Analysis of generalized negative binomial distributions attached to hyperbolic Landau levels

Energy Technology Data Exchange (ETDEWEB)

Chhaiba, Hassan, E-mail: chhaiba.hassan@gmail.com [Department of Mathematics, Faculty of Sciences, Ibn Tofail University, P.O. Box 133, Kénitra (Morocco); Demni, Nizar, E-mail: nizar.demni@univ-rennes1.fr [IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex (France); Mouayn, Zouhair, E-mail: mouayn@fstbm.ac.ma [Department of Mathematics, Faculty of Sciences and Technics (M’Ghila), Sultan Moulay Slimane, P.O. Box 523, Béni Mellal (Morocco)

2016-07-15

To each hyperbolic Landau level of the Poincaré disc is attached a generalized negative binomial distribution. In this paper, we compute the moment generating function of this distribution and supply its atomic decomposition as a perturbation of the negative binomial distribution by a finitely supported measure. Using the Mandel parameter, we also discuss the nonclassical nature of the associated coherent states. Next, we derive a Lévy-Khintchine-type representation of its characteristic function when the latter does not vanish and deduce that it is quasi-infinitely divisible except for the lowest hyperbolic Landau level corresponding to the negative binomial distribution. By considering the total variation of the obtained quasi-Lévy measure, we introduce a new infinitely divisible distribution for which we derive the characteristic function.

Binomial distribution for the charge asymmetry parameter

International Nuclear Information System (INIS)

Chou, T.T.; Yang, C.N.

1984-01-01

It is suggested that for high energy collisions the distribution with respect to the charge asymmetry z = nsub(F) - nsub(B) is binomial, where nsub(F) and nsub(B) are the forward and backward charge multiplicities. (orig.)

Parameter estimation of the zero inflated negative binomial beta exponential distribution

Science.gov (United States)

Sirichantra, Chutima; Bodhisuwan, Winai

2017-11-01

The zero inflated negative binomial-beta exponential (ZINB-BE) distribution is developed, it is an alternative distribution for the excessive zero counts with overdispersion. The ZINB-BE distribution is a mixture of two distributions which are Bernoulli and negative binomial-beta exponential distributions. In this work, some characteristics of the proposed distribution are presented, such as, mean and variance. The maximum likelihood estimation is applied to parameter estimation of the proposed distribution. Finally some results of Monte Carlo simulation study, it seems to have high-efficiency when the sample size is large.

Interpretations and implications of negative binomial distributions of multiparticle productions

International Nuclear Information System (INIS)

Arisawa, Tetsuo

2006-01-01

The number of particles produced in high energy experiments is approximated by a negative binomial distribution. Deriving a representation of the distribution from a stochastic equation, conditions for the process to satisfy the distribution are clarified. Based on them, it is proposed that multiparticle production consists of spontaneous and induced production. The rate of the induced production is proportional to the number of existing particles. The ratio of the two production rates remains constant during the process. The ''NBD space'' is also defined where the number of particles produced in its subspaces follows negative binomial distributions with different parameters

Negative binomial distribution for multiplicity distributions in e/sup +/e/sup -/ annihilation

International Nuclear Information System (INIS)

Chew, C.K.; Lim, Y.K.

1986-01-01

The authors show that the negative binomial distribution fits excellently the available charged-particle multiplicity distributions of e/sup +/e/sup -/ annihilation into hadrons at three different energies √s = 14, 22 and 34 GeV

Chain binomial models and binomial autoregressive processes.

Science.gov (United States)

Weiss, Christian H; Pollett, Philip K

2012-09-01

We establish a connection between a class of chain-binomial models of use in ecology and epidemiology and binomial autoregressive (AR) processes. New results are obtained for the latter, including expressions for the lag-conditional distribution and related quantities. We focus on two types of chain-binomial model, extinction-colonization and colonization-extinction models, and present two approaches to parameter estimation. The asymptotic distributions of the resulting estimators are studied, as well as their finite-sample performance, and we give an application to real data. A connection is made with standard AR models, which also has implications for parameter estimation. © 2011, The International Biometric Society.

On bounds in Poisson approximation for distributions of independent negative-binomial distributed random variables.

Science.gov (United States)

Hung, Tran Loc; Giang, Le Truong

2016-01-01

Using the Stein-Chen method some upper bounds in Poisson approximation for distributions of row-wise triangular arrays of independent negative-binomial distributed random variables are established in this note.

The importance of distribution-choice in modeling substance use data: a comparison of negative binomial, beta binomial, and zero-inflated distributions.

Science.gov (United States)

Wagner, Brandie; Riggs, Paula; Mikulich-Gilbertson, Susan

2015-01-01

It is important to correctly understand the associations among addiction to multiple drugs and between co-occurring substance use and psychiatric disorders. Substance-specific outcomes (e.g. number of days used cannabis) have distributional characteristics which range widely depending on the substance and the sample being evaluated. We recommend a four-part strategy for determining the appropriate distribution for modeling substance use data. We demonstrate this strategy by comparing the model fit and resulting inferences from applying four different distributions to model use of substances that range greatly in the prevalence and frequency of their use. Using Timeline Followback (TLFB) data from a previously-published study, we used negative binomial, beta-binomial and their zero-inflated counterparts to model proportion of days during treatment of cannabis, cigarettes, alcohol, and opioid use. The fit for each distribution was evaluated with statistical model selection criteria, visual plots and a comparison of the resulting inferences. We demonstrate the feasibility and utility of modeling each substance individually and show that no single distribution provides the best fit for all substances. Inferences regarding use of each substance and associations with important clinical variables were not consistent across models and differed by substance. Thus, the distribution chosen for modeling substance use must be carefully selected and evaluated because it may impact the resulting conclusions. Furthermore, the common procedure of aggregating use across different substances may not be ideal.

e+-e- hadronic multiplicity distributions: negative binomial or Poisson

International Nuclear Information System (INIS)

Carruthers, P.; Shih, C.C.

1986-01-01

On the basis of fits to the multiplicity distributions for variable rapidity windows and the forward backward correlation for the 2 jet subset of e + e - data it is impossible to distinguish between a global negative binomial and its generalization, the partially coherent distribution. It is suggested that intensity interferometry, especially the Bose-Einstein correlation, gives information which will discriminate among dynamical models. 16 refs

Beta-binomial regression and bimodal utilization.

Science.gov (United States)

Liu, Chuan-Fen; Burgess, James F; Manning, Willard G; Maciejewski, Matthew L

2013-10-01

To illustrate how the analysis of bimodal U-shaped distributed utilization can be modeled with beta-binomial regression, which is rarely used in health services research. Veterans Affairs (VA) administrative data and Medicare claims in 2001-2004 for 11,123 Medicare-eligible VA primary care users in 2000. We compared means and distributions of VA reliance (the proportion of all VA/Medicare primary care visits occurring in VA) predicted from beta-binomial, binomial, and ordinary least-squares (OLS) models. Beta-binomial model fits the bimodal distribution of VA reliance better than binomial and OLS models due to the nondependence on normality and the greater flexibility in shape parameters. Increased awareness of beta-binomial regression may help analysts apply appropriate methods to outcomes with bimodal or U-shaped distributions. © Health Research and Educational Trust.

The negative binomial distribution as a model for external corrosion defect counts in buried pipelines

International Nuclear Information System (INIS)

Valor, Alma; Alfonso, Lester; Caleyo, Francisco; Vidal, Julio; Perez-Baruch, Eloy; Hallen, José M.

2015-01-01

Highlights: • Observed external-corrosion defects in underground pipelines revealed a tendency to cluster. • The Poisson distribution is unable to fit extensive count data for these type of defects. • In contrast, the negative binomial distribution provides a suitable count model for them. • Two spatial stochastic processes lead to the negative binomial distribution for defect counts. • They are the Gamma-Poisson mixed process and the compound Poisson process. • A Rogeŕs process also arises as a plausible temporal stochastic process leading to corrosion defect clustering and to negative binomially distributed defect counts. - Abstract: The spatial distribution of external corrosion defects in buried pipelines is usually described as a Poisson process, which leads to corrosion defects being randomly distributed along the pipeline. However, in real operating conditions, the spatial distribution of defects considerably departs from Poisson statistics due to the aggregation of defects in groups or clusters. In this work, the statistical analysis of real corrosion data from underground pipelines operating in southern Mexico leads to conclude that the negative binomial distribution provides a better description for defect counts. The origin of this distribution from several processes is discussed. The analysed processes are: mixed Gamma-Poisson, compound Poisson and Roger’s processes. The physical reasons behind them are discussed for the specific case of soil corrosion.

Confidence Intervals for Asbestos Fiber Counts: Approximate Negative Binomial Distribution.

Science.gov (United States)

Bartley, David; Slaven, James; Harper, Martin

2017-03-01

The negative binomial distribution is adopted for analyzing asbestos fiber counts so as to account for both the sampling errors in capturing only a finite number of fibers and the inevitable human variation in identifying and counting sampled fibers. A simple approximation to this distribution is developed for the derivation of quantiles and approximate confidence limits. The success of the approximation depends critically on the use of Stirling's expansion to sufficient order, on exact normalization of the approximating distribution, on reasonable perturbation of quantities from the normal distribution, and on accurately approximating sums by inverse-trapezoidal integration. Accuracy of the approximation developed is checked through simulation and also by comparison to traditional approximate confidence intervals in the specific case that the negative binomial distribution approaches the Poisson distribution. The resulting statistics are shown to relate directly to early research into the accuracy of asbestos sampling and analysis. Uncertainty in estimating mean asbestos fiber concentrations given only a single count is derived. Decision limits (limits of detection) and detection limits are considered for controlling false-positive and false-negative detection assertions and are compared to traditional limits computed assuming normal distributions. Published by Oxford University Press on behalf of the British Occupational Hygiene Society 2017.

Correlation Structures of Correlated Binomial Models and Implied Default Distribution

OpenAIRE

S. Mori; K. Kitsukawa; M. Hisakado

2006-01-01

We show how to analyze and interpret the correlation structures, the conditional expectation values and correlation coefficients of exchangeable Bernoulli random variables. We study implied default distributions for the iTraxx-CJ tranches and some popular probabilistic models, including the Gaussian copula model, Beta binomial distribution model and long-range Ising model. We interpret the differences in their profiles in terms of the correlation structures. The implied default distribution h...

Binomial Distribution Sample Confidence Intervals Estimation 1. Sampling and Medical Key Parameters Calculation

Directory of Open Access Journals (Sweden)

Tudor DRUGAN

2003-08-01

Full Text Available The aim of the paper was to present the usefulness of the binomial distribution in studying of the contingency tables and the problems of approximation to normality of binomial distribution (the limits, advantages, and disadvantages. The classification of the medical keys parameters reported in medical literature and expressing them using the contingency table units based on their mathematical expressions restrict the discussion of the confidence intervals from 34 parameters to 9 mathematical expressions. The problem of obtaining different information starting with the computed confidence interval for a specified method, information like confidence intervals boundaries, percentages of the experimental errors, the standard deviation of the experimental errors and the deviation relative to significance level was solves through implementation in PHP programming language of original algorithms. The cases of expression, which contain two binomial variables, were separately treated. An original method of computing the confidence interval for the case of two-variable expression was proposed and implemented. The graphical representation of the expression of two binomial variables for which the variation domain of one of the variable depend on the other variable was a real problem because the most of the software used interpolation in graphical representation and the surface maps were quadratic instead of triangular. Based on an original algorithm, a module was implements in PHP in order to represent graphically the triangular surface plots. All the implementation described above was uses in computing the confidence intervals and estimating their performance for binomial distributions sample sizes and variable.

Statistical inference for a class of multivariate negative binomial distributions

DEFF Research Database (Denmark)

Rubak, Ege Holger; Møller, Jesper; McCullagh, Peter

This paper considers statistical inference procedures for a class of models for positively correlated count variables called α-permanental random fields, and which can be viewed as a family of multivariate negative binomial distributions. Their appealing probabilistic properties have earlier been...

Using the β-binomial distribution to characterize forest health

Science.gov (United States)

S.J. Zarnoch; R.L. Anderson; R.M. Sheffield

1995-01-01

The β-binomial distribution is suggested as a model for describing and analyzing the dichotomous data obtained from programs monitoring the health of forests in the United States. Maximum likelihood estimation of the parameters is given as well as asymptotic likelihood ratio tests. The procedure is illustrated with data on dogwood anthracnose infection (caused...

Correlated binomial models and correlation structures

International Nuclear Information System (INIS)

Hisakado, Masato; Kitsukawa, Kenji; Mori, Shintaro

2006-01-01

We discuss a general method to construct correlated binomial distributions by imposing several consistent relations on the joint probability function. We obtain self-consistency relations for the conditional correlations and conditional probabilities. The beta-binomial distribution is derived by a strong symmetric assumption on the conditional correlations. Our derivation clarifies the 'correlation' structure of the beta-binomial distribution. It is also possible to study the correlation structures of other probability distributions of exchangeable (homogeneous) correlated Bernoulli random variables. We study some distribution functions and discuss their behaviours in terms of their correlation structures

Multifractal structure of multiplicity distributions and negative binomials

International Nuclear Information System (INIS)

Malik, S.; Delhi, Univ.

1997-01-01

The paper presents experimental results of the multifractal structure analysis in proton-emulsion interactions at 800 GeV. The multiplicity moments have a power law dependence on the mean multiplicity in varying bin sizes of pseudorapidity. The values of generalised dimensions are calculated from the slope value. The multifractal characteristics are also examined in the light of negative binomials. The observed multiplicity moments and those derived from the negative-binomial fits agree well with each other. Also the values of D q , both observed and derived from the negative-binomial fits not only decrease with q typifying multifractality but also agree well each other showing consistency with the negative-binomial form

Use of the negative binomial-truncated Poisson distribution in thunderstorm prediction

Science.gov (United States)

Cohen, A. C.

1971-01-01

A probability model is presented for the distribution of thunderstorms over a small area given that thunderstorm events (1 or more thunderstorms) are occurring over a larger area. The model incorporates the negative binomial and truncated Poisson distributions. Probability tables for Cape Kennedy for spring, summer, and fall months and seasons are presented. The computer program used to compute these probabilities is appended.

Correlation Structures of Correlated Binomial Models and Implied Default Distribution

Science.gov (United States)

Mori, Shintaro; Kitsukawa, Kenji; Hisakado, Masato

2008-11-01

We show how to analyze and interpret the correlation structures, the conditional expectation values and correlation coefficients of exchangeable Bernoulli random variables. We study implied default distributions for the iTraxx-CJ tranches and some popular probabilistic models, including the Gaussian copula model, Beta binomial distribution model and long-range Ising model. We interpret the differences in their profiles in terms of the correlation structures. The implied default distribution has singular correlation structures, reflecting the credit market implications. We point out two possible origins of the singular behavior.

Statistical Inference for a Class of Multivariate Negative Binomial Distributions

DEFF Research Database (Denmark)

Rubak, Ege H.; Møller, Jesper; McCullagh, Peter

This paper considers statistical inference procedures for a class of models for positively correlated count variables called -permanental random fields, and which can be viewed as a family of multivariate negative binomial distributions. Their appealing probabilistic properties have earlier been...... studied in the literature, while this is the first statistical paper on -permanental random fields. The focus is on maximum likelihood estimation, maximum quasi-likelihood estimation and on maximum composite likelihood estimation based on uni- and bivariate distributions. Furthermore, new results...

Negative-binomial multiplicity distributions in the interaction of light ions with 12C at 4.2 GeV/c

International Nuclear Information System (INIS)

Tucholski, A.; Bogdanowicz, J.; Moroz, Z.; Wojtkowska, J.

1989-01-01

Multiplicity distribution of single-charged particles in the interaction of p, d, α and 12 C projectiles with C target nuclei at 4.2 GeV/c were analysed in terms of the negative binomial distribution. The experimental data obtained by the Dubna Propane Bubble Chamber Group were used. It is shown that the experimental distributions are satisfactorily described by the negative-binomial distribution. Values of the parameters of these distributions are discussed. (orig.)

The effect of the negative binomial distribution on the line-width of the micromaser cavity field

International Nuclear Information System (INIS)

Kremid, A. M.

2009-01-01

The influence of negative binomial distribution (NBD) on the line-width of the negative binomial distribution (NBD) on the line-width of the micromaser is considered. The threshold of the micromaser is shifted towards higher values of the pumping parameter q. Moreover the line-width exhibits sharp dips 'resonances' when the cavity temperature reduces to a very low value. These dips are very clear evidence for the occurrence of the so-called trapping states regime in the micromaser. This statistics prevents the appearance of these trapping states, namely by increasing the negative binomial parameter q these dips wash out and the line-width becomes more broadening. For small values of the parameter q the line-width at large values of q randomly oscillates around its transition line. As q becomes large this oscillatory behavior occurs at rarely values of q. (author)

Validity of the negative binomial multiplicity distribution in case of ultra-relativistic nucleus-nucleus interaction in different azimuthal bins

International Nuclear Information System (INIS)

Ghosh, D.; Deb, A.; Haldar, P.K.; Sahoo, S.R.; Maity, D.

2004-01-01

This work studies the validity of the negative binomial distribution in the multiplicity distribution of charged secondaries in 16 O and 32 S interactions with AgBr at 60 GeV/c per nucleon and 200 GeV/c per nucleon, respectively. The validity of negative binomial distribution (NBD) is studied in different azimuthal phase spaces. It is observed that the data can be well parameterized in terms of the NBD law for different azimuthal phase spaces. (authors)

Number-Phase Wigner Representation and Entropic Uncertainty Relations for Binomial and Negative Binomial States

International Nuclear Information System (INIS)

Amitabh, J.; Vaccaro, J.A.; Hill, K.E.

