribution for canonical pairs to motivate a more satisfactory quantum notion of joint distribution, we visit a central limit theorem for such pairs and a resulting family of quantum planar Brownian motions which deform the classical planar Brownian motion, together with a corresponding family of quantum stochastic areas.This article is part of the themed issue 'Hilbert's sixth problem'. © 2018 The Author(s).
Contributions to quantum probability

Energy Technology Data Exchange (ETDEWEB)

Fritz, Tobias

2010-06-25

Chapter 1: On the existence of quantum representations for two dichotomic measurements. Under which conditions do outcome probabilities of measurements possess a quantum-mechanical model? This kind of problem is solved here for the case of two dichotomic von Neumann measurements which can be applied repeatedly to a quantum system with trivial dynamics. The solution uses methods from the theory of operator algebras and the theory of moment problems. The ensuing conditions reveal surprisingly simple relations between certain quantum-mechanical probabilities. It also shown that generally, none of these relations holds in general probabilistic models. This result might facilitate further experimental discrimination between quantum mechanics and other general probabilistic theories. Chapter 2: Possibilistic Physics. I try to outline a framework for fundamental physics where the concept of probability gets replaced by the concept of possibility. Whereas a probabilistic theory assigns a state-dependent probability value to each outcome of each measurement, a possibilistic theory merely assigns one of the state-dependent labels ''possible to occur'' or ''impossible to occur'' to each outcome of each measurement. It is argued that Spekkens' combinatorial toy theory of quantum mechanics is inconsistent in a probabilistic framework, but can be regarded as possibilistic. Then, I introduce the concept of possibilistic local hidden variable models and derive a class of possibilistic Bell inequalities which are violated for the possibilistic Popescu-Rohrlich boxes. The chapter ends with a philosophical discussion on possibilistic vs. probabilistic. It can be argued that, due to better falsifiability properties, a possibilistic theory has higher predictive power than a probabilistic one. Chapter 3: The quantum region for von Neumann measurements with postselection. It is determined under which conditions a probability distribution on a
Computation of Probabilities in Causal Models of History of Science

Directory of Open Access Journals (Sweden)

Osvaldo Pessoa Jr.

2006-12-01

Full Text Available : The aim of this paper is to investigate the ascription of probabilities in a causal model of an episode in the history of science. The aim of such a quantitative approach is to allow the implementation of the causal model in a computer, to run simulations. As an example, we look at the beginning of the science of magnetism, “explaining” — in a probabilistic way, in terms of a single causal model — why the field advanced in China but not in Europe (the difference is due to different prior probabilities of certain cultural manifestations. Given the number of years between the occurrences of two causally connected advances X and Y, one proposes a criterion for stipulating the value pY=X of the conditional probability of an advance Y occurring, given X. Next, one must assume a specific form for the cumulative probability function pY=X(t, which we take to be the time integral of an exponential distribution function, as is done in physics of radioactive decay. Rules for calculating the cumulative functions for more than two events are mentioned, involving composition, disjunction and conjunction of causes. We also consider the problems involved in supposing that the appearance of events in time follows an exponential distribution, which are a consequence of the fact that a composition of causes does not follow an exponential distribution, but a “hypoexponential” one. We suggest that a gamma distribution function might more adequately represent the appearance of advances.
Use of probability tables for propagating uncertainties in neutronics

International Nuclear Information System (INIS)

Coste-Delclaux, M.; Diop, C.M.; Lahaye, S.

2017-01-01

Highlights: • Moment-based probability table formalism is described. • Representation by probability tables of any uncertainty distribution is established. • Multiband equations for two kinds of uncertainty propagation problems are solved. • Numerical examples are provided and validated against Monte Carlo simulations. - Abstract: Probability tables are a generic tool that allows representing any random variable whose probability density function is known. In the field of nuclear reactor physics, this tool is currently used to represent the variation of cross-sections versus energy (neutron transport codes TRIPOLI4®, MCNP, APOLLO2, APOLLO3®, ECCO/ERANOS…). In the present article we show how we can propagate uncertainties, thanks to a probability table representation, through two simple physical problems: an eigenvalue problem (neutron multiplication factor) and a depletion problem.
Updated greenhouse gas and criteria air pollutant emission factors and their probability distribution functions for electricity generating units

International Nuclear Information System (INIS)

Cai, H.; Wang, M.; Elgowainy, A.; Han, J.

2012-01-01

Greenhouse gas (CO 2 , CH 4 and N 2 O, hereinafter GHG) and criteria air pollutant (CO, NO x , VOC, PM 10 , PM 2.5 and SO x , hereinafter CAP) emission factors for various types of power plants burning various fuels with different technologies are important upstream parameters for estimating life-cycle emissions associated with alternative vehicle/fuel systems in the transportation sector, especially electric vehicles. The emission factors are typically expressed in grams of GHG or CAP per kWh of electricity generated by a specific power generation technology. This document describes our approach for updating and expanding GHG and CAP emission factors in the GREET (Greenhouse Gases, Regulated Emissions, and Energy Use in Transportation) model developed at Argonne National Laboratory (see Wang 1999 and the GREET website at http://greet.es.anl.gov/main) for various power generation technologies. These GHG and CAP emissions are used to estimate the impact of electricity use by stationary and transportation applications on their fuel-cycle emissions. The electricity generation mixes and the fuel shares attributable to various combustion technologies at the national, regional and state levels are also updated in this document. The energy conversion efficiencies of electric generating units (EGUs) by fuel type and combustion technology are calculated on the basis of the lower heating values of each fuel, to be consistent with the basis used in GREET for transportation fuels. On the basis of the updated GHG and CAP emission factors and energy efficiencies of EGUs, the probability distribution functions (PDFs), which are functions that describe the relative likelihood for the emission factors and energy efficiencies as random variables to take on a given value by the integral of their own probability distributions, are updated using best-fit statistical curves to characterize the uncertainties associated with GHG and CAP emissions in life-cycle modeling with GREET.
Negative probability in the framework of combined probability

OpenAIRE

Burgin, Mark

2013-01-01

Negative probability has found diverse applications in theoretical physics. Thus, construction of sound and rigorous mathematical foundations for negative probability is important for physics. There are different axiomatizations of conventional probability. So, it is natural that negative probability also has different axiomatic frameworks. In the previous publications (Burgin, 2009; 2010), negative probability was mathematically formalized and rigorously interpreted in the context of extende...
Reliability for some bivariate beta distributions

Directory of Open Access Journals (Sweden)

Nadarajah Saralees

2005-01-01

Full Text Available In the area of stress-strength models there has been a large amount of work as regards estimation of the reliability R=Pr( Xdistributions when X and Y are independent random variables belonging to the same univariate family. In this paper, we consider forms of R when ( X,Y follows a bivariate distribution with dependence between X and Y . In particular, we derive explicit expressions for R when the joint distribution is bivariate beta. The calculations involve the use of special functions.

Reliability for some bivariate gamma distributions

Directory of Open Access Journals (Sweden)

Nadarajah Saralees

2005-01-01

Full Text Available In the area of stress-strength models, there has been a large amount of work as regards estimation of the reliability R=Pr( Xdistributions when X and Y are independent random variables belonging to the same univariate family. In this paper, we consider forms of R when ( X,Y follows a bivariate distribution with dependence between X and Y . In particular, we derive explicit expressions for R when the joint distribution is bivariate gamma. The calculations involve the use of special functions.
A tool for simulating collision probabilities of animals with marine renewable energy devices.

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Pál Schmitt

Full Text Available The mathematical problem of establishing a collision probability distribution is often not trivial. The shape and motion of the animal as well as of the the device must be evaluated in a four-dimensional space (3D motion over time. Earlier work on wind and tidal turbines was limited to a simplified two-dimensional representation, which cannot be applied to many new structures. We present a numerical algorithm to obtain such probability distributions using transient, three-dimensional numerical simulations. The method is demonstrated using a sub-surface tidal kite as an example. Necessary pre- and post-processing of the data created by the model is explained, numerical details and potential issues and limitations in the application of resulting probability distributions are highlighted.
A tool for simulating collision probabilities of animals with marine renewable energy devices.