1998-01-01

We study the recently defined number-phase Wigner function S NP (n,θ) for a single-mode field considered to be in binomial and negative binomial states. These states interpolate between Fock and coherent states and coherent and quasi thermal states, respectively, and thus provide a set of states with properties ranging from uncertain phase and sharp photon number to sharp phase and uncertain photon number. The distribution function S NP (n,θ) gives a graphical representation of the complimentary nature of the number and phase properties of these states. We highlight important differences between Wigner's quasi probability function, which is associated with the position and momentum observables, and S NP (n,θ), which is associated directly with the photon number and phase observables. We also discuss the number-phase entropic uncertainty relation for the binomial and negative binomial states and we show that negative binomial states give a lower phase entropy than states which minimize the phase variance

Negative binomial multiplicity distributions, a new empirical law for high energy collisions

International Nuclear Information System (INIS)

Van Hove, L.; Giovannini, A.

1987-01-01

For a variety of high energy hadron production reactions, recent experiments have confirmed the findings of the UA5 Collaboration that charged particle multiplicities in central (pseudo) rapidity intervals and in full phase space obey negative binomial (NB) distributions. The authors discuss the meaning of this new empirical law on the basis of new data and they show that they support the interpretation of the NB distributions in terms of a cascading mechanism of hardron production

System-Reliability Cumulative-Binomial Program

Science.gov (United States)

Scheuer, Ernest M.; Bowerman, Paul N.

1989-01-01

Cumulative-binomial computer program, NEWTONP, one of set of three programs, calculates cumulative binomial probability distributions for arbitrary inputs. NEWTONP, CUMBIN (NPO-17555), and CROSSER (NPO-17557), used independently of one another. Program finds probability required to yield given system reliability. Used by statisticians and users of statistical procedures, test planners, designers, and numerical analysts. Program written in C.

Common-Reliability Cumulative-Binomial Program

Science.gov (United States)

Scheuer, Ernest, M.; Bowerman, Paul N.

1989-01-01

Cumulative-binomial computer program, CROSSER, one of set of three programs, calculates cumulative binomial probability distributions for arbitrary inputs. CROSSER, CUMBIN (NPO-17555), and NEWTONP (NPO-17556), used independently of one another. Point of equality between reliability of system and common reliability of components found. Used by statisticians and users of statistical procedures, test planners, designers, and numerical analysts. Program written in C.

First study of the negative binomial distribution applied to higher moments of net-charge and net-proton multiplicity distributions

International Nuclear Information System (INIS)

Tarnowsky, Terence J.; Westfall, Gary D.

2013-01-01

A study of the first four moments (mean, variance, skewness, and kurtosis) and their products (κσ 2 and Sσ) of the net-charge and net-proton distributions in Au + Au collisions at √(s NN )=7.7–200 GeV from HIJING simulations has been carried out. The skewness and kurtosis and the collision volume independent products κσ 2 and Sσ have been proposed as sensitive probes for identifying the presence of a QCD critical point. A discrete probability distribution that effectively describes the separate positively and negatively charged particle (or proton and anti-proton) multiplicity distributions is the negative binomial (or binomial) distribution (NBD/BD). The NBD/BD has been used to characterize particle production in high-energy particle and nuclear physics. Their application to the higher moments of the net-charge and net-proton distributions is examined. Differences between κσ 2 and a statistical Poisson assumption of a factor of four (for net-charge) and 40% (for net-protons) can be accounted for by the NBD/BD. This is the first application of the properties of the NBD/BD to describe the behavior of the higher moments of net-charge and net-proton distributions in nucleus–nucleus collisions

Statistical inference involving binomial and negative binomial parameters.

Science.gov (United States)

García-Pérez, Miguel A; Núñez-Antón, Vicente

2009-05-01

Statistical inference about two binomial parameters implies that they are both estimated by binomial sampling. There are occasions in which one aims at testing the equality of two binomial parameters before and after the occurrence of the first success along a sequence of Bernoulli trials. In these cases, the binomial parameter before the first success is estimated by negative binomial sampling whereas that after the first success is estimated by binomial sampling, and both estimates are related. This paper derives statistical tools to test two hypotheses, namely, that both binomial parameters equal some specified value and that both parameters are equal though unknown. Simulation studies are used to show that in small samples both tests are accurate in keeping the nominal Type-I error rates, and also to determine sample size requirements to detect large, medium, and small effects with adequate power. Additional simulations also show that the tests are sufficiently robust to certain violations of their assumptions.

Chromosome aberration analysis based on a beta-binomial distribution

International Nuclear Information System (INIS)

Otake, Masanori; Prentice, R.L.

1983-10-01

Analyses carried out here generalized on earlier studies of chromosomal aberrations in the populations of Hiroshima and Nagasaki, by allowing extra-binomial variation in aberrant cell counts corresponding to within-subject correlations in cell aberrations. Strong within-subject correlations were detected with corresponding standard errors for the average number of aberrant cells that were often substantially larger than was previously assumed. The extra-binomial variation is accomodated in the analysis in the present report, as described in the section on dose-response models, by using a beta-binomial (B-B) variance structure. It is emphasized that we have generally satisfactory agreement between the observed and the B-B fitted frequencies by city-dose category. The chromosomal aberration data considered here are not extensive enough to allow a precise discrimination between competing dose-response models. A quadratic gamma ray and linear neutron model, however, most closely fits the chromosome data. (author)

Use of a negative binomial distribution to describe the presence of Sphyrion laevigatum in Genypterus blacodes

Directory of Open Access Journals (Sweden)

Patricio Peña-Rehbein

Full Text Available This paper describes the frequency and number of Sphyrion laevigatum in the skin of Genypterus blacodes, an important economic resource in Chile. The analysis of a spatial distribution model indicated that the parasites tended to cluster. Variations in the number of parasites per host could be described by a negative binomial distribution. The maximum number of parasites observed per host was two.

CUMBIN - CUMULATIVE BINOMIAL PROGRAMS

Science.gov (United States)

Bowerman, P. N.

1994-01-01

The cumulative binomial program, CUMBIN, is one of a set of three programs which calculate cumulative binomial probability distributions for arbitrary inputs. The three programs, CUMBIN, NEWTONP (NPO-17556), and CROSSER (NPO-17557), can be used independently of one another. CUMBIN can be used by statisticians and users of statistical procedures, test planners, designers, and numerical analysts. The program has been used for reliability/availability calculations. CUMBIN calculates the probability that a system of n components has at least k operating if the probability that any one operating is p and the components are independent. Equivalently, this is the reliability of a k-out-of-n system having independent components with common reliability p. CUMBIN can evaluate the incomplete beta distribution for two positive integer arguments. CUMBIN can also evaluate the cumulative F distribution and the negative binomial distribution, and can determine the sample size in a test design. CUMBIN is designed to work well with all integer values 0 < k <= n. To run the program, the user simply runs the executable version and inputs the information requested by the program. The program is not designed to weed out incorrect inputs, so the user must take care to make sure the inputs are correct. Once all input has been entered, the program calculates and lists the result. The CUMBIN program is written in C. It was developed on an IBM AT with a numeric co-processor using Microsoft C 5.0. Because the source code is written using standard C structures and functions, it should compile correctly with most C compilers. The program format is interactive. It has been implemented under DOS 3.2 and has a memory requirement of 26K. CUMBIN was developed in 1988.

Use of negative binomial distribution to describe the presence of Anisakis in Thyrsites atun.

Science.gov (United States)

Peña-Rehbein, Patricio; De los Ríos-Escalante, Patricio

2012-01-01

Nematodes of the genus Anisakis have marine fishes as intermediate hosts. One of these hosts is Thyrsites atun, an important fishery resource in Chile between 38 and 41° S. This paper describes the frequency and number of Anisakis nematodes in the internal organs of Thyrsites atun. An analysis based on spatial distribution models showed that the parasites tend to be clustered. The variation in the number of parasites per host could be described by the negative binomial distribution. The maximum observed number of parasites was nine parasites per host. The environmental and zoonotic aspects of the study are also discussed.

Bipartite binomial heaps

DEFF Research Database (Denmark)

Elmasry, Amr; Jensen, Claus; Katajainen, Jyrki

2017-01-01

the (total) number of elements stored in the data structure(s) prior to the operation. As the resulting data structure consists of two components that are different variants of binomial heaps, we call it a bipartite binomial heap. Compared to its counterpart, a multipartite binomial heap, the new structure...

Confidence limits for parameters of Poisson and binomial distributions

International Nuclear Information System (INIS)

Arnett, L.M.

1976-04-01

The confidence limits for the frequency in a Poisson process and for the proportion of successes in a binomial process were calculated and tabulated for the situations in which the observed values of the frequency or proportion and an a priori distribution of these parameters are available. Methods are used that produce limits with exactly the stated confidence levels. The confidence interval [a,b] is calculated so that Pr [a less than or equal to lambda less than or equal to b c,μ], where c is the observed value of the parameter, and μ is the a priori hypothesis of the distribution of this parameter. A Bayesian type analysis is used. The intervals calculated are narrower and appreciably different from results, known to be conservative, that are often used in problems of this type. Pearson and Hartley recognized the characteristics of their methods and contemplated that exact methods could someday be used. The calculation of the exact intervals requires involved numerical analyses readily implemented only on digital computers not available to Pearson and Hartley. A Monte Carlo experiment was conducted to verify a selected interval from those calculated. This numerical experiment confirmed the results of the analytical methods and the prediction of Pearson and Hartley that their published tables give conservative results

Zero inflated negative binomial-generalized exponential distributionand its applications

Directory of Open Access Journals (Sweden)

Sirinapa Aryuyuen

2014-08-01

Full Text Available In this paper, we propose a new zero inflated distribution, namely, the zero inflated negative binomial-generalized exponential (ZINB-GE distribution. The new distribution is used for count data with extra zeros and is an alternative for data analysis with over-dispersed count data. Some characteristics of the distribution are given, such as mean, variance, skewness, and kurtosis. Parameter estimation of the ZINB-GE distribution uses maximum likelihood estimation (MLE method. Simulated and observed data are employed to examine this distribution. The results show that the MLE method seems to have high efficiency for large sample sizes. Moreover, the mean square error of parameter estimation is increased when the zero proportion is higher. For the real data sets, this new zero inflated distribution provides a better fit than the zero inflated Poisson and zero inflated negative binomial distributions.

Negative binomial distribution to describe the presence of Trifur tortuosus (Crustacea: Copepoda in Merluccius gayi (Osteichthyes: Gadiformes

Directory of Open Access Journals (Sweden)

Giselle Garcia-Sepulveda

2017-06-01

Full Text Available This paper describes the frequency and number of Trifur tortuosus in the skin of Merluccius gayi, an important economic resource in Chile. Analysis of a spatial distribution model indicated that the parasites tended to cluster. Variations in the number of parasites per host can be described by a negative binomial distribution. The maximum number of parasites observed per host was one, similar patterns was described for other parasites in Chilean marine fishes.

Analytic degree distributions of horizontal visibility graphs mapped from unrelated random series and multifractal binomial measures

Science.gov (United States)

Xie, Wen-Jie; Han, Rui-Qi; Jiang, Zhi-Qiang; Wei, Lijian; Zhou, Wei-Xing

2017-08-01

Complex network is not only a powerful tool for the analysis of complex system, but also a promising way to analyze time series. The algorithm of horizontal visibility graph (HVG) maps time series into graphs, whose degree distributions are numerically and analytically investigated for certain time series. We derive the degree distributions of HVGs through an iterative construction process of HVGs. The degree distributions of the HVG and the directed HVG for random series are derived to be exponential, which confirms the analytical results from other methods. We also obtained the analytical expressions of degree distributions of HVGs and in-degree and out-degree distributions of directed HVGs transformed from multifractal binomial measures, which agree excellently with numerical simulations.

Binomial vs poisson statistics in radiation studies

International Nuclear Information System (INIS)

Foster, J.; Kouris, K.; Spyrou, N.M.; Matthews, I.P.; Welsh National School of Medicine, Cardiff

1983-01-01

The processes of radioactive decay, decay and growth of radioactive species in a radioactive chain, prompt emission(s) from nuclear reactions, conventional activation and cyclic activation are discussed with respect to their underlying statistical density function. By considering the transformation(s) that each nucleus may undergo it is shown that all these processes are fundamentally binomial. Formally, when the number of experiments N is large and the probability of success p is close to zero, the binomial is closely approximated by the Poisson density function. In radiation and nuclear physics, N is always large: each experiment can be conceived of as the observation of the fate of each of the N nuclei initially present. Whether p, the probability that a given nucleus undergoes a prescribed transformation, is close to zero depends on the process and nuclide(s) concerned. Hence, although a binomial description is always valid, the Poisson approximation is not always adequate. Therefore further clarification is provided as to when the binomial distribution must be used in the statistical treatment of detected events. (orig.)

The Validation of a Beta-Binomial Model for Overdispersed Binomial Data.

Science.gov (United States)

Kim, Jongphil; Lee, Ji-Hyun

2017-01-01

The beta-binomial model has been widely used as an analytically tractable alternative that captures the overdispersion of an intra-correlated, binomial random variable, X . However, the model validation for X has been rarely investigated. As a beta-binomial mass function takes on a few different shapes, the model validation is examined for each of the classified shapes in this paper. Further, the mean square error (MSE) is illustrated for each shape by the maximum likelihood estimator (MLE) based on a beta-binomial model approach and the method of moments estimator (MME) in order to gauge when and how much the MLE is biased.

Modeling random telegraph signal noise in CMOS image sensor under low light based on binomial distribution

International Nuclear Information System (INIS)

Zhang Yu; Wang Guangyi; Lu Xinmiao; Hu Yongcai; Xu Jiangtao

2016-01-01

The random telegraph signal noise in the pixel source follower MOSFET is the principle component of the noise in the CMOS image sensor under low light. In this paper, the physical and statistical model of the random telegraph signal noise in the pixel source follower based on the binomial distribution is set up. The number of electrons captured or released by the oxide traps in the unit time is described as the random variables which obey the binomial distribution. As a result, the output states and the corresponding probabilities of the first and the second samples of the correlated double sampling circuit are acquired. The standard deviation of the output states after the correlated double sampling circuit can be obtained accordingly. In the simulation section, one hundred thousand samples of the source follower MOSFET have been simulated, and the simulation results show that the proposed model has the similar statistical characteristics with the existing models under the effect of the channel length and the density of the oxide trap. Moreover, the noise histogram of the proposed model has been evaluated at different environmental temperatures. (paper)

NBLDA: negative binomial linear discriminant analysis for RNA-Seq data.

Science.gov (United States)

Dong, Kai; Zhao, Hongyu; Tong, Tiejun; Wan, Xiang

2016-09-13

RNA-sequencing (RNA-Seq) has become a powerful technology to characterize gene expression profiles because it is more accurate and comprehensive than microarrays. Although statistical methods that have been developed for microarray data can be applied to RNA-Seq data, they are not ideal due to the discrete nature of RNA-Seq data. The Poisson distribution and negative binomial distribution are commonly used to model count data. Recently, Witten (Annals Appl Stat 5:2493-2518, 2011) proposed a Poisson linear discriminant analysis for RNA-Seq data. The Poisson assumption may not be as appropriate as the negative binomial distribution when biological replicates are available and in the presence of overdispersion (i.e., when the variance is larger than or equal to the mean). However, it is more complicated to model negative binomial variables because they involve a dispersion parameter that needs to be estimated. In this paper, we propose a negative binomial linear discriminant analysis for RNA-Seq data. By Bayes' rule, we construct the classifier by fitting a negative binomial model, and propose some plug-in rules to estimate the unknown parameters in the classifier. The relationship between the negative binomial classifier and the Poisson classifier is explored, with a numerical investigation of the impact of dispersion on the discriminant score. Simulation results show the superiority of our proposed method. We also analyze two real RNA-Seq data sets to demonstrate the advantages of our method in real-world applications. We have developed a new classifier using the negative binomial model for RNA-seq data classification. Our simulation results show that our proposed classifier has a better performance than existing works. The proposed classifier can serve as an effective tool for classifying RNA-seq data. Based on the comparison results, we have provided some guidelines for scientists to decide which method should be used in the discriminant analysis of RNA-Seq data

Reliability of environmental sampling culture results using the negative binomial intraclass correlation coefficient.

Science.gov (United States)

Aly, Sharif S; Zhao, Jianyang; Li, Ben; Jiang, Jiming

2014-01-01

The Intraclass Correlation Coefficient (ICC) is commonly used to estimate the similarity between quantitative measures obtained from different sources. Overdispersed data is traditionally transformed so that linear mixed model (LMM) based ICC can be estimated. A common transformation used is the natural logarithm. The reliability of environmental sampling of fecal slurry on freestall pens has been estimated for Mycobacterium avium subsp. paratuberculosis using the natural logarithm transformed culture results. Recently, the negative binomial ICC was defined based on a generalized linear mixed model for negative binomial distributed data. The current study reports on the negative binomial ICC estimate which includes fixed effects using culture results of environmental samples. Simulations using a wide variety of inputs and negative binomial distribution parameters (r; p) showed better performance of the new negative binomial ICC compared to the ICC based on LMM even when negative binomial data was logarithm, and square root transformed. A second comparison that targeted a wider range of ICC values showed that the mean of estimated ICC closely approximated the true ICC.

A Mechanistic Beta-Binomial Probability Model for mRNA Sequencing Data.

Science.gov (United States)

Smith, Gregory R; Birtwistle, Marc R

2016-01-01

A main application for mRNA sequencing (mRNAseq) is determining lists of differentially-expressed genes (DEGs) between two or more conditions. Several software packages exist to produce DEGs from mRNAseq data, but they typically yield different DEGs, sometimes markedly so. The underlying probability model used to describe mRNAseq data is central to deriving DEGs, and not surprisingly most softwares use different models and assumptions to analyze mRNAseq data. Here, we propose a mechanistic justification to model mRNAseq as a binomial process, with data from technical replicates given by a binomial distribution, and data from biological replicates well-described by a beta-binomial distribution. We demonstrate good agreement of this model with two large datasets. We show that an emergent feature of the beta-binomial distribution, given parameter regimes typical for mRNAseq experiments, is the well-known quadratic polynomial scaling of variance with the mean. The so-called dispersion parameter controls this scaling, and our analysis suggests that the dispersion parameter is a continually decreasing function of the mean, as opposed to current approaches that impose an asymptotic value to the dispersion parameter at moderate mean read counts. We show how this leads to current approaches overestimating variance for moderately to highly expressed genes, which inflates false negative rates. Describing mRNAseq data with a beta-binomial distribution thus may be preferred since its parameters are relatable to the mechanistic underpinnings of the technique and may improve the consistency of DEG analysis across softwares, particularly for moderately to highly expressed genes.

On a Fractional Binomial Process

Science.gov (United States)

Cahoy, Dexter O.; Polito, Federico

2012-02-01

The classical binomial process has been studied by Jakeman (J. Phys. A 23:2815-2825, 1990) (and the references therein) and has been used to characterize a series of radiation states in quantum optics. In particular, he studied a classical birth-death process where the chance of birth is proportional to the difference between a larger fixed number and the number of individuals present. It is shown that at large times, an equilibrium is reached which follows a binomial process. In this paper, the classical binomial process is generalized using the techniques of fractional calculus and is called the fractional binomial process. The fractional binomial process is shown to preserve the binomial limit at large times while expanding the class of models that include non-binomial fluctuations (non-Markovian) at regular and small times. As a direct consequence, the generality of the fractional binomial model makes the proposed model more desirable than its classical counterpart in describing real physical processes. More statistical properties are also derived.

Detecting non-binomial sex allocation when developmental mortality operates.

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Wilkinson, Richard D; Kapranas, Apostolos; Hardy, Ian C W

2016-11-07

Optimal sex allocation theory is one of the most intricately developed areas of evolutionary ecology. Under a range of conditions, particularly under population sub-division, selection favours sex being allocated to offspring non-randomly, generating non-binomial variances of offspring group sex ratios. Detecting non-binomial sex allocation is complicated by stochastic developmental mortality, as offspring sex can often only be identified on maturity with the sex of non-maturing offspring remaining unknown. We show that current approaches for detecting non-binomiality have limited ability to detect non-binomial sex allocation when developmental mortality has occurred. We present a new procedure using an explicit model of sex allocation and mortality and develop a Bayesian model selection approach (available as an R package). We use the double and multiplicative binomial distributions to model over- and under-dispersed sex allocation and show how to calculate Bayes factors for comparing these alternative models to the null hypothesis of binomial sex allocation. The ability to detect non-binomial sex allocation is greatly increased, particularly in cases where mortality is common. The use of Bayesian methods allows for the quantification of the evidence in favour of each hypothesis, and our modelling approach provides an improved descriptive capability over existing approaches. We use a simulation study to demonstrate substantial improvements in power for detecting non-binomial sex allocation in situations where current methods fail, and we illustrate the approach in real scenarios using empirically obtained datasets on the sexual composition of groups of gregarious parasitoid wasps. Copyright © 2016 Elsevier Ltd. All rights reserved.

Longitudinal beta-binomial modeling using GEE for overdispersed binomial data.

Science.gov (United States)

Wu, Hongqian; Zhang, Ying; Long, Jeffrey D

2017-03-15

Longitudinal binomial data are frequently generated from multiple questionnaires and assessments in various scientific settings for which the binomial data are often overdispersed. The standard generalized linear mixed effects model may result in severe underestimation of standard errors of estimated regression parameters in such cases and hence potentially bias the statistical inference. In this paper, we propose a longitudinal beta-binomial model for overdispersed binomial data and estimate the regression parameters under a probit model using the generalized estimating equation method. A hybrid algorithm of the Fisher scoring and the method of moments is implemented for computing the method. Extensive simulation studies are conducted to justify the validity of the proposed method. Finally, the proposed method is applied to analyze functional impairment in subjects who are at risk of Huntington disease from a multisite observational study of prodromal Huntington disease. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Estimating negative binomial parameters from occurrence data with detection times.

Science.gov (United States)

Hwang, Wen-Han; Huggins, Richard; Stoklosa, Jakub

2016-11-01

The negative binomial distribution is a common model for the analysis of count data in biology and ecology. In many applications, we may not observe the complete frequency count in a quadrat but only that a species occurred in the quadrat. If only occurrence data are available then the two parameters of the negative binomial distribution, the aggregation index and the mean, are not identifiable. This can be overcome by data augmentation or through modeling the dependence between quadrat occupancies. Here, we propose to record the (first) detection time while collecting occurrence data in a quadrat. We show that under what we call proportionate sampling, where the time to survey a region is proportional to the area of the region, that both negative binomial parameters are estimable. When the mean parameter is larger than two, our proposed approach is more efficient than the data augmentation method developed by Solow and Smith (, Am. Nat. 176, 96-98), and in general is cheaper to conduct. We also investigate the effect of misidentification when collecting negative binomially distributed data, and conclude that, in general, the effect can be simply adjusted for provided that the mean and variance of misidentification probabilities are known. The results are demonstrated in a simulation study and illustrated in several real examples. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Binomial Rings: Axiomatisation, Transfer and Classification

OpenAIRE

Xantcha, Qimh Richey

2011-01-01

Hall's binomial rings, rings with binomial coefficients, are given an axiomatisation and proved identical to the numerical rings studied by Ekedahl. The Binomial Transfer Principle is established, enabling combinatorial proofs of algebraical identities. The finitely generated binomial rings are completely classified. An application to modules over binomial rings is given.

The validity of the negative binomial multiplicity distribution in the case of the relativistic nucleus-nucleus interaction

International Nuclear Information System (INIS)

Ghosh, D.; Mukhopadhyay, A.; Ghosh, A.; Roy, J.

1989-01-01

This letter presents new data on the multiplicity distribution of charged secondaries in 24 Mg interactions with AgBr at 4.5 GeV/c per nucleon. The validity of the negative binomial distribution (NBD) is studied. It is observed that the data can be well parametrized in terms of the NBD law for the whole phase space and also for different pseudo-rapidity bins. A comparison of different parameters with those in the case of h-h interactions reveals some interesting results, the implications of which are discussed. (orig.)

Simulation on Poisson and negative binomial models of count road accident modeling

Science.gov (United States)

Sapuan, M. S.; Razali, A. M.; Zamzuri, Z. H.; Ibrahim, K.

2016-11-01

Accident count data have often been shown to have overdispersion. On the other hand, the data might contain zero count (excess zeros). The simulation study was conducted to create a scenarios which an accident happen in T-junction with the assumption the dependent variables of generated data follows certain distribution namely Poisson and negative binomial distribution with different sample size of n=30 to n=500. The study objective was accomplished by fitting Poisson regression, negative binomial regression and Hurdle negative binomial model to the simulated data. The model validation was compared and the simulation result shows for each different sample size, not all model fit the data nicely even though the data generated from its own distribution especially when the sample size is larger. Furthermore, the larger sample size indicates that more zeros accident count in the dataset.

Measured PET Data Characterization with the Negative Binomial Distribution Model.

Science.gov (United States)

Santarelli, Maria Filomena; Positano, Vincenzo; Landini, Luigi

2017-01-01

Accurate statistical model of PET measurements is a prerequisite for a correct image reconstruction when using statistical image reconstruction algorithms, or when pre-filtering operations must be performed. Although radioactive decay follows a Poisson distribution, deviation from Poisson statistics occurs on projection data prior to reconstruction due to physical effects, measurement errors, correction of scatter and random coincidences. Modelling projection data can aid in understanding the statistical nature of the data in order to develop efficient processing methods and to reduce noise. This paper outlines the statistical behaviour of measured emission data evaluating the goodness of fit of the negative binomial (NB) distribution model to PET data for a wide range of emission activity values. An NB distribution model is characterized by the mean of the data and the dispersion parameter α that describes the deviation from Poisson statistics. Monte Carlo simulations were performed to evaluate: (a) the performances of the dispersion parameter α estimator, (b) the goodness of fit of the NB model for a wide range of activity values. We focused on the effect produced by correction for random and scatter events in the projection (sinogram) domain, due to their importance in quantitative analysis of PET data. The analysis developed herein allowed us to assess the accuracy of the NB distribution model to fit corrected sinogram data, and to evaluate the sensitivity of the dispersion parameter α to quantify deviation from Poisson statistics. By the sinogram ROI-based analysis, it was demonstrated that deviation on the measured data from Poisson statistics can be quantitatively characterized by the dispersion parameter α, in any noise conditions and corrections.

A mixed-binomial model for Likert-type personality measures.

Science.gov (United States)

Allik, Jüri

2014-01-01

Personality measurement is based on the idea that values on an unobservable latent variable determine the distribution of answers on a manifest response scale. Typically, it is assumed in the Item Response Theory (IRT) that latent variables are related to the observed responses through continuous normal or logistic functions, determining the probability with which one of the ordered response alternatives on a Likert-scale item is chosen. Based on an analysis of 1731 self- and other-rated responses on the 240 NEO PI-3 questionnaire items, it was proposed that a viable alternative is a finite number of latent events which are related to manifest responses through a binomial function which has only one parameter-the probability with which a given statement is approved. For the majority of items, the best fit was obtained with a mixed-binomial distribution, which assumes two different subpopulations who endorse items with two different probabilities. It was shown that the fit of the binomial IRT model can be improved by assuming that about 10% of random noise is contained in the answers and by taking into account response biases toward one of the response categories. It was concluded that the binomial response model for the measurement of personality traits may be a workable alternative to the more habitual normal and logistic IRT models.

A comparison of LMC and SDL complexity measures on binomial distributions

Science.gov (United States)

Piqueira, José Roberto C.

2016-02-01

The concept of complexity has been widely discussed in the last forty years, with a lot of thinking contributions coming from all areas of the human knowledge, including Philosophy, Linguistics, History, Biology, Physics, Chemistry and many others, with mathematicians trying to give a rigorous view of it. In this sense, thermodynamics meets information theory and, by using the entropy definition, López-Ruiz, Mancini and Calbet proposed a definition for complexity that is referred as LMC measure. Shiner, Davison and Landsberg, by slightly changing the LMC definition, proposed the SDL measure and the both, LMC and SDL, are satisfactory to measure complexity for a lot of problems. Here, SDL and LMC measures are applied to the case of a binomial probability distribution, trying to clarify how the length of the data set implies complexity and how the success probability of the repeated trials determines how complex the whole set is.

Binomial collisions and near collisions

OpenAIRE

Blokhuis, Aart; Brouwer, Andries; de Weger, Benne

2017-01-01

We describe efficient algorithms to search for cases in which binomial coefficients are equal or almost equal, give a conjecturally complete list of all cases where two binomial coefficients differ by 1, and give some identities for binomial coefficients that seem to be new.

Meta-analysis of studies with bivariate binary outcomes: a marginal beta-binomial model approach.

Science.gov (United States)

Chen, Yong; Hong, Chuan; Ning, Yang; Su, Xiao

2016-01-15

When conducting a meta-analysis of studies with bivariate binary outcomes, challenges arise when the within-study correlation and between-study heterogeneity should be taken into account. In this paper, we propose a marginal beta-binomial model for the meta-analysis of studies with binary outcomes. This model is based on the composite likelihood approach and has several attractive features compared with the existing models such as bivariate generalized linear mixed model (Chu and Cole, 2006) and Sarmanov beta-binomial model (Chen et al., 2012). The advantages of the proposed marginal model include modeling the probabilities in the original scale, not requiring any transformation of probabilities or any link function, having closed-form expression of likelihood function, and no constraints on the correlation parameter. More importantly, because the marginal beta-binomial model is only based on the marginal distributions, it does not suffer from potential misspecification of the joint distribution of bivariate study-specific probabilities. Such misspecification is difficult to detect and can lead to biased inference using currents methods. We compare the performance of the marginal beta-binomial model with the bivariate generalized linear mixed model and the Sarmanov beta-binomial model by simulation studies. Interestingly, the results show that the marginal beta-binomial model performs better than the Sarmanov beta-binomial model, whether or not the true model is Sarmanov beta-binomial, and the marginal beta-binomial model is more robust than the bivariate generalized linear mixed model under model misspecifications. Two meta-analyses of diagnostic accuracy studies and a meta-analysis of case-control studies are conducted for illustration. Copyright © 2015 John Wiley & Sons, Ltd.

Biased binomial assessment of cross-validated estimation of classification accuracies illustrated in diagnosis predictions.

Science.gov (United States)

Noirhomme, Quentin; Lesenfants, Damien; Gomez, Francisco; Soddu, Andrea; Schrouff, Jessica; Garraux, Gaëtan; Luxen, André; Phillips, Christophe; Laureys, Steven

2014-01-01

Multivariate classification is used in neuroimaging studies to infer brain activation or in medical applications to infer diagnosis. Their results are often assessed through either a binomial or a permutation test. Here, we simulated classification results of generated random data to assess the influence of the cross-validation scheme on the significance of results. Distributions built from classification of random data with cross-validation did not follow the binomial distribution. The binomial test is therefore not adapted. On the contrary, the permutation test was unaffected by the cross-validation scheme. The influence of the cross-validation was further illustrated on real-data from a brain-computer interface experiment in patients with disorders of consciousness and from an fMRI study on patients with Parkinson disease. Three out of 16 patients with disorders of consciousness had significant accuracy on binomial testing, but only one showed significant accuracy using permutation testing. In the fMRI experiment, the mental imagery of gait could discriminate significantly between idiopathic Parkinson's disease patients and healthy subjects according to the permutation test but not according to the binomial test. Hence, binomial testing could lead to biased estimation of significance and false positive or negative results. In our view, permutation testing is thus recommended for clinical application of classification with cross-validation.

An efficient binomial model-based measure for sequence comparison and its application.

Science.gov (United States)

Liu, Xiaoqing; Dai, Qi; Li, Lihua; He, Zerong

2011-04-01

Sequence comparison is one of the major tasks in bioinformatics, which could serve as evidence of structural and functional conservation, as well as of evolutionary relations. There are several similarity/dissimilarity measures for sequence comparison, but challenges remains. This paper presented a binomial model-based measure to analyze biological sequences. With help of a random indicator, the occurrence of a word at any position of sequence can be regarded as a random Bernoulli variable, and the distribution of a sum of the word occurrence is well known to be a binomial one. By using a recursive formula, we computed the binomial probability of the word count and proposed a binomial model-based measure based on the relative entropy. The proposed measure was tested by extensive experiments including classification of HEV genotypes and phylogenetic analysis, and further compared with alignment-based and alignment-free measures. The results demonstrate that the proposed measure based on binomial model is more efficient.

Expansion around half-integer values, binomial sums, and inverse binomial sums

International Nuclear Information System (INIS)

Weinzierl, Stefan

2004-01-01

I consider the expansion of transcendental functions in a small parameter around rational numbers. This includes in particular the expansion around half-integer values. I present algorithms which are suitable for an implementation within a symbolic computer algebra system. The method is an extension of the technique of nested sums. The algorithms allow in addition the evaluation of binomial sums, inverse binomial sums and generalizations thereof

Non-binomial distribution of palladium Kα Ln X-ray satellites emitted after excitation by 16O ions

International Nuclear Information System (INIS)

Rymuza, P.; Sujkowski, Z.; Carlen, M.; Dousse, J.C.; Gasser, M.; Kern, J.; Perny, B.; Rheme, C.

1988-02-01

The palladium K α L n X-ray satellites spectrum emitted after excitation by 5.4 MeV/u 16 O ions has been measured. The distribution of the satellites yield is found to be significantly narrower than the binomial one. The deviations can be accounted for by assuming that the L-shell ionization is due to two uncorrelated processes: the direct ionization by impact and the electron capture to the K-shell of the projectile. 12 refs., 1 fig., 1 tab. (author)

Biased binomial assessment of cross-validated estimation of classification accuracies illustrated in diagnosis predictions

Directory of Open Access Journals (Sweden)

Quentin Noirhomme

2014-01-01

Full Text Available Multivariate classification is used in neuroimaging studies to infer brain activation or in medical applications to infer diagnosis. Their results are often assessed through either a binomial or a permutation test. Here, we simulated classification results of generated random data to assess the influence of the cross-validation scheme on the significance of results. Distributions built from classification of random data with cross-validation did not follow the binomial distribution. The binomial test is therefore not adapted. On the contrary, the permutation test was unaffected by the cross-validation scheme. The influence of the cross-validation was further illustrated on real-data from a brain–computer interface experiment in patients with disorders of consciousness and from an fMRI study on patients with Parkinson disease. Three out of 16 patients with disorders of consciousness had significant accuracy on binomial testing, but only one showed significant accuracy using permutation testing. In the fMRI experiment, the mental imagery of gait could discriminate significantly between idiopathic Parkinson's disease patients and healthy subjects according to the permutation test but not according to the binomial test. Hence, binomial testing could lead to biased estimation of significance and false positive or negative results. In our view, permutation testing is thus recommended for clinical application of classification with cross-validation.