Science.gov (United States)

Schmitt, Pál; Culloch, Ross; Lieber, Lilian; Molander, Sverker; Hammar, Linus; Kregting, Louise

2017-01-01

The mathematical problem of establishing a collision probability distribution is often not trivial. The shape and motion of the animal as well as of the the device must be evaluated in a four-dimensional space (3D motion over time). Earlier work on wind and tidal turbines was limited to a simplified two-dimensional representation, which cannot be applied to many new structures. We present a numerical algorithm to obtain such probability distributions using transient, three-dimensional numerical simulations. The method is demonstrated using a sub-surface tidal kite as an example. Necessary pre- and post-processing of the data created by the model is explained, numerical details and potential issues and limitations in the application of resulting probability distributions are highlighted.
Probability densities and the radon variable transformation theorem

International Nuclear Information System (INIS)

Ramshaw, J.D.

1985-01-01

D. T. Gillespie recently derived a random variable transformation theorem relating to the joint probability densities of functionally dependent sets of random variables. The present author points out that the theorem can be derived as an immediate corollary of a simpler and more fundamental relation. In this relation the probability density is represented as a delta function averaged over an unspecified distribution of unspecified internal random variables. The random variable transformation is derived from this relation
Univariate and multiple linear regression analyses for 23 single nucleotide polymorphisms in 14 genes predisposing to chronic glomerular diseases and IgA nephropathy in Han Chinese.

Science.gov (United States)

Wang, Hui; Sui, Weiguo; Xue, Wen; Wu, Junyong; Chen, Jiejing; Dai, Yong

2014-09-01

Immunoglobulin A nephropathy (IgAN) is a complex trait regulated by the interaction among multiple physiologic regulatory systems and probably involving numerous genes, which leads to inconsistent findings in genetic studies. One possibility of failure to replicate some single-locus results is that the underlying genetics of IgAN nephropathy is based on multiple genes with minor effects. To learn the association between 23 single nucleotide polymorphisms (SNPs) in 14 genes predisposing to chronic glomerular diseases and IgAN in Han males, the 23 SNPs genotypes of 21 Han males were detected and analyzed with a BaiO gene chip, and their associations were analyzed with univariate analysis and multiple linear regression analysis. Analysis showed that CTLA4 rs231726 and CR2 rs1048971 revealed a significant association with IgAN. These findings support the multi-gene nature of the etiology of IgAN and propose a potential gene-gene interactive model for future studies.
Probability Judgements in Multi-Stage Problems : Experimental Evidence of Systematic Biases

NARCIS (Netherlands)

Gneezy, U.

1996-01-01

We report empirical evidence that in problems of random walk with positive drift, bounded rationality leads individuals to under-estimate the probability of success in the long run.In particular, individuals who were given the stage by stage probability distribution failed to aggregate this
Multivariate log-skew-elliptical distributions with applications to precipitation data

KAUST Repository

Marchenko, Yulia V.

2009-07-13

We introduce a family of multivariate log-skew-elliptical distributions, extending the list of multivariate distributions with positive support. We investigate their probabilistic properties such as stochastic representations, marginal and conditional distributions, and existence of moments, as well as inferential properties. We demonstrate, for example, that as for the log-t distribution, the positive moments of the log-skew-t distribution do not exist. Our emphasis is on two special cases, the log-skew-normal and log-skew-t distributions, which we use to analyze US national (univariate) and regional (multivariate) monthly precipitation data. © 2009 John Wiley & Sons, Ltd.
Multivariate log-skew-elliptical distributions with applications to precipitation data

KAUST Repository

Marchenko, Yulia V.; Genton, Marc G.

2009-01-01

We introduce a family of multivariate log-skew-elliptical distributions, extending the list of multivariate distributions with positive support. We investigate their probabilistic properties such as stochastic representations, marginal and conditional distributions, and existence of moments, as well as inferential properties. We demonstrate, for example, that as for the log-t distribution, the positive moments of the log-skew-t distribution do not exist. Our emphasis is on two special cases, the log-skew-normal and log-skew-t distributions, which we use to analyze US national (univariate) and regional (multivariate) monthly precipitation data. © 2009 John Wiley & Sons, Ltd.
Computing exact bundle compliance control charts via probability generating functions.

Science.gov (United States)

Chen, Binchao; Matis, Timothy; Benneyan, James

2016-06-01

Compliance to evidenced-base practices, individually and in 'bundles', remains an important focus of healthcare quality improvement for many clinical conditions. The exact probability distribution of composite bundle compliance measures used to develop corresponding control charts and other statistical tests is based on a fairly large convolution whose direct calculation can be computationally prohibitive. Various series expansions and other approximation approaches have been proposed, each with computational and accuracy tradeoffs, especially in the tails. This same probability distribution also arises in other important healthcare applications, such as for risk-adjusted outcomes and bed demand prediction, with the same computational difficulties. As an alternative, we use probability generating functions to rapidly obtain exact results and illustrate the improved accuracy and detection over other methods. Numerical testing across a wide range of applications demonstrates the computational efficiency and accuracy of this approach.
Error probabilities in default Bayesian hypothesis testing

NARCIS (Netherlands)

Gu, Xin; Hoijtink, Herbert; Mulder, J,

2016-01-01

This paper investigates the classical type I and type II error probabilities of default Bayes factors for a Bayesian t test. Default Bayes factors quantify the relative evidence between the null hypothesis and the unrestricted alternative hypothesis without needing to specify prior distributions for
New exponential, logarithm and q-probability in the non-extensive statistical physics

OpenAIRE

Chung, Won Sang

2013-01-01

In this paper, a new exponential and logarithm related to the non-extensive statistical physics is proposed by using the q-sum and q-product which satisfy the distributivity. And we discuss the q-mapping from an ordinary probability to q-probability. The q-entropy defined by the idea of q-probability is shown to be q-additive.
Fast Reliability Assessing Method for Distribution Network with Distributed Renewable Energy Generation

Science.gov (United States)

Chen, Fan; Huang, Shaoxiong; Ding, Jinjin; Ding, Jinjin; Gao, Bo; Xie, Yuguang; Wang, Xiaoming

2018-01-01

This paper proposes a fast reliability assessing method for distribution grid with distributed renewable energy generation. First, the Weibull distribution and the Beta distribution are used to describe the probability distribution characteristics of wind speed and solar irradiance respectively, and the models of wind farm, solar park and local load are built for reliability assessment. Then based on power system production cost simulation probability discretization and linearization power flow, a optimal power flow objected with minimum cost of conventional power generation is to be resolved. Thus a reliability assessment for distribution grid is implemented fast and accurately. The Loss Of Load Probability (LOLP) and Expected Energy Not Supplied (EENS) are selected as the reliability index, a simulation for IEEE RBTS BUS6 system in MATLAB indicates that the fast reliability assessing method calculates the reliability index much faster with the accuracy ensured when compared with Monte Carlo method.
用于统计测试概率分布生成的自动搜索方法%Automated Search Method for Statistical Test Probability Distribution Generation

Institute of Scientific and Technical Information of China (English)

周晓莹; 高建华

2013-01-01

A strategy based on automated search for probability distribution construction is proposed, which comprises the design of representation format and evaluation function for the probability distribution. Combining with simulated annealing algorithm, an indicator is defined to formalize the automated search process based on the Markov model. Experimental results show that the method effectively improves the accuracy of the automated search, which can reduce the expense of statistical test by providing the statistical test with fairly efficient test data since it successfully finds the neat-optimal probability distribution within a certain time.%提出一种基于自动搜索的概率分布生成方法,设计对概率分布的表示形式与评估函数,同时结合模拟退火算法设计基于马尔可夫模型的自动搜索过程.实验结果表明,该方法能够有效地提高自动搜索的准确性,在一定时间内成功找到接近最优的概率分布,生成高效的测试数据,同时达到降低统计测试成本的目的.
Does probability of occurrence relate to population dynamics?

Science.gov (United States)

Thuiller, Wilfried; Münkemüller, Tamara; Schiffers, Katja H; Georges, Damien; Dullinger, Stefan; Eckhart, Vincent M; Edwards, Thomas C; Gravel, Dominique; Kunstler, Georges; Merow, Cory; Moore, Kara; Piedallu, Christian; Vissault, Steve; Zimmermann, Niklaus E; Zurell, Damaris; Schurr, Frank M

2014-12-01

Hutchinson defined species' realized niche as the set of environmental conditions in which populations can persist in the presence of competitors. In terms of demography, the realized niche corresponds to the environments where the intrinsic growth rate ( r ) of populations is positive. Observed species occurrences should reflect the realized niche when additional processes like dispersal and local extinction lags do not have overwhelming effects. Despite the foundational nature of these ideas, quantitative assessments of the relationship between range-wide demographic performance and occurrence probability have not been made. This assessment is needed both to improve our conceptual understanding of species' niches and ranges and to develop reliable mechanistic models of species geographic distributions that incorporate demography and species interactions. The objective of this study is to analyse how demographic parameters (intrinsic growth rate r and carrying capacity K ) and population density ( N ) relate to occurrence probability ( P occ ). We hypothesized that these relationships vary with species' competitive ability. Demographic parameters, density, and occurrence probability were estimated for 108 tree species from four temperate forest inventory surveys (Québec, Western US, France and Switzerland). We used published information of shade tolerance as indicators of light competition strategy, assuming that high tolerance denotes high competitive capacity in stable forest environments. Interestingly, relationships between demographic parameters and occurrence probability did not vary substantially across degrees of shade tolerance and regions. Although they were influenced by the uncertainty in the estimation of the demographic parameters, we found that r was generally negatively correlated with P occ , while N, and for most regions K, was generally positively correlated with P occ . Thus, in temperate forest trees the regions of highest occurrence
Noncentral Chi-Square versus Normal Distributions in Describing the Likelihood Ratio Statistic: The Univariate Case and Its Multivariate Implication

Science.gov (United States)

Yuan, Ke-Hai

2008-01-01

In the literature of mean and covariance structure analysis, noncentral chi-square distribution is commonly used to describe the behavior of the likelihood ratio (LR) statistic under alternative hypothesis. Due to the inaccessibility of the rather technical literature for the distribution of the LR statistic, it is widely believed that the…
An analytic approach to probability tables for the unresolved resonance region

Directory of Open Access Journals (Sweden)

Brown David

2017-01-01

Full Text Available The Unresolved Resonance Region (URR connects the fast neutron region with the Resolved Resonance Region (RRR. The URR is problematic since resonances are not resolvable experimentally yet the fluctuations in the neutron cross sections play a discernible and technologically important role: the URR in a typical nucleus is in the 100 keV – 2 MeV window where the typical fission spectrum peaks. The URR also represents the transition between R-matrix theory used to described isolated resonances and Hauser-Feshbach theory which accurately describes the average cross sections. In practice, only average or systematic features of the resonances in the URR are known and are tabulated in evaluations in a nuclear data library such as ENDF/B-VII.1. Codes such as AMPX and NJOY can compute the probability distribution of the cross section in the URR under some assumptions using Monte Carlo realizations of sets of resonances. These probability distributions are stored in the so-called PURR tables. In our work, we begin to develop a scheme for computing the covariance of the cross section probability distribution analytically. Our approach offers the possibility of defining the limits of applicability of Hauser-Feshbach theory and suggests a way to calculate PURR tables directly from systematics for nuclei whose RRR is unknown, provided one makes appropriate assumptions about the shape of the cross section probability distribution.
How to model a negligible probability under the WTO sanitary and phytosanitary agreement?

Science.gov (United States)

Powell, Mark R

2013-06-01

Since the 1997 EC--Hormones decision, World Trade Organization (WTO) Dispute Settlement Panels have wrestled with the question of what constitutes a negligible risk under the Sanitary and Phytosanitary Agreement. More recently, the 2010 WTO Australia--Apples Panel focused considerable attention on the appropriate quantitative model for a negligible probability in a risk assessment. The 2006 Australian Import Risk Analysis for Apples from New Zealand translated narrative probability statements into quantitative ranges. The uncertainty about a "negligible" probability was characterized as a uniform distribution with a minimum value of zero and a maximum value of 10(-6) . The Australia - Apples Panel found that the use of this distribution would tend to overestimate the likelihood of "negligible" events and indicated that a triangular distribution with a most probable value of zero and a maximum value of 10⁻⁶ would correct the bias. The Panel observed that the midpoint of the uniform distribution is 5 × 10⁻⁷ but did not consider that the triangular distribution has an expected value of 3.3 × 10⁻⁷. Therefore, if this triangular distribution is the appropriate correction, the magnitude of the bias found by the Panel appears modest. The Panel's detailed critique of the Australian risk assessment, and the conclusions of the WTO Appellate Body about the materiality of flaws found by the Panel, may have important implications for the standard of review for risk assessments under the WTO SPS Agreement. © 2012 Society for Risk Analysis.
Univariate and multivariate forecasting of hourly solar radiation with artificial intelligence techniques

Energy Technology Data Exchange (ETDEWEB)

Sfetsos, A. [7 Pirsou Str., Athens (Greece); Coonick, A.H. [Imperial Coll. of Science Technology and Medicine, Dept. of Electrical and Electronic Engineering, London (United Kingdom)

2000-07-01

This paper introduces a new approach for the forecasting of mean hourly global solar radiation received by a horizontal surface. In addition to the traditional linear methods, several artificial-intelligence-based techniques are studied. These include linear, feed-forward, recurrent Elman and Radial Basis neural networks alongside the adaptive neuro-fuzzy inference scheme. The problem is examined initially for the univariate case, and is extended to include additional meteorological parameters in the process of estimating the optimum model. The results indicate that the developed artificial intelligence models predict the solar radiation time series more effectively compared to the conventional procedures based on the clearness index. The forecasting ability of some models can be further enhanced with the use of additional meteorological parameters. (Author)
The Effect of High Frequency Pulse on the Discharge Probability in Micro EDM

Science.gov (United States)

Liu, Y.; Qu, Y.; Zhang, W.; Ma, F.; Sha, Z.; Wang, Y.; Rolfe, B.; Zhang, S.

2017-12-01

High frequency pulse improves the machining efficiency of micro electric discharge machining (micro EDM), while it also brings some changes in micro EDM process. This paper focuses on the influence of skin-effect under the high frequency pulse on energy distribution and transmission in micro EDM, based on which, the rules of discharge probability of electrode end face are also analysed. On the basis of the electrical discharge process under the condition of high frequency pulse in micro EDM, COMSOL Multiphysics software is used to establish energy transmission model in micro electrode. The discharge energy distribution and transmission within tool electrode under different pulse frequencies, electrical currents, and permeability situation are studied in order to get the distribution pattern of current density and electric field intensity in the electrode end face under the influence of electrical parameters change. The electric field intensity distribution is regarded as the influencing parameter of discharge probability on the electrode end. Finally, MATLAB is used to fit the curve and obtain the distribution of discharge probability of electrode end face.
Ruin probability of the renewal model with risky investment and large claims

Institute of Scientific and Technical Information of China (English)

2009-01-01

The ruin probability of the renewal risk model with investment strategy for a capital market index is investigated in this paper.For claim sizes with common distribution of extended regular variation,we study the asymptotic behaviour of the ruin probability.As a corollary,we establish a simple asymptotic formula for the ruin probability for the case of Pareto-like claims.