NEWTONP - CUMULATIVE BINOMIAL PROGRAMS

Science.gov (United States)

Bowerman, P. N.

1994-01-01

The cumulative binomial program, NEWTONP, is one of a set of three programs which calculate cumulative binomial probability distributions for arbitrary inputs. The three programs, NEWTONP, CUMBIN (NPO-17555), and CROSSER (NPO-17557), can be used independently of one another. NEWTONP can be used by statisticians and users of statistical procedures, test planners, designers, and numerical analysts. The program has been used for reliability/availability calculations. NEWTONP calculates the probably p required to yield a given system reliability V for a k-out-of-n system. It can also be used to determine the Clopper-Pearson confidence limits (either one-sided or two-sided) for the parameter p of a Bernoulli distribution. NEWTONP can determine Bayesian probability limits for a proportion (if the beta prior has positive integer parameters). It can determine the percentiles of incomplete beta distributions with positive integer parameters. It can also determine the percentiles of F distributions and the midian plotting positions in probability plotting. NEWTONP is designed to work well with all integer values 0 < k <= n. To run the program, the user simply runs the executable version and inputs the information requested by the program. NEWTONP is not designed to weed out incorrect inputs, so the user must take care to make sure the inputs are correct. Once all input has been entered, the program calculates and lists the result. It also lists the number of iterations of Newton's method required to calculate the answer within the given error. The NEWTONP program is written in C. It was developed on an IBM AT with a numeric co-processor using Microsoft C 5.0. Because the source code is written using standard C structures and functions, it should compile correctly with most C compilers. The program format is interactive. It has been implemented under DOS 3.2 and has a memory requirement of 26K. NEWTONP was developed in 1988.

Pooling overdispersed binomial data to estimate event rate.

Science.gov (United States)

Young-Xu, Yinong; Chan, K Arnold

2008-08-19

The beta-binomial model is one of the methods that can be used to validly combine event rates from overdispersed binomial data. Our objective is to provide a full description of this method and to update and broaden its applications in clinical and public health research. We describe the statistical theories behind the beta-binomial model and the associated estimation methods. We supply information about statistical software that can provide beta-binomial estimations. Using a published example, we illustrate the application of the beta-binomial model when pooling overdispersed binomial data. In an example regarding the safety of oral antifungal treatments, we had 41 treatment arms with event rates varying from 0% to 13.89%. Using the beta-binomial model, we obtained a summary event rate of 3.44% with a standard error of 0.59%. The parameters of the beta-binomial model took the values of 1.24 for alpha and 34.73 for beta. The beta-binomial model can provide a robust estimate for the summary event rate by pooling overdispersed binomial data from different studies. The explanation of the method and the demonstration of its applications should help researchers incorporate the beta-binomial method as they aggregate probabilities of events from heterogeneous studies.

Pooling overdispersed binomial data to estimate event rate

Directory of Open Access Journals (Sweden)

Chan K Arnold

2008-08-01

Full Text Available Abstract Background The beta-binomial model is one of the methods that can be used to validly combine event rates from overdispersed binomial data. Our objective is to provide a full description of this method and to update and broaden its applications in clinical and public health research. Methods We describe the statistical theories behind the beta-binomial model and the associated estimation methods. We supply information about statistical software that can provide beta-binomial estimations. Using a published example, we illustrate the application of the beta-binomial model when pooling overdispersed binomial data. Results In an example regarding the safety of oral antifungal treatments, we had 41 treatment arms with event rates varying from 0% to 13.89%. Using the beta-binomial model, we obtained a summary event rate of 3.44% with a standard error of 0.59%. The parameters of the beta-binomial model took the values of 1.24 for alpha and 34.73 for beta. Conclusion The beta-binomial model can provide a robust estimate for the summary event rate by pooling overdispersed binomial data from different studies. The explanation of the method and the demonstration of its applications should help researchers incorporate the beta-binomial method as they aggregate probabilities of events from heterogeneous studies.

Una prueba de razón de verosimilitudes para discriminar entre la distribución Poisson, Binomial y Binomial Negativa.

OpenAIRE

López Martínez, Laura Elizabeth

2010-01-01

En este trabajo se realiza inferencia estadística en la distribución Binomial Negativa Generalizada (BNG) y los modelos que anida, los cuales son Binomial, Binomial Negativa y Poisson. Se aborda el problema de estimación de parámetros en la distribución BNG y se propone una prueba de razón de verosimilitud generalizada para discernir si un conjunto de datos se ajusta en particular al modelo Binomial, Binomial Negativa o Poisson. Además, se estudian las potencias y tamaños de la prueba p...

Log-binomial models: exploring failed convergence.

Science.gov (United States)

Williamson, Tyler; Eliasziw, Misha; Fick, Gordon Hilton

2013-12-13

Relative risk is a summary metric that is commonly used in epidemiological investigations. Increasingly, epidemiologists are using log-binomial models to study the impact of a set of predictor variables on a single binary outcome, as they naturally offer relative risks. However, standard statistical software may report failed convergence when attempting to fit log-binomial models in certain settings. The methods that have been proposed in the literature for dealing with failed convergence use approximate solutions to avoid the issue. This research looks directly at the log-likelihood function for the simplest log-binomial model where failed convergence has been observed, a model with a single linear predictor with three levels. The possible causes of failed convergence are explored and potential solutions are presented for some cases. Among the principal causes is a failure of the fitting algorithm to converge despite the log-likelihood function having a single finite maximum. Despite these limitations, log-binomial models are a viable option for epidemiologists wishing to describe the relationship between a set of predictors and a binary outcome where relative risk is the desired summary measure. Epidemiologists are encouraged to continue to use log-binomial models and advocate for improvements to the fitting algorithms to promote the widespread use of log-binomial models.

Zero inflated Poisson and negative binomial regression models: application in education.

Science.gov (United States)

Salehi, Masoud; Roudbari, Masoud

2015-01-01

The number of failed courses and semesters in students are indicators of their performance. These amounts have zero inflated (ZI) distributions. Using ZI Poisson and negative binomial distributions we can model these count data to find the associated factors and estimate the parameters. This study aims at to investigate the important factors related to the educational performance of students. This cross-sectional study performed in 2008-2009 at Iran University of Medical Sciences (IUMS) with a population of almost 6000 students, 670 students selected using stratified random sampling. The educational and demographical data were collected using the University records. The study design was approved at IUMS and the students' data kept confidential. The descriptive statistics and ZI Poisson and negative binomial regressions were used to analyze the data. The data were analyzed using STATA. In the number of failed semesters, Poisson and negative binomial distributions with ZI, students' total average and quota system had the most roles. For the number of failed courses, total average, and being in undergraduate or master levels had the most effect in both models. In all models the total average have the most effect on the number of failed courses or semesters. The next important factor is quota system in failed semester and undergraduate and master levels in failed courses. Therefore, average has an important inverse effect on the numbers of failed courses and semester.

Jumps in binomial AR(1) processes

OpenAIRE

Weiß , Christian H.

2009-01-01

Abstract We consider the binomial AR(1) model for serially dependent processes of binomial counts. After a review of its definition and known properties, we investigate marginal and serial properties of jumps in such processes. Based on these results, we propose the jumps control chart for monitoring a binomial AR(1) process. We show how to evaluate the performance of this control chart and give design recommendations. correspondance: Tel.: +49 931 31 84968; ...

A Bayesian Approach to Functional Mixed Effect Modeling for Longitudinal Data with Binomial Outcomes

Science.gov (United States)

Kliethermes, Stephanie; Oleson, Jacob

2014-01-01

Longitudinal growth patterns are routinely seen in medical studies where individual and population growth is followed over a period of time. Many current methods for modeling growth presuppose a parametric relationship between the outcome and time (e.g., linear, quadratic); however, these relationships may not accurately capture growth over time. Functional mixed effects (FME) models provide flexibility in handling longitudinal data with nonparametric temporal trends. Although FME methods are well-developed for continuous, normally distributed outcome measures, nonparametric methods for handling categorical outcomes are limited. We consider the situation with binomially distributed longitudinal outcomes. Although percent correct data can be modeled assuming normality, estimates outside the parameter space are possible and thus estimated curves can be unrealistic. We propose a binomial FME model using Bayesian methodology to account for growth curves with binomial (percentage) outcomes. The usefulness of our methods is demonstrated using a longitudinal study of speech perception outcomes from cochlear implant users where we successfully model both the population and individual growth trajectories. Simulation studies also advocate the usefulness of the binomial model particularly when outcomes occur near the boundary of the probability parameter space and in situations with a small number of trials. PMID:24723495

Comparison of multinomial and binomial proportion methods for analysis of multinomial count data.

Science.gov (United States)

Galyean, M L; Wester, D B

2010-10-01

Simulation methods were used to generate 1,000 experiments, each with 3 treatments and 10 experimental units/treatment, in completely randomized (CRD) and randomized complete block designs. Data were counts in 3 ordered or 4 nominal categories from multinomial distributions. For the 3-category analyses, category probabilities were 0.6, 0.3, and 0.1, respectively, for 2 of the treatments, and 0.5, 0.35, and 0.15 for the third treatment. In the 4-category analysis (CRD only), probabilities were 0.3, 0.3, 0.2, and 0.2 for treatments 1 and 2 vs. 0.4, 0.4, 0.1, and 0.1 for treatment 3. The 3-category data were analyzed with generalized linear mixed models as an ordered multinomial distribution with a cumulative logit link or by regrouping the data (e.g., counts in 1 category/sum of counts in all categories), followed by analysis of single categories as binomial proportions. Similarly, the 4-category data were analyzed as a nominal multinomial distribution with a glogit link or by grouping data as binomial proportions. For the 3-category CRD analyses, empirically determined type I error rates based on pair-wise comparisons (F- and Wald chi(2) tests) did not differ between multinomial and individual binomial category analyses with 10 (P = 0.38 to 0.60) or 50 (P = 0.19 to 0.67) sampling units/experimental unit. When analyzed as binomial proportions, power estimates varied among categories, with analysis of the category with the greatest counts yielding power similar to the multinomial analysis. Agreement between methods (percentage of experiments with the same results for the overall test for treatment effects) varied considerably among categories analyzed and sampling unit scenarios for the 3-category CRD analyses. Power (F-test) was 24.3, 49.1, 66.9, 83.5, 86.8, and 99.7% for 10, 20, 30, 40, 50, and 100 sampling units/experimental unit for the 3-category multinomial CRD analyses. Results with randomized complete block design simulations were similar to those with the CRD

Marginalized zero-inflated negative binomial regression with application to dental caries.

Science.gov (United States)

Preisser, John S; Das, Kalyan; Long, D Leann; Divaris, Kimon

2016-05-10

The zero-inflated negative binomial regression model (ZINB) is often employed in diverse fields such as dentistry, health care utilization, highway safety, and medicine to examine relationships between exposures of interest and overdispersed count outcomes exhibiting many zeros. The regression coefficients of ZINB have latent class interpretations for a susceptible subpopulation at risk for the disease/condition under study with counts generated from a negative binomial distribution and for a non-susceptible subpopulation that provides only zero counts. The ZINB parameters, however, are not well-suited for estimating overall exposure effects, specifically, in quantifying the effect of an explanatory variable in the overall mixture population. In this paper, a marginalized zero-inflated negative binomial regression (MZINB) model for independent responses is proposed to model the population marginal mean count directly, providing straightforward inference for overall exposure effects based on maximum likelihood estimation. Through simulation studies, the finite sample performance of MZINB is compared with marginalized zero-inflated Poisson, Poisson, and negative binomial regression. The MZINB model is applied in the evaluation of a school-based fluoride mouthrinse program on dental caries in 677 children. Copyright © 2015 John Wiley & Sons, Ltd.

Use of negative binomial distribution to describe the presence of Anisakis in Thyrsites atun Uso de distribuição binomial negativa para descrever a presença de Anisakis em Thyrsites atun

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Patricio Peña-Rehbein

2012-03-01

Full Text Available Nematodes of the genus Anisakis have marine fishes as intermediate hosts. One of these hosts is Thyrsites atun, an important fishery resource in Chile between 38 and 41° S. This paper describes the frequency and number of Anisakis nematodes in the internal organs of Thyrsites atun. An analysis based on spatial distribution models showed that the parasites tend to be clustered. The variation in the number of parasites per host could be described by the negative binomial distribution. The maximum observed number of parasites was nine parasites per host. The environmental and zoonotic aspects of the study are also discussed.Nematóides do gênero Anisakis têm nos peixes marinhos seus hospedeiros intermediários. Um desses hospedeiros é Thyrsites atun, um importante recurso pesqueiro no Chile entre 38 e 41° S. Este artigo descreve a freqüência e o número de nematóides Anisakis nos órgãos internos de Thyrsites atun. Uma análise baseada em modelos de distribuição espacial demonstrou que os parasitos tendem a ficar agrupados. A variação numérica de parasitas por hospedeiro pôde ser descrita por distribuição binomial negativa. O número máximo observado de parasitas por hospedeiro foi nove. Os aspectos ambientais e zoonóticos desse estudo também serão discutidos.

Beta-binomial model for meta-analysis of odds ratios.

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Bakbergenuly, Ilyas; Kulinskaya, Elena

2017-05-20

In meta-analysis of odds ratios (ORs), heterogeneity between the studies is usually modelled via the additive random effects model (REM). An alternative, multiplicative REM for ORs uses overdispersion. The multiplicative factor in this overdispersion model (ODM) can be interpreted as an intra-class correlation (ICC) parameter. This model naturally arises when the probabilities of an event in one or both arms of a comparative study are themselves beta-distributed, resulting in beta-binomial distributions. We propose two new estimators of the ICC for meta-analysis in this setting. One is based on the inverted Breslow-Day test, and the other on the improved gamma approximation by Kulinskaya and Dollinger (2015, p. 26) to the distribution of Cochran's Q. The performance of these and several other estimators of ICC on bias and coverage is studied by simulation. Additionally, the Mantel-Haenszel approach to estimation of ORs is extended to the beta-binomial model, and we study performance of various ICC estimators when used in the Mantel-Haenszel or the inverse-variance method to combine ORs in meta-analysis. The results of the simulations show that the improved gamma-based estimator of ICC is superior for small sample sizes, and the Breslow-Day-based estimator is the best for n⩾100. The Mantel-Haenszel-based estimator of OR is very biased and is not recommended. The inverse-variance approach is also somewhat biased for ORs≠1, but this bias is not very large in practical settings. Developed methods and R programs, provided in the Web Appendix, make the beta-binomial model a feasible alternative to the standard REM for meta-analysis of ORs. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd. © 2017 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

A Bayesian approach to functional mixed-effects modeling for longitudinal data with binomial outcomes.

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Kliethermes, Stephanie; Oleson, Jacob

2014-08-15

Longitudinal growth patterns are routinely seen in medical studies where individual growth and population growth are followed up over a period of time. Many current methods for modeling growth presuppose a parametric relationship between the outcome and time (e.g., linear and quadratic); however, these relationships may not accurately capture growth over time. Functional mixed-effects (FME) models provide flexibility in handling longitudinal data with nonparametric temporal trends. Although FME methods are well developed for continuous, normally distributed outcome measures, nonparametric methods for handling categorical outcomes are limited. We consider the situation with binomially distributed longitudinal outcomes. Although percent correct data can be modeled assuming normality, estimates outside the parameter space are possible, and thus, estimated curves can be unrealistic. We propose a binomial FME model using Bayesian methodology to account for growth curves with binomial (percentage) outcomes. The usefulness of our methods is demonstrated using a longitudinal study of speech perception outcomes from cochlear implant users where we successfully model both the population and individual growth trajectories. Simulation studies also advocate the usefulness of the binomial model particularly when outcomes occur near the boundary of the probability parameter space and in situations with a small number of trials. Copyright © 2014 John Wiley & Sons, Ltd.

PENERAPAN REGRESI BINOMIAL NEGATIF UNTUK MENGATASI OVERDISPERSI PADA REGRESI POISSON

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PUTU SUSAN PRADAWATI

2013-09-01

Full Text Available Poisson regression was used to analyze the count data which Poisson distributed. Poisson regression analysis requires state equidispersion, in which the mean value of the response variable is equal to the value of the variance. However, there are deviations in which the value of the response variable variance is greater than the mean. This is called overdispersion. If overdispersion happens and Poisson Regression analysis is being used, then underestimated standard errors will be obtained. Negative Binomial Regression can handle overdispersion because it contains a dispersion parameter. From the simulation data which experienced overdispersion in the Poisson Regression model it was found that the Negative Binomial Regression was better than the Poisson Regression model.

CROSSER - CUMULATIVE BINOMIAL PROGRAMS

Science.gov (United States)

Bowerman, P. N.