Generalized Probability Functions

Directory of Open Access Journals (Sweden)

Alexandre Souto Martinez

2009-01-01

Full Text Available From the integration of nonsymmetrical hyperboles, a one-parameter generalization of the logarithmic function is obtained. Inverting this function, one obtains the generalized exponential function. Motivated by the mathematical curiosity, we show that these generalized functions are suitable to generalize some probability density functions (pdfs. A very reliable rank distribution can be conveniently described by the generalized exponential function. Finally, we turn the attention to the generalization of one- and two-tail stretched exponential functions. We obtain, as particular cases, the generalized error function, the Zipf-Mandelbrot pdf, the generalized Gaussian and Laplace pdf. Their cumulative functions and moments were also obtained analytically.
A Balanced Approach to Adaptive Probability Density Estimation

Directory of Open Access Journals (Sweden)

Julio A. Kovacs

2017-04-01

Full Text Available Our development of a Fast (Mutual Information Matching (FIM of molecular dynamics time series data led us to the general problem of how to accurately estimate the probability density function of a random variable, especially in cases of very uneven samples. Here, we propose a novel Balanced Adaptive Density Estimation (BADE method that effectively optimizes the amount of smoothing at each point. To do this, BADE relies on an efficient nearest-neighbor search which results in good scaling for large data sizes. Our tests on simulated data show that BADE exhibits equal or better accuracy than existing methods, and visual tests on univariate and bivariate experimental data show that the results are also aesthetically pleasing. This is due in part to the use of a visual criterion for setting the smoothing level of the density estimate. Our results suggest that BADE offers an attractive new take on the fundamental density estimation problem in statistics. We have applied it on molecular dynamics simulations of membrane pore formation. We also expect BADE to be generally useful for low-dimensional applications in other statistical application domains such as bioinformatics, signal processing and econometrics.
Theoretical analysis on the probability of initiating persistent fission chain

International Nuclear Information System (INIS)

Liu Jianjun; Wang Zhe; Zhang Ben'ai

2005-01-01

For the finite multiplying system of fissile material in the presence of a weak neutron source, the authors analyses problems on the probability of initiating a persistent fission chain through reckoning the stochastic theory of neutron multiplication. In the theoretical treatment, the conventional point reactor conception model is developed to an improved form with position x and velocity v dependence. The estimated results including approximate value of the probability mentioned above and its distribution are given by means of diffusion approximation and compared with those with previous point reactor conception model. They are basically consistent, however the present model can provide details on the distribution. (authors)
Characterisation of seasonal flood types according to timescales in mixed probability distributions

Science.gov (United States)

Fischer, Svenja; Schumann, Andreas; Schulte, Markus

2016-08-01

When flood statistics are based on annual maximum series (AMS), the sample often contains flood peaks, which differ in their genesis. If the ratios among event types change over the range of observations, the extrapolation of a probability distribution function (pdf) can be dominated by a majority of events that belong to a certain flood type. If this type is not typical for extraordinarily large extremes, such an extrapolation of the pdf is misleading. To avoid this breach of the assumption of homogeneity, seasonal models were developed that differ between winter and summer floods. We show that a distinction between summer and winter floods is not always sufficient if seasonal series include events with different geneses. Here, we differentiate floods by their timescales into groups of long and short events. A statistical method for such a distinction of events is presented. To demonstrate their applicability, timescales for winter and summer floods in a German river basin were estimated. It is shown that summer floods can be separated into two main groups, but in our study region, the sample of winter floods consists of at least three different flood types. The pdfs of the two groups of summer floods are combined via a new mixing model. This model considers that information about parallel events that uses their maximum values only is incomplete because some of the realisations are overlaid. A statistical method resulting in an amendment of statistical parameters is proposed. The application in a German case study demonstrates the advantages of the new model, with specific emphasis on flood types.
Probability and information theory, with applications to radar

CERN Document Server

Woodward, P M; Higinbotham, W

1964-01-01

Electronics and Instrumentation, Second Edition, Volume 3: Probability and Information Theory with Applications to Radar provides information pertinent to the development on research carried out in electronics and applied physics. This book presents the established mathematical techniques that provide the code in which so much of the mathematical theory of electronics and radar is expressed.Organized into eight chapters, this edition begins with an overview of the geometry of probability distributions in which moments play a significant role. This text then examines the mathematical methods in
Hamiltonian theories quantization based on a probability operator

International Nuclear Information System (INIS)

Entral'go, E.E.

1986-01-01

The quantization method with a linear reflection of classical coordinate-momentum-time functions Λ(q,p,t) at quantum operators in a space of quantum states ψ, is considered. The probability operator satisfies a system of equations representing the principles of dynamical and canonical correspondences between the classical and quantum theories. The quantization based on a probability operator leads to a quantum theory with a nonnegative joint coordinate-momentum distribution function for any state ψ. The main consequences of quantum mechanics with a probability operator are discussed in comparison with the generally accepted quantum and classical theories. It is shown that a probability operator leads to an appearance of some new notions called ''subquantum'' ones. Hence the quantum theory with a probability operator does not pretend to any complete description of physical reality in terms of classical variables and by this reason contains no problems like Einstein-Podolsky-Rosen paradox. The results of some concrete problems are given: a free particle, a harmonic oscillator, an electron in the Coulomb field. These results give hope on the possibility of an experimental verification of the quantization based on a probability operator
Ignition probabilities for Compact Ignition Tokamak designs

International Nuclear Information System (INIS)

Stotler, D.P.; Goldston, R.J.

1989-09-01

A global power balance code employing Monte Carlo techniques had been developed to study the ''probability of ignition'' and has been applied to several different configurations of the Compact Ignition Tokamak (CIT). Probability distributions for the critical physics parameters in the code were estimated using existing experimental data. This included a statistical evaluation of the uncertainty in extrapolating the energy confinement time. A substantial probability of ignition is predicted for CIT if peaked density profiles can be achieved or if one of the two higher plasma current configurations is employed. In other cases, values of the energy multiplication factor Q of order 10 are generally obtained. The Ignitor-U and ARIES designs are also examined briefly. Comparisons of our empirically based confinement assumptions with two theory-based transport models yield conflicting results. 41 refs., 11 figs
Probability

CERN Document Server

Shiryaev, A N

1996-01-01

This book contains a systematic treatment of probability from the ground up, starting with intuitive ideas and gradually developing more sophisticated subjects, such as random walks, martingales, Markov chains, ergodic theory, weak convergence of probability measures, stationary stochastic processes, and the Kalman-Bucy filter Many examples are discussed in detail, and there are a large number of exercises The book is accessible to advanced undergraduates and can be used as a text for self-study This new edition contains substantial revisions and updated references The reader will find a deeper study of topics such as the distance between probability measures, metrization of weak convergence, and contiguity of probability measures Proofs for a number of some important results which were merely stated in the first edition have been added The author included new material on the probability of large deviations, and on the central limit theorem for sums of dependent random variables
Emptiness formation probability of XX-chain in diffusion process

International Nuclear Information System (INIS)

Ogata, Yoshiko

2004-01-01

We study the distribution of emptiness formation probability of XX-model in the diffusion process. There exits a Gaussian decay as well as an exponential decay. The Gaussian decay is caused by the existence of zero point in the Fermi distribution function. The correlation length for each point of scaling factor varies up to the initial condition, monotonically or non-monotonically
Estimation and prediction of maximum daily rainfall at Sagar Island using best fit probability models

Science.gov (United States)

Mandal, S.; Choudhury, B. U.