1994-01-01

The cumulative binomial program, CROSSER, is one of a set of three programs which calculate cumulative binomial probability distributions for arbitrary inputs. The three programs, CROSSER, CUMBIN (NPO-17555), and NEWTONP (NPO-17556), can be used independently of one another. CROSSER can be used by statisticians and users of statistical procedures, test planners, designers, and numerical analysts. The program has been used for reliability/availability calculations. CROSSER calculates the point at which the reliability of a k-out-of-n system equals the common reliability of the n components. It is designed to work well with all integer values 0 < k <= n. To run the program, the user simply runs the executable version and inputs the information requested by the program. The program is not designed to weed out incorrect inputs, so the user must take care to make sure the inputs are correct. Once all input has been entered, the program calculates and lists the result. It also lists the number of iterations of Newton's method required to calculate the answer within the given error. The CROSSER program is written in C. It was developed on an IBM AT with a numeric co-processor using Microsoft C 5.0. Because the source code is written using standard C structures and functions, it should compile correctly with most C compilers. The program format is interactive. It has been implemented under DOS 3.2 and has a memory requirement of 26K. CROSSER was developed in 1988.

A comparison of observation-level random effect and Beta-Binomial models for modelling overdispersion in Binomial data in ecology & evolution.

Science.gov (United States)

Harrison, Xavier A

2015-01-01

Overdispersion is a common feature of models of biological data, but researchers often fail to model the excess variation driving the overdispersion, resulting in biased parameter estimates and standard errors. Quantifying and modeling overdispersion when it is present is therefore critical for robust biological inference. One means to account for overdispersion is to add an observation-level random effect (OLRE) to a model, where each data point receives a unique level of a random effect that can absorb the extra-parametric variation in the data. Although some studies have investigated the utility of OLRE to model overdispersion in Poisson count data, studies doing so for Binomial proportion data are scarce. Here I use a simulation approach to investigate the ability of both OLRE models and Beta-Binomial models to recover unbiased parameter estimates in mixed effects models of Binomial data under various degrees of overdispersion. In addition, as ecologists often fit random intercept terms to models when the random effect sample size is low (model types under a range of random effect sample sizes when overdispersion is present. Simulation results revealed that the efficacy of OLRE depends on the process that generated the overdispersion; OLRE failed to cope with overdispersion generated from a Beta-Binomial mixture model, leading to biased slope and intercept estimates, but performed well for overdispersion generated by adding random noise to the linear predictor. Comparison of parameter estimates from an OLRE model with those from its corresponding Beta-Binomial model readily identified when OLRE were performing poorly due to disagreement between effect sizes, and this strategy should be employed whenever OLRE are used for Binomial data to assess their reliability. Beta-Binomial models performed well across all contexts, but showed a tendency to underestimate effect sizes when modelling non-Beta-Binomial data. Finally, both OLRE and Beta-Binomial models performed

Generation of the reciprocal-binomial state for optical fields

International Nuclear Information System (INIS)

Valverde, C.; Avelar, A.T.; Baseia, B.; Malbouisson, J.M.C.

2003-01-01

We compare the efficiencies of two interesting schemes to generate truncated states of the light field in running modes, namely the 'quantum scissors' and the 'beam-splitter array' schemes. The latter is applied to create the reciprocal-binomial state as a travelling wave, required to implement recent experimental proposals of phase-distribution determination and of quantum lithography

Stochastic analysis of complex reaction networks using binomial moment equations.

Science.gov (United States)

Barzel, Baruch; Biham, Ofer

2012-09-01

The stochastic analysis of complex reaction networks is a difficult problem because the number of microscopic states in such systems increases exponentially with the number of reactive species. Direct integration of the master equation is thus infeasible and is most often replaced by Monte Carlo simulations. While Monte Carlo simulations are a highly effective tool, equation-based formulations are more amenable to analytical treatment and may provide deeper insight into the dynamics of the network. Here, we present a highly efficient equation-based method for the analysis of stochastic reaction networks. The method is based on the recently introduced binomial moment equations [Barzel and Biham, Phys. Rev. Lett. 106, 150602 (2011)]. The binomial moments are linear combinations of the ordinary moments of the probability distribution function of the population sizes of the interacting species. They capture the essential combinatorics of the reaction processes reflecting their stoichiometric structure. This leads to a simple and transparent form of the equations, and allows a highly efficient and surprisingly simple truncation scheme. Unlike ordinary moment equations, in which the inclusion of high order moments is prohibitively complicated, the binomial moment equations can be easily constructed up to any desired order. The result is a set of equations that enables the stochastic analysis of complex reaction networks under a broad range of conditions. The number of equations is dramatically reduced from the exponential proliferation of the master equation to a polynomial (and often quadratic) dependence on the number of reactive species in the binomial moment equations. The aim of this paper is twofold: to present a complete derivation of the binomial moment equations; to demonstrate the applicability of the moment equations for a representative set of example networks, in which stochastic effects play an important role.

Problems on Divisibility of Binomial Coefficients

Science.gov (United States)

Osler, Thomas J.; Smoak, James

2004-01-01

Twelve unusual problems involving divisibility of the binomial coefficients are represented in this article. The problems are listed in "The Problems" section. All twelve problems have short solutions which are listed in "The Solutions" section. These problems could be assigned to students in any course in which the binomial theorem and Pascal's…

Predicting Cumulative Incidence Probability by Direct Binomial Regression

DEFF Research Database (Denmark)

Scheike, Thomas H.; Zhang, Mei-Jie

Binomial modelling; cumulative incidence probability; cause-specific hazards; subdistribution hazard......Binomial modelling; cumulative incidence probability; cause-specific hazards; subdistribution hazard...

A comparison of observation-level random effect and Beta-Binomial models for modelling overdispersion in Binomial data in ecology & evolution

Directory of Open Access Journals (Sweden)

Xavier A. Harrison

2015-07-01

Full Text Available Overdispersion is a common feature of models of biological data, but researchers often fail to model the excess variation driving the overdispersion, resulting in biased parameter estimates and standard errors. Quantifying and modeling overdispersion when it is present is therefore critical for robust biological inference. One means to account for overdispersion is to add an observation-level random effect (OLRE to a model, where each data point receives a unique level of a random effect that can absorb the extra-parametric variation in the data. Although some studies have investigated the utility of OLRE to model overdispersion in Poisson count data, studies doing so for Binomial proportion data are scarce. Here I use a simulation approach to investigate the ability of both OLRE models and Beta-Binomial models to recover unbiased parameter estimates in mixed effects models of Binomial data under various degrees of overdispersion. In addition, as ecologists often fit random intercept terms to models when the random effect sample size is low (<5 levels, I investigate the performance of both model types under a range of random effect sample sizes when overdispersion is present. Simulation results revealed that the efficacy of OLRE depends on the process that generated the overdispersion; OLRE failed to cope with overdispersion generated from a Beta-Binomial mixture model, leading to biased slope and intercept estimates, but performed well for overdispersion generated by adding random noise to the linear predictor. Comparison of parameter estimates from an OLRE model with those from its corresponding Beta-Binomial model readily identified when OLRE were performing poorly due to disagreement between effect sizes, and this strategy should be employed whenever OLRE are used for Binomial data to assess their reliability. Beta-Binomial models performed well across all contexts, but showed a tendency to underestimate effect sizes when modelling non-Beta-Binomial

Comparison of beta-binomial regression model approaches to analyze health-related quality of life data.

Science.gov (United States)

Najera-Zuloaga, Josu; Lee, Dae-Jin; Arostegui, Inmaculada

2017-01-01

Health-related quality of life has become an increasingly important indicator of health status in clinical trials and epidemiological research. Moreover, the study of the relationship of health-related quality of life with patients and disease characteristics has become one of the primary aims of many health-related quality of life studies. Health-related quality of life scores are usually assumed to be distributed as binomial random variables and often highly skewed. The use of the beta-binomial distribution in the regression context has been proposed to model such data; however, the beta-binomial regression has been performed by means of two different approaches in the literature: (i) beta-binomial distribution with a logistic link; and (ii) hierarchical generalized linear models. None of the existing literature in the analysis of health-related quality of life survey data has performed a comparison of both approaches in terms of adequacy and regression parameter interpretation context. This paper is motivated by the analysis of a real data application of health-related quality of life outcomes in patients with Chronic Obstructive Pulmonary Disease, where the use of both approaches yields to contradictory results in terms of covariate effects significance and consequently the interpretation of the most relevant factors in health-related quality of life. We present an explanation of the results in both methodologies through a simulation study and address the need to apply the proper approach in the analysis of health-related quality of life survey data for practitioners, providing an R package.

Analysis of hypoglycemic events using negative binomial models.

Science.gov (United States)

Luo, Junxiang; Qu, Yongming

2013-01-01

Negative binomial regression is a standard model to analyze hypoglycemic events in diabetes clinical trials. Adjusting for baseline covariates could potentially increase the estimation efficiency of negative binomial regression. However, adjusting for covariates raises concerns about model misspecification, in which the negative binomial regression is not robust because of its requirement for strong model assumptions. In some literature, it was suggested to correct the standard error of the maximum likelihood estimator through introducing overdispersion, which can be estimated by the Deviance or Pearson Chi-square. We proposed to conduct the negative binomial regression using Sandwich estimation to calculate the covariance matrix of the parameter estimates together with Pearson overdispersion correction (denoted by NBSP). In this research, we compared several commonly used negative binomial model options with our proposed NBSP. Simulations and real data analyses showed that NBSP is the most robust to model misspecification, and the estimation efficiency will be improved by adjusting for baseline hypoglycemia. Copyright © 2013 John Wiley & Sons, Ltd.

Perbandingan Regresi Binomial Negatif dan Regresi Conway-Maxwell-Poisson dalam Mengatasi Overdispersi pada Regresi Poisson

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Lusi Eka Afri

2017-03-01

estimation and to downward bias parameter estimation (underestimate. This study aims to compare the Negative Binomial Regression model and Conway-Maxwell-Poisson (COM- Poisson regression model to overcome over dispersion of Poisson distribution data based on deviance test statistics. The data used in this study are simulation data and applied case data. The simulation data were obtained by generating the Poisson distribution data containing over dispersion using the R programming language based on data characteristic such as ?, the probability (p of zero value and the sample size (n. The generated data is used to get the estimated parameter coefficient of the negative binomial regression and COM-Poisson. Keywords: overdispersion, negative binomial regression and Conway-Maxwell-Poisson regression

Properties of parameter estimation techniques for a beta-binomial failure model. Final technical report

International Nuclear Information System (INIS)

Shultis, J.K.; Buranapan, W.; Eckhoff, N.D.

1981-12-01

Of considerable importance in the safety analysis of nuclear power plants are methods to estimate the probability of failure-on-demand, p, of a plant component that normally is inactive and that may fail when activated or stressed. Properties of five methods for estimating from failure-on-demand data the parameters of the beta prior distribution in a compound beta-binomial probability model are examined. Simulated failure data generated from a known beta-binomial marginal distribution are used to estimate values of the beta parameters by (1) matching moments of the prior distribution to those of the data, (2) the maximum likelihood method based on the prior distribution, (3) a weighted marginal matching moments method, (4) an unweighted marginal matching moments method, and (5) the maximum likelihood method based on the marginal distribution. For small sample sizes (N = or < 10) with data typical of low failure probability components, it was found that the simple prior matching moments method is often superior (e.g. smallest bias and mean squared error) while for larger sample sizes the marginal maximum likelihood estimators appear to be best

Forward selection two sample binomial test

Science.gov (United States)

Wong, Kam-Fai; Wong, Weng-Kee; Lin, Miao-Shan

2016-01-01

Fisher’s exact test (FET) is a conditional method that is frequently used to analyze data in a 2 × 2 table for small samples. This test is conservative and attempts have been made to modify the test to make it less conservative. For example, Crans and Shuster (2008) proposed adding more points in the rejection region to make the test more powerful. We provide another way to modify the test to make it less conservative by using two independent binomial distributions as the reference distribution for the test statistic. We compare our new test with several methods and show that our test has advantages over existing methods in terms of control of the type 1 and type 2 errors. We reanalyze results from an oncology trial using our proposed method and our software which is freely available to the reader. PMID:27335577

[The reentrant binomial model of nuclear anomalies growth in rhabdomyosarcoma RA-23 cell populations under increasing doze of rare ionizing radiation].

Science.gov (United States)

Alekseeva, N P; Alekseev, A O; Vakhtin, Iu B; Kravtsov, V Iu; Kuzovatov, S N; Skorikova, T I

2008-01-01

Distributions of nuclear morphology anomalies in transplantable rabdomiosarcoma RA-23 cell populations were investigated under effect of ionizing radiation from 0 to 45 Gy. Internuclear bridges, nuclear protrusions and dumbbell-shaped nuclei were accepted for morphological anomalies. Empirical distributions of the number of anomalies per 100 nuclei were used. The adequate model of reentrant binomial distribution has been found. The sum of binomial random variables with binomial number of summands has such distribution. Averages of these random variables were named, accordingly, internal and external average reentrant components. Their maximum likelihood estimations were received. Statistical properties of these estimations were investigated by means of statistical modeling. It has been received that at equally significant correlation between the radiation dose and the average of nuclear anomalies in cell populations after two-three cellular cycles from the moment of irradiation in vivo the irradiation doze significantly correlates with internal average reentrant component, and in remote descendants of cell transplants irradiated in vitro - with external one.

Computational results on the compound binomial risk model with nonhomogeneous claim occurrences

NARCIS (Netherlands)

Tuncel, A.; Tank, F.

2013-01-01

The aim of this paper is to give a recursive formula for non-ruin (survival) probability when the claim occurrences are nonhomogeneous in the compound binomial risk model. We give recursive formulas for non-ruin (survival) probability and for distribution of the total number of claims under the

The Binomial Coefficient for Negative Arguments

OpenAIRE

Kronenburg, M. J.

2011-01-01

The definition of the binomial coefficient in terms of gamma functions also allows non-integer arguments. For nonnegative integer arguments the gamma functions reduce to factorials, leading to the well-known Pascal triangle. Using a symmetry formula for the gamma function, this definition is extended to negative integer arguments, making the symmetry identity for binomial coefficients valid for all integer arguments. The agreement of this definition with some other identities and with the bin...

Discovering Binomial Identities with PascGaloisJE

Science.gov (United States)

Evans, Tyler J.

2008-01-01

We describe exercises in which students use PascGaloisJE to formulate conjectures about certain binomial identities which hold when the binomial coefficients are interpreted as elements in the cyclic group Z[subscript p] of integers modulo a prime integer "p". In addition to having an appealing visual component, these exercises are open-ended and…

Tomography of binomial states of the radiation field

NARCIS (Netherlands)

Bazrafkan, MR; Man'ko, [No Value

2004-01-01

The symplectic, optical, and photon-number tomographic symbols of binomial states of the radiation field are studied. Explicit relations for all tomograms of the binomial states are obtained. Two measures for nonclassical properties of these states are discussed.

Application of binomial-edited CPMG to shale characterization.

Science.gov (United States)

Washburn, Kathryn E; Birdwell, Justin E

2014-09-01

Unconventional shale resources may contain a significant amount of hydrogen in organic solids such as kerogen, but it is not possible to directly detect these solids with many NMR systems. Binomial-edited pulse sequences capitalize on magnetization transfer between solids, semi-solids, and liquids to provide an indirect method of detecting solid organic materials in shales. When the organic solids can be directly measured, binomial-editing helps distinguish between different phases. We applied a binomial-edited CPMG pulse sequence to a range of natural and experimentally-altered shale samples. The most substantial signal loss is seen in shales rich in organic solids while fluids associated with inorganic pores seem essentially unaffected. This suggests that binomial-editing is a potential method for determining fluid locations, solid organic content, and kerogen-bitumen discrimination. Copyright © 2014 Elsevier Inc. All rights reserved.

A class of orthogonal nonrecursive binomial filters.

Science.gov (United States)

Haddad, R. A.

1971-01-01

The time- and frequency-domain properties of the orthogonal binomial sequences are presented. It is shown that these sequences, or digital filters based on them, can be generated using adders and delay elements only. The frequency-domain behavior of these nonrecursive binomial filters suggests a number of applications as low-pass Gaussian filters or as inexpensive bandpass filters.

Genome-enabled predictions for binomial traits in sugar beet populations.

Science.gov (United States)

Biscarini, Filippo; Stevanato, Piergiorgio; Broccanello, Chiara; Stella, Alessandra; Saccomani, Massimo

2014-07-22

Genomic information can be used to predict not only continuous but also categorical (e.g. binomial) traits. Several traits of interest in human medicine and agriculture present a discrete distribution of phenotypes (e.g. disease status). Root vigor in sugar beet (B. vulgaris) is an example of binomial trait of agronomic importance. In this paper, a panel of 192 SNPs (single nucleotide polymorphisms) was used to genotype 124 sugar beet individual plants from 18 lines, and to classify them as showing "high" or "low" root vigor. A threshold model was used to fit the relationship between binomial root vigor and SNP genotypes, through the matrix of genomic relationships between individuals in a genomic BLUP (G-BLUP) approach. From a 5-fold cross-validation scheme, 500 testing subsets were generated. The estimated average cross-validation error rate was 0.000731 (0.073%). Only 9 out of 12326 test observations (500 replicates for an average test set size of 24.65) were misclassified. The estimated prediction accuracy was quite high. Such accurate predictions may be related to the high estimated heritability for root vigor (0.783) and to the few genes with large effect underlying the trait. Despite the sparse SNP panel, there was sufficient within-scaffold LD where SNPs with large effect on root vigor were located to allow for genome-enabled predictions to work.

Bayesian inference for disease prevalence using negative binomial group testing

Science.gov (United States)

Pritchard, Nicholas A.; Tebbs, Joshua M.

2011-01-01

Group testing, also known as pooled testing, and inverse sampling are both widely used methods of data collection when the goal is to estimate a small proportion. Taking a Bayesian approach, we consider the new problem of estimating disease prevalence from group testing when inverse (negative binomial) sampling is used. Using different distributions to incorporate prior knowledge of disease incidence and different loss functions, we derive closed form expressions for posterior distributions and resulting point and credible interval estimators. We then evaluate our new estimators, on Bayesian and classical grounds, and apply our methods to a West Nile Virus data set. PMID:21259308

Meta-analysis for diagnostic accuracy studies: a new statistical model using beta-binomial distributions and bivariate copulas.

Science.gov (United States)

Kuss, Oliver; Hoyer, Annika; Solms, Alexander

2014-01-15

There are still challenges when meta-analyzing data from studies on diagnostic accuracy. This is mainly due to the bivariate nature of the response where information on sensitivity and specificity must be summarized while accounting for their correlation within a single trial. In this paper, we propose a new statistical model for the meta-analysis for diagnostic accuracy studies. This model uses beta-binomial distributions for the marginal numbers of true positives and true negatives and links these margins by a bivariate copula distribution. The new model comes with all the features of the current standard model, a bivariate logistic regression model with random effects, but has the additional advantages of a closed likelihood function and a larger flexibility for the correlation structure of sensitivity and specificity. In a simulation study, which compares three copula models and two implementations of the standard model, the Plackett and the Gauss copula do rarely perform worse but frequently better than the standard model. We use an example from a meta-analysis to judge the diagnostic accuracy of telomerase (a urinary tumor marker) for the diagnosis of primary bladder cancer for illustration. Copyright © 2013 John Wiley & Sons, Ltd.

Linking parasite populations in hosts to parasite populations in space through Taylor's law and the negative binomial distribution.

Science.gov (United States)

Cohen, Joel E; Poulin, Robert; Lagrue, Clément

2017-01-03

The spatial distribution of individuals of any species is a basic concern of ecology. The spatial distribution of parasites matters to control and conservation of parasites that affect human and nonhuman populations. This paper develops a quantitative theory to predict the spatial distribution of parasites based on the distribution of parasites in hosts and the spatial distribution of hosts. Four models are tested against observations of metazoan hosts and their parasites in littoral zones of four lakes in Otago, New Zealand. These models differ in two dichotomous assumptions, constituting a 2 × 2 theoretical design. One assumption specifies whether the variance function of the number of parasites per host individual is described by Taylor's law (TL) or the negative binomial distribution (NBD). The other assumption specifies whether the numbers of parasite individuals within each host in a square meter of habitat are independent or perfectly correlated among host individuals. We find empirically that the variance-mean relationship of the numbers of parasites per square meter is very well described by TL but is not well described by NBD. Two models that posit perfect correlation of the parasite loads of hosts in a square meter of habitat approximate observations much better than two models that posit independence of parasite loads of hosts in a square meter, regardless of whether the variance-mean relationship of parasites per host individual obeys TL or NBD. We infer that high local interhost correlations in parasite load strongly influence the spatial distribution of parasites. Local hotspots could influence control and conservation of parasites.

Generalization of Binomial Coefficients to Numbers on the Nodes of Graphs

NARCIS (Netherlands)

Khmelnitskaya, A.; van der Laan, G.; Talman, Dolf

2016-01-01

The triangular array of binomial coefficients, or Pascal's triangle, is formed by starting with an apex of 1. Every row of Pascal's triangle can be seen as a line-graph, to each node of which the corresponding binomial coefficient is assigned. We show that the binomial coefficient of a node is equal

Generalization of binomial coefficients to numbers on the nodes of graphs

NARCIS (Netherlands)

Khmelnitskaya, Anna Borisovna; van der Laan, Gerard; Talman, Dolf

The triangular array of binomial coefficients, or Pascal's triangle, is formed by starting with an apex of 1. Every row of Pascal's triangle can be seen as a line-graph, to each node of which the corresponding binomial coefficient is assigned. We show that the binomial coefficient of a node is equal

[Using log-binomial model for estimating the prevalence ratio].

Science.gov (United States)

Ye, Rong; Gao, Yan-hui; Yang, Yi; Chen, Yue

2010-05-01

To estimate the prevalence ratios, using a log-binomial model with or without continuous covariates. Prevalence ratios for individuals' attitude towards smoking-ban legislation associated with smoking status, estimated by using a log-binomial model were compared with odds ratios estimated by logistic regression model. In the log-binomial modeling, maximum likelihood method was used when there were no continuous covariates and COPY approach was used if the model did not converge, for example due to the existence of continuous covariates. We examined the association between individuals' attitude towards smoking-ban legislation and smoking status in men and women. Prevalence ratio and odds ratio estimation provided similar results for the association in women since smoking was not common. In men however, the odds ratio estimates were markedly larger than the prevalence ratios due to a higher prevalence of outcome. The log-binomial model did not converge when age was included as a continuous covariate and COPY method was used to deal with the situation. All analysis was performed by SAS. Prevalence ratio seemed to better measure the association than odds ratio when prevalence is high. SAS programs were provided to calculate the prevalence ratios with or without continuous covariates in the log-binomial regression analysis.

Smoothness in Binomial Edge Ideals

Directory of Open Access Journals (Sweden)

Hamid Damadi

2016-06-01

Full Text Available In this paper we study some geometric properties of the algebraic set associated to the binomial edge ideal of a graph. We study the singularity and smoothness of the algebraic set associated to the binomial edge ideal of a graph. Some of these algebraic sets are irreducible and some of them are reducible. If every irreducible component of the algebraic set is smooth we call the graph an edge smooth graph, otherwise it is called an edge singular graph. We show that complete graphs are edge smooth and introduce two conditions such that the graph G is edge singular if and only if it satisfies these conditions. Then, it is shown that cycles and most of trees are edge singular. In addition, it is proved that complete bipartite graphs are edge smooth.

Negative binomial models for abundance estimation of multiple closed populations

Science.gov (United States)

Boyce, Mark S.; MacKenzie, Darry I.; Manly, Bryan F.J.; Haroldson, Mark A.; Moody, David W.

2001-01-01

Counts of uniquely identified individuals in a population offer opportunities to estimate abundance. However, for various reasons such counts may be burdened by heterogeneity in the probability of being detected. Theoretical arguments and empirical evidence demonstrate that the negative binomial distribution (NBD) is a useful characterization for counts from biological populations with heterogeneity. We propose a method that focuses on estimating multiple populations by simultaneously using a suite of models derived from the NBD. We used this approach to estimate the number of female grizzly bears (Ursus arctos) with cubs-of-the-year in the Yellowstone ecosystem, for each year, 1986-1998. Akaike's Information Criteria (AIC) indicated that a negative binomial model with a constant level of heterogeneity across all years was best for characterizing the sighting frequencies of female grizzly bears. A lack-of-fit test indicated the model adequately described the collected data. Bootstrap techniques were used to estimate standard errors and 95% confidence intervals. We provide a Monte Carlo technique, which confirms that the Yellowstone ecosystem grizzly bear population increased during the period 1986-1998.

Perbandingan Metode Binomial dan Metode Black-Scholes Dalam Penentuan Harga Opsi

Directory of Open Access Journals (Sweden)

Surya Amami Pramuditya

2016-04-01

Full Text Available ABSTRAKOpsi adalah kontrak antara pemegang dan penulis  (buyer (holder dan seller (writer di mana penulis (writer memberikan hak (bukan kewajiban kepada holder untuk membeli atau menjual aset dari writer pada harga tertentu (strike atau latihan harga dan pada waktu tertentu dalam waktu (tanggal kadaluwarsa atau jatuh tempo waktu. Ada beberapa cara untuk menentukan harga opsi, diantaranya adalah  Metode Black-Scholes dan Metode Binomial. Metode binomial berasal dari model pergerakan harga saham yang membagi waktu interval [0, T] menjadi n sama panjang. Sedangkan metode Black-Scholes, dimodelkan dengan pergerakan harga saham sebagai suatu proses stokastik. Semakin besar partisi waktu n pada Metode Binomial, maka nilai opsinya akan konvergen ke nilai opsi Metode Black-Scholes.Kata kunci: opsi, Binomial, Black-Scholes.ABSTRACT Option is a contract between the holder and the writer in which the writer gives the right (not the obligation to the holder to buy or sell an asset of a writer at a specified price (the strike or exercise price and at a specified time in the future (expiry date or maturity time. There are several ways to determine the price of options, including the Black-Scholes Method and Binomial Method. Binomial method come from a model of stock price movement that divide time interval [0, T] into n equally long. While the Black Scholes method, the stock price movement is modeled as a stochastic process. More larger the partition of time n in Binomial Method, the value option will converge to the value option in Black-Scholes Method.Key words: Options, Binomial, Black-Scholes

Negative binomial distribution fits to multiplicity distributions is restricted δη intervals from central O+Cu collisions at 14.6A GeV/c and their implication for open-quotes Intermittencyclose quotes

International Nuclear Information System (INIS)

Tannenbaum, M.J.

1993-01-01

Experience in analyzing the data from Light and Heavy Ion Collisions in terms of distributions rather than moments suggests that conventional fluctuations of multiplicity and transverse energy can be well described by Gamma or Negative Binomial Distributions (NBD). Multiplicity distributions were obtained for central 16 O+Cu collisions in bins of δη= 0.1,0.2, 0.3 .... 0.5,1.0, where the bin of 1.0 covers 1.2 < η < 2.2 in the laboratory. NBD fits were performed to these distributions with excellent results in all δη bins. The κ parameter of the NBD fit increases linearly with the δη interval, which is a totally unexpected and particularly striking result. Due to the well known property of the NBD under convolution, this result indicates that the multiplicity distributions in adjacent bins of pseudorapidity δη ∼ 0.1 are largely statistically independent. The relationship to 2-particle correlations and open-quotes Intermittencyclose quotes will be discussed

Modeling Tetanus Neonatorum case using the regression of negative binomial and zero-inflated negative binomial

Science.gov (United States)

Amaliana, Luthfatul; Sa'adah, Umu; Wayan Surya Wardhani, Ni

2017-12-01

Tetanus Neonatorum is an infectious disease that can be prevented by immunization. The number of Tetanus Neonatorum cases in East Java Province is the highest in Indonesia until 2015. Tetanus Neonatorum data contain over dispersion and big enough proportion of zero-inflation. Negative Binomial (NB) regression is an alternative method when over dispersion happens in Poisson regression. However, the data containing over dispersion and zero-inflation are more appropriately analyzed by using Zero-Inflated Negative Binomial (ZINB) regression. The purpose of this study are: (1) to model Tetanus Neonatorum cases in East Java Province with 71.05 percent proportion of zero-inflation by using NB and ZINB regression, (2) to obtain the best model. The result of this study indicates that ZINB is better than NB regression with smaller AIC.

Development of sample size allocation program using hypergeometric distribution

International Nuclear Information System (INIS)

Kim, Hyun Tae; Kwack, Eun Ho; Park, Wan Soo; Min, Kyung Soo; Park, Chan Sik

1996-01-01

The objective of this research is the development of sample allocation program using hypergeometric distribution with objected-oriented method. When IAEA(International Atomic Energy Agency) performs inspection, it simply applies a standard binomial distribution which describes sampling with replacement instead of a hypergeometric distribution which describes sampling without replacement in sample allocation to up to three verification methods. The objective of the IAEA inspection is the timely detection of diversion of significant quantities of nuclear material, therefore game theory is applied to its sampling plan. It is necessary to use hypergeometric distribution directly or approximate distribution to secure statistical accuracy. Improved binomial approximation developed by Mr. J. L. Jaech and correctly applied binomial approximation are more closer to hypergeometric distribution in sample size calculation than the simply applied binomial approximation of the IAEA. Object-oriented programs of 1. sample approximate-allocation with correctly applied standard binomial approximation, 2. sample approximate-allocation with improved binomial approximation, and 3. sample approximate-allocation with hypergeometric distribution were developed with Visual C ++ and corresponding programs were developed with EXCEL(using Visual Basic for Application). 8 tabs., 15 refs. (Author)

Speech-discrimination scores modeled as a binomial variable.

Science.gov (United States)

Thornton, A R; Raffin, M J

1978-09-01

Many studies have reported variability data for tests of speech discrimination, and the disparate results of these studies have not been given a simple explanation. Arguments over the relative merits of 25- vs 50-word tests have ignored the basic mathematical properties inherent in the use of percentage scores. The present study models performance on clinical tests of speech discrimination as a binomial variable. A binomial model was developed, and some of its characteristics were tested against data from 4120 scores obtained on the CID Auditory Test W-22. A table for determining significant deviations between scores was generated and compared to observed differences in half-list scores for the W-22 tests. Good agreement was found between predicted and observed values. Implications of the binomial characteristics of speech-discrimination scores are discussed.

Weighted profile likelihood-based confidence interval for the difference between two proportions with paired binomial data.

Science.gov (United States)

Pradhan, Vivek; Saha, Krishna K; Banerjee, Tathagata; Evans, John C

2014-07-30

Inference on the difference between two binomial proportions in the paired binomial setting is often an important problem in many biomedical investigations. Tang et al. (2010, Statistics in Medicine) discussed six methods to construct confidence intervals (henceforth, we abbreviate it as CI) for the difference between two proportions in paired binomial setting using method of variance estimates recovery. In this article, we propose weighted profile likelihood-based CIs for the difference between proportions of a paired binomial distribution. However, instead of the usual likelihood, we use weighted likelihood that is essentially making adjustments to the cell frequencies of a 2 × 2 table in the spirit of Agresti and Min (2005, Statistics in Medicine). We then conduct numerical studies to compare the performances of the proposed CIs with that of Tang et al. and Agresti and Min in terms of coverage probabilities and expected lengths. Our numerical study clearly indicates that the weighted profile likelihood-based intervals and Jeffreys interval (cf. Tang et al.) are superior in terms of achieving the nominal level, and in terms of expected lengths, they are competitive. Finally, we illustrate the use of the proposed CIs with real-life examples. Copyright © 2014 John Wiley & Sons, Ltd.

Modelling noise in second generation sequencing forensic genetics STR data using a one-inflated (zero-truncated) negative binomial model

DEFF Research Database (Denmark)

Vilsen, Søren B.; Tvedebrink, Torben; Mogensen, Helle Smidt

2015-01-01

We present a model fitting the distribution of non-systematic errors in STR second generation sequencing, SGS, analysis. The model fits the distribution of non-systematic errors, i.e. the noise, using a one-inflated, zero-truncated, negative binomial model. The model is a two component model...

[Evaluation of estimation of prevalence ratio using bayesian log-binomial regression model].

Science.gov (United States)

Gao, W L; Lin, H; Liu, X N; Ren, X W; Li, J S; Shen, X P; Zhu, S L

2017-03-10

To evaluate the estimation of prevalence ratio ( PR ) by using bayesian log-binomial regression model and its application, we estimated the PR of medical care-seeking prevalence to caregivers' recognition of risk signs of diarrhea in their infants by using bayesian log-binomial regression model in Openbugs software. The results showed that caregivers' recognition of infant' s risk signs of diarrhea was associated significantly with a 13% increase of medical care-seeking. Meanwhile, we compared the differences in PR 's point estimation and its interval estimation of medical care-seeking prevalence to caregivers' recognition of risk signs of diarrhea and convergence of three models (model 1: not adjusting for the covariates; model 2: adjusting for duration of caregivers' education, model 3: adjusting for distance between village and township and child month-age based on model 2) between bayesian log-binomial regression model and conventional log-binomial regression model. The results showed that all three bayesian log-binomial regression models were convergence and the estimated PRs were 1.130(95 %CI : 1.005-1.265), 1.128(95 %CI : 1.001-1.264) and 1.132(95 %CI : 1.004-1.267), respectively. Conventional log-binomial regression model 1 and model 2 were convergence and their PRs were 1.130(95 % CI : 1.055-1.206) and 1.126(95 % CI : 1.051-1.203), respectively, but the model 3 was misconvergence, so COPY method was used to estimate PR , which was 1.125 (95 %CI : 1.051-1.200). In addition, the point estimation and interval estimation of PRs from three bayesian log-binomial regression models differed slightly from those of PRs from conventional log-binomial regression model, but they had a good consistency in estimating PR . Therefore, bayesian log-binomial regression model can effectively estimate PR with less misconvergence and have more advantages in application compared with conventional log-binomial regression model.

A methodology to design heuristics for model selection based on the characteristics of data: Application to investigate when the Negative Binomial Lindley (NB-L) is preferred over the Negative Binomial (NB).

Science.gov (United States)

Shirazi, Mohammadali; Dhavala, Soma Sekhar; Lord, Dominique; Geedipally, Srinivas Reddy

2017-10-01

Safety analysts usually use post-modeling methods, such as the Goodness-of-Fit statistics or the Likelihood Ratio Test, to decide between two or more competitive distributions or models. Such metrics require all competitive distributions to be fitted to the data before any comparisons can be accomplished. Given the continuous growth in introducing new statistical distributions, choosing the best one using such post-modeling methods is not a trivial task, in addition to all theoretical or numerical issues the analyst may face during the analysis. Furthermore, and most importantly, these measures or tests do not provide any intuitions into why a specific distribution (or model) is preferred over another (Goodness-of-Logic). This paper ponders into these issues by proposing a methodology to design heuristics for Model Selection based on the characteristics of data, in terms of descriptive summary statistics, before fitting the models. The proposed methodology employs two analytic tools: (1) Monte-Carlo Simulations and (2) Machine Learning Classifiers, to design easy heuristics to predict the label of the 'most-likely-true' distribution for analyzing data. The proposed methodology was applied to investigate when the recently introduced Negative Binomial Lindley (NB-L) distribution is preferred over the Negative Binomial (NB) distribution. Heuristics were designed to select the 'most-likely-true' distribution between these two distributions, given a set of prescribed summary statistics of data. The proposed heuristics were successfully compared against classical tests for several real or observed datasets. Not only they are easy to use and do not need any post-modeling inputs, but also, using these heuristics, the analyst can attain useful information about why the NB-L is preferred over the NB - or vice versa- when modeling data. Copyright © 2017 Elsevier Ltd. All rights reserved.