2015-07-01

Sagar Island, setting on the continental shelf of Bay of Bengal, is one of the most vulnerable deltas to the occurrence of extreme rainfall-driven climatic hazards. Information on probability of occurrence of maximum daily rainfall will be useful in devising risk management for sustaining rainfed agrarian economy vis-a-vis food and livelihood security. Using six probability distribution models and long-term (1982-2010) daily rainfall data, we studied the probability of occurrence of annual, seasonal and monthly maximum daily rainfall (MDR) in the island. To select the best fit distribution models for annual, seasonal and monthly time series based on maximum rank with minimum value of test statistics, three statistical goodness of fit tests, viz. Kolmogorove-Smirnov test (K-S), Anderson Darling test ( A 2 ) and Chi-Square test ( X 2) were employed. The fourth probability distribution was identified from the highest overall score obtained from the three goodness of fit tests. Results revealed that normal probability distribution was best fitted for annual, post-monsoon and summer seasons MDR, while Lognormal, Weibull and Pearson 5 were best fitted for pre-monsoon, monsoon and winter seasons, respectively. The estimated annual MDR were 50, 69, 86, 106 and 114 mm for return periods of 2, 5, 10, 20 and 25 years, respectively. The probability of getting an annual MDR of >50, >100, >150, >200 and >250 mm were estimated as 99, 85, 40, 12 and 03 % level of exceedance, respectively. The monsoon, summer and winter seasons exhibited comparatively higher probabilities (78 to 85 %) for MDR of >100 mm and moderate probabilities (37 to 46 %) for >150 mm. For different recurrence intervals, the percent probability of MDR varied widely across intra- and inter-annual periods. In the island, rainfall anomaly can pose a climatic threat to the sustainability of agricultural production and thus needs adequate adaptation and mitigation measures.
Probability Analysis of the Wave-Slamming Pressure Values of the Horizontal Deck with Elastic Support

Science.gov (United States)

Zuo, Weiguang; Liu, Ming; Fan, Tianhui; Wang, Pengtao

2018-06-01

This paper presents the probability distribution of the slamming pressure from an experimental study of regular wave slamming on an elastically supported horizontal deck. The time series of the slamming pressure during the wave impact were first obtained through statistical analyses on experimental data. The exceeding probability distribution of the maximum slamming pressure peak and distribution parameters were analyzed, and the results show that the exceeding probability distribution of the maximum slamming pressure peak accords with the three-parameter Weibull distribution. Furthermore, the range and relationships of the distribution parameters were studied. The sum of the location parameter D and the scale parameter L was approximately equal to 1.0, and the exceeding probability was more than 36.79% when the random peak was equal to the sample average during the wave impact. The variation of the distribution parameters and slamming pressure under different model conditions were comprehensively presented, and the parameter values of the Weibull distribution of wave-slamming pressure peaks were different due to different test models. The parameter values were found to decrease due to the increased stiffness of the elastic support. The damage criterion of the structure model caused by the wave impact was initially discussed, and the structure model was destroyed when the average slamming time was greater than a certain value during the duration of the wave impact. The conclusions of the experimental study were then described.
Bayesian probability theory applications in the physical sciences

CERN Document Server

Linden, Wolfgang von der; Toussaint, Udo von

2014-01-01

From the basics to the forefront of modern research, this book presents all aspects of probability theory, statistics and data analysis from a Bayesian perspective for physicists and engineers. The book presents the roots, applications and numerical implementation of probability theory, and covers advanced topics such as maximum entropy distributions, stochastic processes, parameter estimation, model selection, hypothesis testing and experimental design. In addition, it explores state-of-the art numerical techniques required to solve demanding real-world problems. The book is ideal for students and researchers in physical sciences and engineering.
Parisian ruin probability for spectrally negative L\\'{e}vy processes

OpenAIRE

Ronnie Loeffen; Irmina Czarna; Zbigniew Palmowski

2011-01-01

In this note we give, for a spectrally negative Lévy process, a compact formula for the Parisian ruin probability, which is defined by the probability that the process exhibits an excursion below zero, with a length that exceeds a certain fixed period $r$. The formula involves only the scale function of the spectrally negative Lévy process and the distribution of the process at time $r$.
Theoretical-probability evaluation of the fire hazard of coal accumulations

Energy Technology Data Exchange (ETDEWEB)

Sikora, F F

1978-01-01

An evaluation is suggested for the fire hazard of coal accumulations, based on determining the probability of an endogenic fire. This probability is computed by using the statistical characteristics of the temperature distribution of spontaneous heating in large accumulations, and the criteria of Gluzberg's fire hazard that is determined by the coal's physico-chemical properties, oxygen concentration, and the size of the accumulations. 4 references.
Transformation of Bayesian posterior distribution into a basic analytical distribution

International Nuclear Information System (INIS)

Jordan Cizelj, R.; Vrbanic, I.

2002-01-01

Bayesian estimation is well-known approach that is widely used in Probabilistic Safety Analyses for the estimation of input model reliability parameters, such as component failure rates or probabilities of failure upon demand. In this approach, a prior distribution, which contains some generic knowledge about a parameter is combined with likelihood function, which contains plant-specific data about the parameter. Depending on the type of prior distribution, the resulting posterior distribution can be estimated numerically or analytically. In many instances only a numerical Bayesian integration can be performed. In such a case the posterior is provided in the form of tabular discrete distribution. On the other hand, it is much more convenient to have a parameter's uncertainty distribution that is to be input into a PSA model to be provided in the form of some basic analytical probability distribution, such as lognormal, gamma or beta distribution. One reason is that this enables much more convenient propagation of parameters' uncertainties through the model up to the so-called top events, such as plant system unavailability or core damage frequency. Additionally, software tools used to run PSA models often require that parameter's uncertainty distribution is defined in the form of one among the several allowed basic types of distributions. In such a case the posterior distribution that came as a product of Bayesian estimation needs to be transformed into an appropriate basic analytical form. In this paper, some approaches on transformation of posterior distribution to a basic probability distribution are proposed and discussed. They are illustrated by an example from NPP Krsko PSA model.(author)
Stress assessment based on EEG univariate features and functional connectivity measures.

Science.gov (United States)

Alonso, J F; Romero, S; Ballester, M R; Antonijoan, R M; Mañanas, M A

2015-07-01

The biological response to stress originates in the brain but involves different biochemical and physiological effects. Many common clinical methods to assess stress are based on the presence of specific hormones and on features extracted from different signals, including electrocardiogram, blood pressure, skin temperature, or galvanic skin response. The aim of this paper was to assess stress using EEG-based variables obtained from univariate analysis and functional connectivity evaluation. Two different stressors, the Stroop test and sleep deprivation, were applied to 30 volunteers to find common EEG patterns related to stress effects. Results showed a decrease of the high alpha power (11 to 12 Hz), an increase in the high beta band (23 to 36 Hz, considered a busy brain indicator), and a decrease in the approximate entropy. Moreover, connectivity showed that the high beta coherence and the interhemispheric nonlinear couplings, measured by the cross mutual information function, increased significantly for both stressors, suggesting that useful stress indexes may be obtained from EEG-based features.
Modeling the potential risk factors of bovine viral diarrhea prevalence in Egypt using univariable and multivariable logistic regression analyses

Directory of Open Access Journals (Sweden)

Abdelfattah M. Selim

2018-03-01

Full Text Available Aim: The present cross-sectional study was conducted to determine the seroprevalence and potential risk factors associated with Bovine viral diarrhea virus (BVDV disease in cattle and buffaloes in Egypt, to model the potential risk factors associated with the disease using logistic regression (LR models, and to fit the best predictive model for the current data. Materials and Methods: A total of 740 blood samples were collected within November 2012-March 2013 from animals aged between 6 months and 3 years. The potential risk factors studied were species, age, sex, and herd location. All serum samples were examined with indirect ELIZA test for antibody detection. Data were analyzed with different statistical approaches such as Chi-square test, odds ratios (OR, univariable, and multivariable LR models. Results: Results revealed a non-significant association between being seropositive with BVDV and all risk factors, except for species of animal. Seroprevalence percentages were 40% and 23% for cattle and buffaloes, respectively. OR for all categories were close to one with the highest OR for cattle relative to buffaloes, which was 2.237. Likelihood ratio tests showed a significant drop of the -2LL from univariable LR to multivariable LR models. Conclusion: There was an evidence of high seroprevalence of BVDV among cattle as compared with buffaloes with the possibility of infection in different age groups of animals. In addition, multivariable LR model was proved to provide more information for association and prediction purposes relative to univariable LR models and Chi-square tests if we have more than one predictor.
Updated greenhouse gas and criteria air pollutant emission factors and their probability distribution functions for electricity generating units