Penggunaan Model Binomial Pada Penentuan Harga Opsi Saham Karyawan

Directory of Open Access Journals (Sweden)

Dara Puspita Anggraeni

2015-11-01

Full Text Available Binomial Model for Valuing Employee Stock Options. Employee Stock Options (ESO differ from standard exchange-traded options. The three main differences in a valuation model for employee stock options : Vesting Period, Exit Rate and Non-Transferability. In this thesis, the model for valuing employee stock options discussed. This model are implement with a generalized binomial model.

Newton Binomial Formulas in Schubert Calculus

OpenAIRE

Cordovez, Jorge; Gatto, Letterio; Santiago, Taise

2008-01-01

We prove Newton's binomial formulas for Schubert Calculus to determine numbers of base point free linear series on the projective line with prescribed ramification divisor supported at given distinct points.

Metaprop: a Stata command to perform meta-analysis of binomial data.

Science.gov (United States)

Nyaga, Victoria N; Arbyn, Marc; Aerts, Marc

2014-01-01

Meta-analyses have become an essential tool in synthesizing evidence on clinical and epidemiological questions derived from a multitude of similar studies assessing the particular issue. Appropriate and accessible statistical software is needed to produce the summary statistic of interest. Metaprop is a statistical program implemented to perform meta-analyses of proportions in Stata. It builds further on the existing Stata procedure metan which is typically used to pool effects (risk ratios, odds ratios, differences of risks or means) but which is also used to pool proportions. Metaprop implements procedures which are specific to binomial data and allows computation of exact binomial and score test-based confidence intervals. It provides appropriate methods for dealing with proportions close to or at the margins where the normal approximation procedures often break down, by use of the binomial distribution to model the within-study variability or by allowing Freeman-Tukey double arcsine transformation to stabilize the variances. Metaprop was applied on two published meta-analyses: 1) prevalence of HPV-infection in women with a Pap smear showing ASC-US; 2) cure rate after treatment for cervical precancer using cold coagulation. The first meta-analysis showed a pooled HPV-prevalence of 43% (95% CI: 38%-48%). In the second meta-analysis, the pooled percentage of cured women was 94% (95% CI: 86%-97%). By using metaprop, no studies with 0% or 100% proportions were excluded from the meta-analysis. Furthermore, study specific and pooled confidence intervals always were within admissible values, contrary to the original publication, where metan was used.

On some binomial [Formula: see text]-difference sequence spaces.

Science.gov (United States)

Meng, Jian; Song, Meimei

2017-01-01

In this paper, we introduce the binomial sequence spaces [Formula: see text], [Formula: see text] and [Formula: see text] by combining the binomial transformation and difference operator. We prove the BK -property and some inclusion relations. Furthermore, we obtain Schauder bases and compute the α -, β - and γ -duals of these sequence spaces. Finally, we characterize matrix transformations on the sequence space [Formula: see text].

Binomial and enumerative sampling of Tetranychus urticae (Acari: Tetranychidae) on peppermint in California.

Science.gov (United States)

Tollerup, Kris E; Marcum, Daniel; Wilson, Rob; Godfrey, Larry

2013-08-01

The two-spotted spider mite, Tetranychus urticae Koch, is an economic pest on peppermint [Mentha x piperita (L.), 'Black Mitcham'] grown in California. A sampling plan for T. urticae was developed under Pacific Northwest conditions in the early 1980s and has been used by California growers since approximately 1998. This sampling plan, however, is cumbersome and a poor predictor of T. urticae densities in California. Between June and August, the numbers of immature and adult T. urticae were counted on leaves at three commercial peppermint fields (sites) in 2010 and a single field in 2011. In each of seven locations per site, 45 leaves were sampled, that is, 9 leaves per five stems. Leaf samples were stratified by collecting three leaves from the top, middle, and bottom strata per stem. The on-plant distribution of T. urticae did not significantly differ among the stem strata through the growing season. Binomial and enumerative sampling plans were developed using generic Taylor's power law coefficient values. The best fit of our data for binomial sampling occurred using a tally threshold of T = 0. The optimum number of leaves required for T urticae at the critical density of five mites per leaf was 20 for the binomial and 23 for the enumerative sampling plans, respectively. Sampling models were validated using Resampling for Validation of Sampling Plan Software.

A fast algorithm for computing binomial coefficients modulo powers of two.

Science.gov (United States)

Andreica, Mugurel Ionut

2013-01-01

I present a new algorithm for computing binomial coefficients modulo 2N. The proposed method has an O(N3·Multiplication(N)+N4) preprocessing time, after which a binomial coefficient C(P, Q) with 0≤Q≤P≤2N-1 can be computed modulo 2N in O(N2·log(N)·Multiplication(N)) time. Multiplication(N) denotes the time complexity of multiplying two N-bit numbers, which can range from O(N2) to O(N·log(N)·log(log(N))) or better. Thus, the overall time complexity for evaluating M binomial coefficients C(P, Q) modulo 2N with 0≤Q≤P≤2N-1 is O((N3+M·N2·log(N))·Multiplication(N)+N4). After preprocessing, we can actually compute binomial coefficients modulo any 2R with R≤N. For larger values of P and Q, variations of Lucas' theorem must be used first in order to reduce the computation to the evaluation of multiple (O(log(P))) binomial coefficients C(P', Q') (or restricted types of factorials P'!) modulo 2N with 0≤Q'≤P'≤2N-1.

Marginal likelihood estimation of negative binomial parameters with applications to RNA-seq data.

Science.gov (United States)

León-Novelo, Luis; Fuentes, Claudio; Emerson, Sarah

2017-10-01

RNA-Seq data characteristically exhibits large variances, which need to be appropriately accounted for in any proposed model. We first explore the effects of this variability on the maximum likelihood estimator (MLE) of the dispersion parameter of the negative binomial distribution, and propose instead to use an estimator obtained via maximization of the marginal likelihood in a conjugate Bayesian framework. We show, via simulation studies, that the marginal MLE can better control this variation and produce a more stable and reliable estimator. We then formulate a conjugate Bayesian hierarchical model, and use this new estimator to propose a Bayesian hypothesis test to detect differentially expressed genes in RNA-Seq data. We use numerical studies to show that our much simpler approach is competitive with other negative binomial based procedures, and we use a real data set to illustrate the implementation and flexibility of the procedure. © The Author 2017. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Entanglement of Generalized Two-Mode Binomial States and Teleportation

International Nuclear Information System (INIS)

Wang Dongmei; Yu Youhong

2009-01-01

The entanglement of the generalized two-mode binomial states in the phase damping channel is studied by making use of the relative entropy of the entanglement. It is shown that the factors of q and p play the crucial roles in control the relative entropy of the entanglement. Furthermore, we propose a scheme of teleporting an unknown state via the generalized two-mode binomial states, and calculate the mean fidelity of the scheme. (general)

Optimized Binomial Quantum States of Complex Oscillators with Real Spectrum

International Nuclear Information System (INIS)

Zelaya, K D; Rosas-Ortiz, O

2016-01-01

Classical and nonclassical states of quantum complex oscillators with real spectrum are presented. Such states are bi-orthonormal superpositions of n +1 energy eigenvectors of the system with binomial-like coefficients. For large values of n these optimized binomial states behave as photon added coherent states when the imaginary part of the potential is cancelled. (paper)

Comparison: Binomial model and Black Scholes model

Directory of Open Access Journals (Sweden)

Amir Ahmad Dar

2018-03-01

Full Text Available The Binomial Model and the Black Scholes Model are the popular methods that are used to solve the option pricing problems. Binomial Model is a simple statistical method and Black Scholes model requires a solution of a stochastic differential equation. Pricing of European call and a put option is a very difficult method used by actuaries. The main goal of this study is to differentiate the Binominal model and the Black Scholes model by using two statistical model - t-test and Tukey model at one period. Finally, the result showed that there is no significant difference between the means of the European options by using the above two models.

Integer Solutions of Binomial Coefficients

Science.gov (United States)

Gilbertson, Nicholas J.

2016-01-01

A good formula is like a good story, rich in description, powerful in communication, and eye-opening to readers. The formula presented in this article for determining the coefficients of the binomial expansion of (x + y)n is one such "good read." The beauty of this formula is in its simplicity--both describing a quantitative situation…

Sample size calculation for comparing two negative binomial rates.

Science.gov (United States)

Zhu, Haiyuan; Lakkis, Hassan

2014-02-10

Negative binomial model has been increasingly used to model the count data in recent clinical trials. It is frequently chosen over Poisson model in cases of overdispersed count data that are commonly seen in clinical trials. One of the challenges of applying negative binomial model in clinical trial design is the sample size estimation. In practice, simulation methods have been frequently used for sample size estimation. In this paper, an explicit formula is developed to calculate sample size based on the negative binomial model. Depending on different approaches to estimate the variance under null hypothesis, three variations of the sample size formula are proposed and discussed. Important characteristics of the formula include its accuracy and its ability to explicitly incorporate dispersion parameter and exposure time. The performance of the formula with each variation is assessed using simulations. Copyright © 2013 John Wiley & Sons, Ltd.

Quantum Theory for the Binomial Model in Finance Thoery

OpenAIRE

Chen, Zeqian

2001-01-01

In this paper, a quantum model for the binomial market in finance is proposed. We show that its risk-neutral world exhibits an intriguing structure as a disk in the unit ball of ${\\bf R}^3,$ whose radius is a function of the risk-free interest rate with two thresholds which prevent arbitrage opportunities from this quantum market. Furthermore, from the quantum mechanical point of view we re-deduce the Cox-Ross-Rubinstein binomial option pricing formula by considering Maxwell-Boltzmann statist...

Water-selective excitation of short T2 species with binomial pulses.

Science.gov (United States)

Deligianni, Xeni; Bär, Peter; Scheffler, Klaus; Trattnig, Siegfried; Bieri, Oliver

2014-09-01

For imaging of fibrous musculoskeletal components, ultra-short echo time methods are often combined with fat suppression. Due to the increased chemical shift, spectral excitation of water might become a favorable option at ultra-high fields. Thus, this study aims to compare and explore short binomial excitation schemes for spectrally selective imaging of fibrous tissue components with short transverse relaxation time (T2 ). Water selective 1-1-binomial excitation is compared with nonselective imaging using a sub-millisecond spoiled gradient echo technique for in vivo imaging of fibrous tissue at 3T and 7T. Simulations indicate a maximum signal loss from binomial excitation of approximately 30% in the limit of very short T2 (0.1 ms), as compared to nonselective imaging; decreasing rapidly with increasing field strength and increasing T2 , e.g., to 19% at 3T and 10% at 7T for T2 of 1 ms. In agreement with simulations, a binomial phase close to 90° yielded minimum signal loss: approximately 6% at 3T and close to 0% at 7T for menisci, and for ligaments 9% and 13%, respectively. Overall, for imaging of short-lived T2 components, short 1-1 binomial excitation schemes prove to offer marginal signal loss especially at ultra-high fields with overall improved scanning efficiency. Copyright © 2013 Wiley Periodicals, Inc.

Censored Hurdle Negative Binomial Regression (Case Study: Neonatorum Tetanus Case in Indonesia)

Science.gov (United States)

Yuli Rusdiana, Riza; Zain, Ismaini; Wulan Purnami, Santi

2017-06-01

Hurdle negative binomial model regression is a method that can be used for discreate dependent variable, excess zero and under- and overdispersion. It uses two parts approach. The first part estimates zero elements from dependent variable is zero hurdle model and the second part estimates not zero elements (non-negative integer) from dependent variable is called truncated negative binomial models. The discrete dependent variable in such cases is censored for some values. The type of censor that will be studied in this research is right censored. This study aims to obtain the parameter estimator hurdle negative binomial regression for right censored dependent variable. In the assessment of parameter estimation methods used Maximum Likelihood Estimator (MLE). Hurdle negative binomial model regression for right censored dependent variable is applied on the number of neonatorum tetanus cases in Indonesia. The type data is count data which contains zero values in some observations and other variety value. This study also aims to obtain the parameter estimator and test statistic censored hurdle negative binomial model. Based on the regression results, the factors that influence neonatorum tetanus case in Indonesia is the percentage of baby health care coverage and neonatal visits.

Binomial test models and item difficulty

NARCIS (Netherlands)

van der Linden, Willem J.

1979-01-01

In choosing a binomial test model, it is important to know exactly what conditions are imposed on item difficulty. In this paper these conditions are examined for both a deterministic and a stochastic conception of item responses. It appears that they are more restrictive than is generally

Low reheating temperatures in monomial and binomial inflationary models

International Nuclear Information System (INIS)

Rehagen, Thomas; Gelmini, Graciela B.

2015-01-01

We investigate the allowed range of reheating temperature values in light of the Planck 2015 results and the recent joint analysis of Cosmic Microwave Background (CMB) data from the BICEP2/Keck Array and Planck experiments, using monomial and binomial inflationary potentials. While the well studied ϕ 2 inflationary potential is no longer favored by current CMB data, as well as ϕ p with p>2, a ϕ 1 potential and canonical reheating (w re =0) provide a good fit to the CMB measurements. In this last case, we find that the Planck 2015 68% confidence limit upper bound on the spectral index, n s , implies an upper bound on the reheating temperature of T re ≲6×10 10 GeV, and excludes instantaneous reheating. The low reheating temperatures allowed by this model open the possibility that dark matter could be produced during the reheating period instead of when the Universe is radiation dominated, which could lead to very different predictions for the relic density and momentum distribution of WIMPs, sterile neutrinos, and axions. We also study binomial inflationary potentials and show the effects of a small departure from a ϕ 1 potential. We find that as a subdominant ϕ 2 term in the potential increases, first instantaneous reheating becomes allowed, and then the lowest possible reheating temperature of T re =4 MeV is excluded by the Planck 2015 68% confidence limit

Two-part zero-inflated negative binomial regression model for quantitative trait loci mapping with count trait.

Science.gov (United States)

Moghimbeigi, Abbas

2015-05-07

Poisson regression models provide a standard framework for quantitative trait locus (QTL) mapping of count traits. In practice, however, count traits are often over-dispersed relative to the Poisson distribution. In these situations, the zero-inflated Poisson (ZIP), zero-inflated generalized Poisson (ZIGP) and zero-inflated negative binomial (ZINB) regression may be useful for QTL mapping of count traits. Added genetic variables to the negative binomial part equation, may also affect extra zero data. In this study, to overcome these challenges, I apply two-part ZINB model. The EM algorithm with Newton-Raphson method in the M-step uses for estimating parameters. An application of the two-part ZINB model for QTL mapping is considered to detect associations between the formation of gallstone and the genotype of markers. Copyright © 2015 Elsevier Ltd. All rights reserved.

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/ .

Binomial mitotic segregation of MYCN-carrying double minutes in neuroblastoma illustrates the role of randomness in oncogene amplification.

Directory of Open Access Journals (Sweden)

Gisela Lundberg

2008-08-01

Full Text Available Amplification of the oncogene MYCN in double minutes (DMs is a common finding in neuroblastoma (NB. Because DMs lack centromeric sequences it has been unclear how NB cells retain and amplify extrachromosomal MYCN copies during tumour development.We show that MYCN-carrying DMs in NB cells translocate from the nuclear interior to the periphery of the condensing chromatin at transition from interphase to prophase and are preferentially located adjacent to the telomere repeat sequences of the chromosomes throughout cell division. However, DM segregation was not affected by disruption of the telosome nucleoprotein complex and DMs readily migrated from human to murine chromatin in human/mouse cell hybrids, indicating that they do not bind to specific positional elements in human chromosomes. Scoring DM copy-numbers in ana/telophase cells revealed that DM segregation could be closely approximated by a binomial random distribution. Colony-forming assay demonstrated a strong growth-advantage for NB cells with high DM (MYCN copy-numbers, compared to NB cells with lower copy-numbers. In fact, the overall distribution of DMs in growing NB cell populations could be readily reproduced by a mathematical model assuming binomial segregation at cell division combined with a proliferative advantage for cells with high DM copy-numbers.Binomial segregation at cell division explains the high degree of MYCN copy-number variability in NB. Our findings also provide a proof-of-principle for oncogene amplification through creation of genetic diversity by random events followed by Darwinian selection.

Squeezing and other non-classical features in k-photon anharmonic oscillator in binomial and negative binomial states of the field

International Nuclear Information System (INIS)

Joshi, A.; Lawande, S.V.