Energy Technology Data Exchange (ETDEWEB)

Cai, H.; Wang, M.; Elgowainy, A.; Han, J. (Energy Systems)

2012-07-06

Greenhouse gas (CO{sub 2}, CH{sub 4} and N{sub 2}O, hereinafter GHG) and criteria air pollutant (CO, NO{sub x}, VOC, PM{sub 10}, PM{sub 2.5} and SO{sub x}, hereinafter CAP) emission factors for various types of power plants burning various fuels with different technologies are important upstream parameters for estimating life-cycle emissions associated with alternative vehicle/fuel systems in the transportation sector, especially electric vehicles. The emission factors are typically expressed in grams of GHG or CAP per kWh of electricity generated by a specific power generation technology. This document describes our approach for updating and expanding GHG and CAP emission factors in the GREET (Greenhouse Gases, Regulated Emissions, and Energy Use in Transportation) model developed at Argonne National Laboratory (see Wang 1999 and the GREET website at http://greet.es.anl.gov/main) for various power generation technologies. These GHG and CAP emissions are used to estimate the impact of electricity use by stationary and transportation applications on their fuel-cycle emissions. The electricity generation mixes and the fuel shares attributable to various combustion technologies at the national, regional and state levels are also updated in this document. The energy conversion efficiencies of electric generating units (EGUs) by fuel type and combustion technology are calculated on the basis of the lower heating values of each fuel, to be consistent with the basis used in GREET for transportation fuels. On the basis of the updated GHG and CAP emission factors and energy efficiencies of EGUs, the probability distribution functions (PDFs), which are functions that describe the relative likelihood for the emission factors and energy efficiencies as random variables to take on a given value by the integral of their own probability distributions, are updated using best-fit statistical curves to characterize the uncertainties associated with GHG and CAP emissions in life
Assessing Efficiency of D-Vine Copula ARMA-GARCH Method in Value at Risk Forecasting: Evidence from PSE Listed Companies

Directory of Open Access Journals (Sweden)

Václav Klepáč

2015-01-01

Full Text Available The article points out the possibilities of using static D-Vine copula ARMA-GARCH model for estimation of 1 day ahead market Value at Risk. For the illustration we use data of the four companies listed on Prague Stock Exchange in range from 2010 to 2014. Vine copula approach allows us to construct high-dimensional copula from both elliptical and Archimedean bivariate copulas, i.e. multivariate probability distribution, created from process innovations. Due to a deeper shortage of existing domestic results or comparison studies with advanced volatility governed VaR forecasts we backtested D-Vine copula ARMA-GARCH model against the VaR rolling out of sample forecast from October 2012 to April 2014 of chosen benchmark models, e.g. multivariate VAR-GO-GARCH, VAR-DCC-GARCH and univariate ARMA-GARCH type models. Common backtesting via Kupiec and Christoffersen procedures offer generalization that technological superiority of model supports accuracy only in case of an univariate modeling – working with non-basic GARCH models and innovations with leptokurtic distributions. Multivariate VAR governed type models and static Copula Vines performed in stated backtesting comparison worse than selected univariate ARMA-GARCH, i.e. it have overestimated the level of actual market risk, probably due to hardly tractable time-varying dependence structure.
USING THE WEB-SERVICES WOLFRAM|ALPHA TO SOLVE PROBLEMS IN PROBABILITY THEORY

Directory of Open Access Journals (Sweden)

Taras Kobylnyk

2015-10-01

Full Text Available The trend towards the use of remote network resources on the Internet clearly delineated. Traditional training combined with increasingly networked, remote technologies become popular cloud computing. Research methods of probability theory are used in various fields. Of particular note is the use of methods of probability theory in psychological and educational research in statistical analysis of experimental data. Conducting such research is impossible without the use of modern information technology. Given the advantages of web-based software, the article describes web-service Wolfram|Alpha. Detailed analysis of the possibilities of using web-service Wolfram|Alpha for solving problems of probability theory. In the case studies described the results of queries for solving of probability theory, in particular the sections random events and random variables. Considered and analyzed the problem of the number of occurrences of event A in n independent trials using Wolfram|Alpha, detailed analysis of the possibilities of using the service Wolfram|Alpha for the study of continuous random variable that has a normal and uniform probability distribution, including calculating the probability of getting the value of a random variable in a given interval. The problem in applying the binomial and hypergeometric probability distribution of a discrete random variable and demonstrates the possibility of using the service Wolfram|Alpha for solving it.

Weak value distributions for spin 1/2

Science.gov (United States)

Berry, M. V.; Dennis, M. R.; McRoberts, B.; Shukla, P.

2011-05-01

The simplest weak measurement is of a component of spin 1/2. For this observable, the probability distributions of the real and imaginary parts of the weak value, and their joint probability distribution, are calculated exactly for pre- and postselected states uniformly distributed over the surface of the Poincaré-Bloch sphere. The superweak probability, that the real part of the weak value lies outside the spectral range, is 1/3. This case, with just two eigenvalues, complements our previous calculation (Berry and Shukla 2010 J. Phys. A: Math. Theor. 43 354024) of the universal form of the weak value probability distribution for an operator with many eigenvalues.
Weak value distributions for spin 1/2

International Nuclear Information System (INIS)

Berry, M V; Dennis, M R; McRoberts, B; Shukla, P

2011-01-01

The simplest weak measurement is of a component of spin 1/2. For this observable, the probability distributions of the real and imaginary parts of the weak value, and their joint probability distribution, are calculated exactly for pre- and postselected states uniformly distributed over the surface of the Poincare-Bloch sphere. The superweak probability, that the real part of the weak value lies outside the spectral range, is 1/3. This case, with just two eigenvalues, complements our previous calculation (Berry and Shukla 2010 J. Phys. A: Math. Theor. 43 354024) of the universal form of the weak value probability distribution for an operator with many eigenvalues.
Probability, statistics, and associated computing techniques

International Nuclear Information System (INIS)

James, F.

1983-01-01

This chapter attempts to explore the extent to which it is possible for the experimental physicist to find optimal statistical techniques to provide a unique and unambiguous quantitative measure of the significance of raw data. Discusses statistics as the inverse of probability; normal theory of parameter estimation; normal theory (Gaussian measurements); the universality of the Gaussian distribution; real-life resolution functions; combination and propagation of uncertainties; the sum or difference of 2 variables; local theory, or the propagation of small errors; error on the ratio of 2 discrete variables; the propagation of large errors; confidence intervals; classical theory; Bayesian theory; use of the likelihood function; the second derivative of the log-likelihood function; multiparameter confidence intervals; the method of MINOS; least squares; the Gauss-Markov theorem; maximum likelihood for uniform error distribution; the Chebyshev fit; the parameter uncertainties; the efficiency of the Chebyshev estimator; error symmetrization; robustness vs. efficiency; testing of hypotheses (e.g., the Neyman-Pearson test); goodness-of-fit; distribution-free tests; comparing two one-dimensional distributions; comparing multidimensional distributions; and permutation tests for comparing two point sets
Does probability of occurrence relate to population dynamics?

Science.gov (United States)

Thuiller, Wilfried; Münkemüller, Tamara; Schiffers, Katja H.; Georges, Damien; Dullinger, Stefan; Eckhart, Vincent M.; Edwards, Thomas C.; Gravel, Dominique; Kunstler, Georges; Merow, Cory; Moore, Kara; Piedallu, Christian; Vissault, Steve; Zimmermann, Niklaus E.; Zurell, Damaris; Schurr, Frank M.

2014-01-01

Hutchinson defined species' realized niche as the set of environmental conditions in which populations can persist in the presence of competitors. In terms of demography, the realized niche corresponds to the environments where the intrinsic growth rate (r) of populations is positive. Observed species occurrences should reflect the realized niche when additional processes like dispersal and local extinction lags do not have overwhelming effects. Despite the foundational nature of these ideas, quantitative assessments of the relationship between range-wide demographic performance and occurrence probability have not been made. This assessment is needed both to improve our conceptual understanding of species' niches and ranges and to develop reliable mechanistic models of species geographic distributions that incorporate demography and species interactions.The objective of this study is to analyse how demographic parameters (intrinsic growth rate r and carrying capacity K ) and population density (N ) relate to occurrence probability (Pocc ). We hypothesized that these relationships vary with species' competitive ability. Demographic parameters, density, and occurrence probability were estimated for 108 tree species from four temperate forest inventory surveys (Québec, western USA, France and Switzerland). We used published information of shade tolerance as indicators of light competition strategy, assuming that high tolerance denotes high competitive capacity in stable forest environments.Interestingly, relationships between demographic parameters and occurrence probability did not vary substantially across degrees of shade tolerance and regions. Although they were influenced by the uncertainty in the estimation of the demographic parameters, we found that r was generally negatively correlated with Pocc, while N, and for most regions K, was generally positively correlated with Pocc. Thus, in temperate forest trees the regions of highest occurrence
Estimating the joint survival probabilities of married individuals

NARCIS (Netherlands)

Sanders, Lisanne; Melenberg, Bertrand

We estimate the joint survival probability of spouses using a large random sample drawn from a Dutch census. As benchmarks we use two bivariate Weibull models. We consider more flexible models, using a semi-nonparametric approach, by extending the independent Weibull distribution using squared
Scaling Qualitative Probability

OpenAIRE

Burgin, Mark

2017-01-01

There are different approaches to qualitative probability, which includes subjective probability. We developed a representation of qualitative probability based on relational systems, which allows modeling uncertainty by probability structures and is more coherent than existing approaches. This setting makes it possible proving that any comparative probability is induced by some probability structure (Theorem 2.1), that classical probability is a probability structure (Theorem 2.2) and that i...
Penalized Maximum Likelihood Estimation for univariate normal mixture distributions

International Nuclear Information System (INIS)

Ridolfi, A.; Idier, J.

2001-01-01

Due to singularities of the likelihood function, the maximum likelihood approach for the estimation of the parameters of normal mixture models is an acknowledged ill posed optimization problem. Ill posedness is solved by penalizing the likelihood function. In the Bayesian framework, it amounts to incorporating an inverted gamma prior in the likelihood function. A penalized version of the EM algorithm is derived, which is still explicit and which intrinsically assures that the estimates are not singular. Numerical evidence of the latter property is put forward with a test
Autoregressive processes with exponentially decaying probability distribution functions: applications to daily variations of a stock market index.

Science.gov (United States)

Porto, Markus; Roman, H Eduardo

2002-04-01

We consider autoregressive conditional heteroskedasticity (ARCH) processes in which the variance sigma(2)(y) depends linearly on the absolute value of the random variable y as sigma(2)(y) = a+b absolute value of y. While for the standard model, where sigma(2)(y) = a + b y(2), the corresponding probability distribution function (PDF) P(y) decays as a power law for absolute value of y-->infinity, in the linear case it decays exponentially as P(y) approximately exp(-alpha absolute value of y), with alpha = 2/b. We extend these results to the more general case sigma(2)(y) = a+b absolute value of y(q), with 0 history of the ARCH process is taken into account, the resulting PDF becomes a stretched exponential even for q = 1, with a stretched exponent beta = 2/3, in a much better agreement with the empirical data.
Quantum Zeno and anti-Zeno effects measured by transition probabilities

Energy Technology Data Exchange (ETDEWEB)

Zhang, Wenxian, E-mail: wxzhang@whu.edu.cn [School of Physics and Technology, Wuhan University, Wuhan, Hubei 430072 (China); Department of Optical Science and Engineering, Fudan University, Shanghai 200433 (China); CEMS, RIKEN, Saitama 351-0198 (Japan); Kavli Institute for Theoretical Physics China, CAS, Beijing 100190 (China); Kofman, A.G. [CEMS, RIKEN, Saitama 351-0198 (Japan); Department of Physics, The University of Michigan, Ann Arbor, MI 48109-1040 (United States); Zhuang, Jun [Department of Optical Science and Engineering, Fudan University, Shanghai 200433 (China); You, J.Q. [Beijing Computational Science Research Center, Beijing 10084 (China); Department of Physics, Fudan University, Shanghai 200433 (China); CEMS, RIKEN, Saitama 351-0198 (Japan); Nori, Franco [CEMS, RIKEN, Saitama 351-0198 (Japan); Department of Physics, The University of Michigan, Ann Arbor, MI 48109-1040 (United States)

2013-10-30

Using numerical calculations, we compare the transition probabilities of many spins in random magnetic fields, subject to either frequent projective measurements, frequent phase modulations, or a mix of modulations and measurements. For various distribution functions, we find the transition probability under frequent modulations is suppressed most if the pulse delay is short and the evolution time is larger than a critical value. Furthermore, decay freezing occurs only under frequent modulations as the pulse delay approaches zero. In the large pulse-delay region, however, the transition probabilities under frequent modulations are highest among the three control methods.
Probability, Statistics, and Stochastic Processes

CERN Document Server

Olofsson, Peter

2012-01-01

This book provides a unique and balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. The Second Edition features new coverage of analysis of variance (ANOVA), consistency and efficiency of estimators, asymptotic theory for maximum likelihood estimators, empirical distribution function and the Kolmogorov-Smirnov test, general linear models, multiple comparisons, Markov chain Monte Carlo (MCMC), Brownian motion, martingales, and
Probability density fittings of corrosion test-data: Implications on ...

Indian Academy of Sciences (India)

Steel-reinforced concrete; probability distribution functions; corrosion ... to be present in the corrosive system at a suitable concentration (Holoway et al 2004; Söylev & ..... voltage, equivalent to voltage drop, across a resistor divided by the ...
Direct probability mapping of contaminants

International Nuclear Information System (INIS)

Rautman, C.A.

1993-01-01

Exhaustive characterization of a contaminated site is a physical and practical impossibility. Descriptions of the nature, extent, and level of contamination, as well as decisions regarding proposed remediation activities, must be made in a state of uncertainty based upon limited physical sampling. Geostatistical simulation provides powerful tools for investigating contaminant levels, and in particular, for identifying and using the spatial interrelationships among a set of isolated sample values. This additional information can be used to assess the likelihood of encountering contamination at unsampled locations and to evaluate the risk associated with decisions to remediate or not to remediate specific regions within a site. Past operation of the DOE Feed Materials Production Center has contaminated a site near Fernald, Ohio, with natural uranium. Soil geochemical data have been collected as part of the Uranium-in-Soils Integrated Demonstration Project. These data have been used to construct a number of stochastic images of potential contamination for parcels approximately the size of a selective remediation unit. Each such image accurately reflects the actual measured sample values, and reproduces the univariate statistics and spatial character of the extant data. Post-processing of a large number of these equally likely, statistically similar images produces maps directly showing the probability of exceeding specified levels of contamination. Evaluation of the geostatistical simulations can yield maps representing the expected magnitude of the contamination for various regions and other information that may be important in determining a suitable remediation process or in sizing equipment to accomplish the restoration
Effects of translation-rotation coupling on the displacement probability distribution functions of boomerang colloidal particles

Science.gov (United States)

Chakrabarty, Ayan; Wang, Feng; Sun, Kai; Wei, Qi-Huo

Prior studies have shown that low symmetry particles such as micro-boomerangs exhibit behaviour of Brownian motion rather different from that of high symmetry particles because convenient tracking points (TPs) are usually inconsistent with the center of hydrodynamic stress (CoH) where the translational and rotational motions are decoupled. In this paper we study the effects of the translation-rotation coupling on the displacement probability distribution functions (PDFs) of the boomerang colloid particles with symmetric arms. By tracking the motions of different points on the particle symmetry axis, we show that as the distance between the TP and the CoH is increased, the effects of translation-rotation coupling becomes pronounced, making the short-time 2D PDF for fixed initial orientation to change from elliptical to crescent shape and the angle averaged PDFs from ellipsoidal-particle-like PDF to a shape with a Gaussian top and long displacement tails. We also observed that at long times the PDFs revert to Gaussian. This crescent shape of 2D PDF provides a clear physical picture of the non-zero mean displacements observed in boomerangs particles.
Transmuted Lindley-Geometric Distribution and its applications

OpenAIRE

Merovci, Faton; Elbatal, Ibrahim

2013-01-01

A functional composition of the cumulative distribution function of one probability distribution with the inverse cumulative distribution function of another is called the transmutation map. In this article, we will use the quadratic rank transmutation map (QRTM) in order to generate a flexible family of probability distributions taking Lindley geometric distribution as the base value distribution by introducing a new parameter that would offer more distributional flexibility. It will be show...
Drug binding affinities and potencies are best described by a log-normal distribution and use of geometric means

International Nuclear Information System (INIS)

Stanisic, D.; Hancock, A.A.; Kyncl, J.J.; Lin, C.T.; Bush, E.N.

1986-01-01

(-)-Norepinephrine (NE) is used as an internal standard in their in vitro adrenergic assays, and the concentration of NE which produces a half-maximal inhibition of specific radioligand binding (affinity; K/sub I/), or half-maximal contractile response (potency; ED 50 ) has been measured numerous times. The goodness-of-fit test for normality was performed on both normal (Gaussian) or log 10 -normal frequency histograms of these data using the SAS Univariate procedure. Specific binding of 3 H-prazosin to rat liver (α 1 -), 3 H rauwolscine to rat cortex (α 2 -) and 3 H-dihydroalprenolol to rat ventricle (β 1 -) or rat lung (β 2 -receptors) was inhibited by NE; the distributions of NE K/sub I/'s at all these sites were skewed to the right, with highly significant (p 50 's of NE in isolated rabbit aorta (α 1 ), phenoxybenzamine-treated dog saphenous vein (α 2 ) and guinea pig atrium (β 1 ). The vasorelaxant potency of atrial natriuretic hormone in histamine-contracted rabbit aorta also was better described by a log-normal distribution, indicating that log-normalcy is probably a general phenomenon of drug-receptor interactions. Because data of this type appear to be log-normally distributed, geometric means should be used in parametric statistical analyses
Nuisance forecasting. Univariate modelling and very-short-term forecasting of winter smog episodes; Immissionsprognose. Univariate Modellierung und Kuerzestfristvorhersage von Wintersmogsituationen

Energy Technology Data Exchange (ETDEWEB)

Schlink, U.

1996-12-31

The work evaluates specifically the nuisance data provided by the measuring station in the centre of Leipig during the period from 1980 to 1993, with the aim to develop an algorithm for making very short-term forecasts of excessive nuisances. Forecasting was to be univariate, i.e., based exclusively on the half-hourly readings of SO{sub 2} concentrations taken in the past. As shown by Fourier analysis, there exist three main and mutually independent spectral regions: the high-frequency sector (period < 12 hours) of unstable irregularities, the seasonal sector with the periods of 24 and 12 hours, and the low-frequency sector (period > 24 hours). After breaking the measuring series up into components, the low-frequency sector is termed trend component, or trend for short. For obtaining the components, a Kalman filter is used. It was found that smog episodes are most adequately described by the trend component. This is therefore more closely investigated. The phase representation then shows characteristic trajectories of the trends. (orig./KW) [Deutsch] In der vorliegende Arbeit wurden speziell die Immissionsdaten der Messstation Leipzig-Mitte des Zeitraumes 1980-1993 mit dem Ziel der Erstellung eines Algorithmus fuer die Kuerzestfristprognose von Ueberschreitungssituationen untersucht. Die Prognosestellung sollte allein anhand der in der Vergangenheit registrierten Halbstundenwerte der SO{sub 2}-Konzentration, also univariat erfolgen. Wie die Fourieranalyse zeigt, gibt es drei wesentliche und voneinander unabhaengige Spektralbereiche: Den hochfrequenten Bereich (Periode <12 Stunden) der instabilen Irregularitaeten, den saisonalen Anteil mit den Perioden von 24 und 12 Stunden und den niedrigfrequenten Bereich (Periode >24 Stunden). Letzterer wird nach einer Zerlegung der Messreihe in Komponenten als Trendkomponente (oder kurz Trend) bezeichnet. Fuer die Komponentenzerlegung wird ein Kalman-Filter verwendet. Es stellt sich heraus, dass Smogepisoden am deutlichsten
Hydrological model calibration for flood prediction in current and future climates using probability distributions of observed peak flows and model based rainfall

Science.gov (United States)

Haberlandt, Uwe; Wallner, Markus; Radtke, Imke

2013-04-01

Derived flood frequency analysis based on continuous hydrological modelling is very demanding regarding the required length and temporal resolution of precipitation input data. Often such flood predictions are obtained using long precipitation time series from stochastic approaches or from regional climate models as input. However, the calibration of the hydrological model is usually done using short time series of observed data. This inconsistent employment of different data types for calibration and application of a hydrological model increases its uncertainty. Here, it is proposed to calibrate a hydrological model directly on probability distributions of observed peak flows using model based rainfall in line with its later application. Two examples are given to illustrate the idea. The first one deals with classical derived flood frequency analysis using input data from an hourly stochastic rainfall model. The second one concerns a climate impact analysis using hourly precipitation from a regional climate model. The results show that: (I) the same type of precipitation input data should be used for calibration and application of the hydrological model, (II) a model calibrated on extreme conditions works quite well for average conditions but not vice versa, (III) the calibration of the hydrological model using regional climate model data works as an implicit bias correction method and (IV) the best performance for flood estimation is usually obtained when model based precipitation and observed probability distribution of peak flows are used for model calibration.
Dropping Probability Reduction in OBS Networks: A Simple Approach

KAUST Repository

Elrasad, Amr; Rabia, Sherif; Mahmoud, Mohamed; Aly, Moustafa H.; Shihada, Basem

2016-01-01

by being adaptable to different offset-time and burst length distributions. We observed that applying a limited range of wavelength conversion, burst blocking probability is reduced by several orders of magnitudes and yields a better burst delivery ratio
Generation, combination and extension of random set approximations to coherent lower and upper probabilities

International Nuclear Information System (INIS)

Hall, Jim W.; Lawry, Jonathan

2004-01-01

Random set theory provides a convenient mechanism for representing uncertain knowledge including probabilistic and set-based information, and extending it through a function. This paper focuses upon the situation when the available information is in terms of coherent lower and upper probabilities, which are encountered, for example, when a probability distribution is specified by interval parameters. We propose an Iterative Rescaling Method (IRM) for constructing a random set with corresponding belief and plausibility measures that are a close outer approximation to the lower and upper probabilities. The approach is compared with the discrete approximation method of Williamson and Downs (sometimes referred to as the p-box), which generates a closer approximation to lower and upper cumulative probability distributions but in most cases a less accurate approximation to the lower and upper probabilities on the remainder of the power set. Four combination methods are compared by application to example random sets generated using the IRM
Newton/Poisson-Distribution Program

Science.gov (United States)

Bowerman, Paul N.; Scheuer, Ernest M.

1990-01-01

NEWTPOIS, one of two computer programs making calculations involving cumulative Poisson distributions. NEWTPOIS (NPO-17715) and CUMPOIS (NPO-17714) used independently of one another. NEWTPOIS determines Poisson parameter for given cumulative probability, from which one obtains percentiles for gamma distributions with integer shape parameters and percentiles for X(sup2) distributions with even degrees of freedom. Used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. Program written in C.

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