1990-01-01

A systematic study of squeezing obtained from k-photon anharmonic oscillator (with interaction hamiltonian of the form (a † ) k , k ≥ 2) interacting with light whose statistics can be varied from sub-Poissonian to poissonian via binomial state of field and super-Poissonian to poissonian via negative binomial state of field is presented. The authors predict that for all values of k there is a tendency increase in squeezing with increased sub-Poissonian character of the field while the reverse is true with super-Poissonian field. They also present non-classical behavior of the first order coherence function explicitly for k = 2 case (i.e., for two-photon anharmonic oscillator model used for a Kerr-like medium) with variation in the statistics of the input light

Use of the Beta-Binomial Model for Central Statistical Monitoring of Multicenter Clinical Trials

OpenAIRE

Desmet, Lieven; Venet, David; Doffagne, Erik; Timmermans, Catherine; Legrand, Catherine; Burzykowski, Tomasz; Buyse, Marc

2017-01-01

As part of central statistical monitoring of multicenter clinical trial data, we propose a procedure based on the beta-binomial distribution for the detection of centers with atypical values for the probability of some event. The procedure makes no assumptions about the typical event proportion and uses the event counts from all centers to derive a reference model. The procedure is shown through simulations to have high sensitivity and high specificity if the contamination rate is small and t...

Relacionando las distribuciones binomial negativa y logarítmica vía sus series asociadas

OpenAIRE

Sadinle, Mauricio

2011-01-01

La distribución binomial negativa está asociada a la serie obtenida de derivar la serie logarítmica. Recíprocamente, la distribución logarítmica está asociada a la serie obtenida de integrar la serie asociada a la distribución binomial negativa. El parámetro del número de fallas de la distribución Binomial negativa es el número de derivadas necesarias para obtener la serie binomial negativa de la serie logarítmica. El razonamiento presentado puede emplearse como un método alternativo para pro...

Abstract knowledge versus direct experience in processing of binomial expressions.

Science.gov (United States)

Morgan, Emily; Levy, Roger

2016-12-01

We ask whether word order preferences for binomial expressions of the form A and B (e.g. bread and butter) are driven by abstract linguistic knowledge of ordering constraints referencing the semantic, phonological, and lexical properties of the constituent words, or by prior direct experience with the specific items in questions. Using forced-choice and self-paced reading tasks, we demonstrate that online processing of never-before-seen binomials is influenced by abstract knowledge of ordering constraints, which we estimate with a probabilistic model. In contrast, online processing of highly frequent binomials is primarily driven by direct experience, which we estimate from corpus frequency counts. We propose a trade-off wherein processing of novel expressions relies upon abstract knowledge, while reliance upon direct experience increases with increased exposure to an expression. Our findings support theories of language processing in which both compositional generation and direct, holistic reuse of multi-word expressions play crucial roles. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.

Typification of the binomial Sedum boissierianum Hausskncht Crassulaceae

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Valentin Bârcă

2016-06-01

Full Text Available Genus Sedum, described by Linne in 1753, a polyphyletic genus of flowering plants in the family Crassulaceae, was extensively studied both by scholars and succulents enthusiasts. Despite the great attention it has received over time, many binomials lack types and consistent taxonomic treatments. My currently undergoing process of the comprehensive revision of the genus Sedum in România and the Balkans called for the clarification of taxonomical status and typification of several basionyms described based on plants collected from the Balkans and the region around the Black Sea. Almost a century and a half ago, Haussknecht intensely studied flora of Near East and assigned several binomials to plants of the genus Sedum, some of which were neglected and forgotten although they represent interesting taxa. The binomial Sedum boissierianum Haussknecht first appeared in schedae as nomen nudum around 1892, for specimens originating from Near East, but was later validated by Froederstroem in 1932. Following extensive revision of the relevant literature and herbarium specimens, I located original material for this taxon in several herbaria in Europe (BUCF, LD, P, Z. I hereby designate the lectotype and isolectotypes for this basionym and furthermore provide pictures of the herbarium specimens and pinpoint on a map the original collections sites for the designated types.

Estimation Parameters And Modelling Zero Inflated Negative Binomial

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Cindy Cahyaning Astuti

2016-11-01

Full Text Available Regression analysis is used to determine relationship between one or several response variable (Y with one or several predictor variables (X. Regression model between predictor variables and the Poisson distributed response variable is called Poisson Regression Model. Since, Poisson Regression requires an equality between mean and variance, it is not appropriate to apply this model on overdispersion (variance is higher than mean. Poisson regression model is commonly used to analyze the count data. On the count data type, it is often to encounteredd some observations that have zero value with large proportion of zero value on the response variable (zero Inflation. Poisson regression can be used to analyze count data but it has not been able to solve problem of excess zero value on the response variable. An alternative model which is more suitable for overdispersion data and can solve the problem of excess zero value on the response variable is Zero Inflated Negative Binomial (ZINB. In this research, ZINB is applied on the case of Tetanus Neonatorum in East Java. The aim of this research is to examine the likelihood function and to form an algorithm to estimate the parameter of ZINB and also applying ZINB model in the case of Tetanus Neonatorum in East Java. Maximum Likelihood Estimation (MLE method is used to estimate the parameter on ZINB and the likelihood function is maximized using Expectation Maximization (EM algorithm. Test results of ZINB regression model showed that the predictor variable have a partial significant effect at negative binomial model is the percentage of pregnant women visits and the percentage of maternal health personnel assisted, while the predictor variables that have a partial significant effect at zero inflation model is the percentage of neonatus visits.

A comparison of methods for the analysis of binomial clustered outcomes in behavioral research.

Science.gov (United States)

Ferrari, Alberto; Comelli, Mario

2016-12-01

In behavioral research, data consisting of a per-subject proportion of "successes" and "failures" over a finite number of trials often arise. This clustered binary data are usually non-normally distributed, which can distort inference if the usual general linear model is applied and sample size is small. A number of more advanced methods is available, but they are often technically challenging and a comparative assessment of their performances in behavioral setups has not been performed. We studied the performances of some methods applicable to the analysis of proportions; namely linear regression, Poisson regression, beta-binomial regression and Generalized Linear Mixed Models (GLMMs). We report on a simulation study evaluating power and Type I error rate of these models in hypothetical scenarios met by behavioral researchers; plus, we describe results from the application of these methods on data from real experiments. Our results show that, while GLMMs are powerful instruments for the analysis of clustered binary outcomes, beta-binomial regression can outperform them in a range of scenarios. Linear regression gave results consistent with the nominal level of significance, but was overall less powerful. Poisson regression, instead, mostly led to anticonservative inference. GLMMs and beta-binomial regression are generally more powerful than linear regression; yet linear regression is robust to model misspecification in some conditions, whereas Poisson regression suffers heavily from violations of the assumptions when used to model proportion data. We conclude providing directions to behavioral scientists dealing with clustered binary data and small sample sizes. Copyright © 2016 Elsevier B.V. All rights reserved.

Adaptive estimation of binomial probabilities under misclassification

NARCIS (Netherlands)

Albers, Willem/Wim; Veldman, H.J.

1984-01-01

If misclassification occurs the standard binomial estimator is usually seriously biased. It is known that an improvement can be achieved by using more than one observer in classifying the sample elements. Here it will be investigated which number of observers is optimal given the total number of

A comparison of Poisson-one-inflated power series distributions for ...

African Journals Online (AJOL)

A class of Poisson-one-inflated power series distributions (the binomial, the Poisson, the negative binomial, the geometric, the log-series and the misrecorded Poisson) are proposed for modeling rural out-migration at the household level. The probability mass functions of the mixture distributions are derived and fitted to the ...

The analysis of incontinence episodes and other count data in patients with overactive bladder by Poisson and negative binomial regression.

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Martina, R; Kay, R; van Maanen, R; Ridder, A

2015-01-01

Clinical studies in overactive bladder have traditionally used analysis of covariance or nonparametric methods to analyse the number of incontinence episodes and other count data. It is known that if the underlying distributional assumptions of a particular parametric method do not hold, an alternative parametric method may be more efficient than a nonparametric one, which makes no assumptions regarding the underlying distribution of the data. Therefore, there are advantages in using methods based on the Poisson distribution or extensions of that method, which incorporate specific features that provide a modelling framework for count data. One challenge with count data is overdispersion, but methods are available that can account for this through the introduction of random effect terms in the modelling, and it is this modelling framework that leads to the negative binomial distribution. These models can also provide clinicians with a clearer and more appropriate interpretation of treatment effects in terms of rate ratios. In this paper, the previously used parametric and non-parametric approaches are contrasted with those based on Poisson regression and various extensions in trials evaluating solifenacin and mirabegron in patients with overactive bladder. In these applications, negative binomial models are seen to fit the data well. Copyright © 2014 John Wiley & Sons, Ltd.

Improved binomial charts for high-quality processes

NARCIS (Netherlands)

Albers, Willem/Wim

For processes concerning attribute data with (very) small failure rate p, often negative binomial control charts are used. The decision whether to stop or continue is made each time r failures have occurred, for some r≥1. Finding the optimal r for detecting a given increase of p first requires

On pricing futures options on random binomial tree

International Nuclear Information System (INIS)

Bayram, Kamola; Ganikhodjaev, Nasir

2013-01-01

The discrete-time approach to real option valuation has typically been implemented in the finance literature using a binomial tree framework. Instead we develop a new model by randomizing the environment and call such model a random binomial tree. Whereas the usual model has only one environment (u, d) where the price of underlying asset can move by u times up and d times down, and pair (u, d) is constant over the life of the underlying asset, in our new model the underlying security is moving in two environments namely (u 1 , d 1 ) and (u 2 , d 2 ). Thus we obtain two volatilities σ 1 and σ 2 . This new approach enables calculations reflecting the real market since it consider the two states of market normal and extra ordinal. In this paper we define and study Futures options for such models.

On extinction time of a generalized endemic chain-binomial model.

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Aydogmus, Ozgur

2016-09-01

We considered a chain-binomial epidemic model not conferring immunity after infection. Mean field dynamics of the model has been analyzed and conditions for the existence of a stable endemic equilibrium are determined. The behavior of the chain-binomial process is probabilistically linked to the mean field equation. As a result of this link, we were able to show that the mean extinction time of the epidemic increases at least exponentially as the population size grows. We also present simulation results for the process to validate our analytical findings. Copyright © 2016 Elsevier Inc. All rights reserved.

Pythagoras, Binomial, and de Moivre Revisited Through Differential Equations

OpenAIRE

Singh, Jitender; Bajaj, Renu

2018-01-01

The classical Pythagoras theorem, binomial theorem, de Moivre's formula, and numerous other deductions are made using the uniqueness theorem for the initial value problems in linear ordinary differential equations.

Distribution pattern of public transport passenger in Yogyakarta, Indonesia

Science.gov (United States)

Narendra, Alfa; Malkhamah, Siti; Sopha, Bertha Maya

2018-03-01

The arrival and departure distribution pattern of Trans Jogja bus passenger is one of the fundamental model for simulation. The purpose of this paper is to build models of passengers flows. This research used passengers data from January to May 2014. There is no policy that change the operation system affecting the nature of this pattern nowadays. The roads, buses, land uses, schedule, and people are relatively still the same. The data then categorized based on the direction, days, and location. Moreover, each category was fitted into some well-known discrete distributions. Those distributions are compared based on its AIC value and BIC. The chosen distribution model has the smallest AIC and BIC value and the negative binomial distribution found has the smallest AIC and BIC value. Probability mass function (PMF) plots of those models were compared to draw generic model from each categorical negative binomial distribution models. The value of accepted generic negative binomial distribution is 0.7064 and 1.4504 of mu. The minimum and maximum passenger vector value of distribution are is 0 and 41.

Studying the Binomial Distribution Using LabVIEW

Science.gov (United States)

George, Danielle J.; Hammer, Nathan I.

2015-01-01

This undergraduate physical chemistry laboratory exercise introduces students to the study of probability distributions both experimentally and using computer simulations. Students perform the classic coin toss experiment individually and then pool all of their data together to study the effect of experimental sample size on the binomial…

Some normed binomial difference sequence spaces related to the [Formula: see text] spaces.

Science.gov (United States)

Song, Meimei; Meng, Jian

2017-01-01

The aim of this paper is to introduce the normed binomial sequence spaces [Formula: see text] by combining the binomial transformation and difference operator, where [Formula: see text]. We prove that these spaces are linearly isomorphic to the spaces [Formula: see text] and [Formula: see text], respectively. Furthermore, we compute Schauder bases and the α -, β - and γ -duals of these sequence spaces.

Possibility and Challenges of Conversion of Current Virus Species Names to Linnaean Binomials

Energy Technology Data Exchange (ETDEWEB)

Postler, Thomas S.; Clawson, Anna N.; Amarasinghe, Gaya K.; Basler, Christopher F.; Bavari, Sbina; Benkő, Mária; Blasdell, Kim R.; Briese, Thomas; Buchmeier, Michael J.; Bukreyev, Alexander; Calisher, Charles H.; Chandran, Kartik; Charrel, Rémi; Clegg, Christopher S.; Collins, Peter L.; Juan Carlos, De La Torre; Derisi, Joseph L.; Dietzgen, Ralf G.; Dolnik, Olga; Dürrwald, Ralf; Dye, John M.; Easton, Andrew J.; Emonet, Sébastian; Formenty, Pierre; Fouchier, Ron A. M.; Ghedin, Elodie; Gonzalez, Jean-Paul; Harrach, Balázs; Hewson, Roger; Horie, Masayuki; Jiāng, Dàohóng; Kobinger, Gary; Kondo, Hideki; Kropinski, Andrew M.; Krupovic, Mart; Kurath, Gael; Lamb, Robert A.; Leroy, Eric M.; Lukashevich, Igor S.; Maisner, Andrea; Mushegian, Arcady R.; Netesov, Sergey V.; Nowotny, Norbert; Patterson, Jean L.; Payne, Susan L.; PaWeska, Janusz T.; Peters, Clarence J.; Radoshitzky, Sheli R.; Rima, Bertus K.; Romanowski, Victor; Rubbenstroth, Dennis; Sabanadzovic, Sead; Sanfaçon, Hélène; Salvato, Maria S.; Schwemmle, Martin; Smither, Sophie J.; Stenglein, Mark D.; Stone, David M.; Takada, Ayato; Tesh, Robert B.; Tomonaga, Keizo; Tordo, Noël; Towner, Jonathan S.; Vasilakis, Nikos; Volchkov, Viktor E.; Wahl-Jensen, Victoria; Walker, Peter J.; Wang, Lin-Fa; Varsani, Arvind; Whitfield, Anna E.; Zerbini, F. Murilo; Kuhn, Jens H.

2016-10-22

Botanical, mycological, zoological, and prokaryotic species names follow the Linnaean format, consisting of an italicized Latinized binomen with a capitalized genus name and a lower case species epithet (e.g., Homo sapiens). Virus species names, however, do not follow a uniform format, and, even when binomial, are not Linnaean in style. In this thought exercise, we attempted to convert all currently official names of species included in the virus family Arenaviridae and the virus order Mononegavirales to Linnaean binomials, and to identify and address associated challenges and concerns. Surprisingly, this endeavor was not as complicated or time-consuming as even the authors of this article expected when conceiving the experiment. [Arenaviridae; binomials; ICTV; International Committee on Taxonomy of Viruses; Mononegavirales; virus nomenclature; virus taxonomy.

Revealing Word Order: Using Serial Position in Binomials to Predict Properties of the Speaker

Science.gov (United States)

Iliev, Rumen; Smirnova, Anastasia

2016-01-01

Three studies test the link between word order in binomials and psychological and demographic characteristics of a speaker. While linguists have already suggested that psychological, cultural and societal factors are important in choosing word order in binomials, the vast majority of relevant research was focused on general factors and on broadly…

Selecting Tools to Model Integer and Binomial Multiplication

Science.gov (United States)

Pratt, Sarah Smitherman; Eddy, Colleen M.

2017-01-01

Mathematics teachers frequently provide concrete manipulatives to students during instruction; however, the rationale for using certain manipulatives in conjunction with concepts may not be explored. This article focuses on area models that are currently used in classrooms to provide concrete examples of integer and binomial multiplication. The…

Discrimination of numerical proportions: A comparison of binomial and Gaussian models.

Science.gov (United States)

Raidvee, Aire; Lember, Jüri; Allik, Jüri

2017-01-01

Observers discriminated the numerical proportion of two sets of elements (N = 9, 13, 33, and 65) that differed either by color or orientation. According to the standard Thurstonian approach, the accuracy of proportion discrimination is determined by irreducible noise in the nervous system that stochastically transforms the number of presented visual elements onto a continuum of psychological states representing numerosity. As an alternative to this customary approach, we propose a Thurstonian-binomial model, which assumes discrete perceptual states, each of which is associated with a certain visual element. It is shown that the probability β with which each visual element can be noticed and registered by the perceptual system can explain data of numerical proportion discrimination at least as well as the continuous Thurstonian-Gaussian model, and better, if the greater parsimony of the Thurstonian-binomial model is taken into account using AIC model selection. We conclude that Gaussian and binomial models represent two different fundamental principles-internal noise vs. using only a fraction of available information-which are both plausible descriptions of visual perception.

Extra-binomial variation approach for analysis of pooled DNA sequencing data

Science.gov (United States)

Wallace, Chris

2012-01-01

Motivation: The invention of next-generation sequencing technology has made it possible to study the rare variants that are more likely to pinpoint causal disease genes. To make such experiments financially viable, DNA samples from several subjects are often pooled before sequencing. This induces large between-pool variation which, together with other sources of experimental error, creates over-dispersed data. Statistical analysis of pooled sequencing data needs to appropriately model this additional variance to avoid inflating the false-positive rate. Results: We propose a new statistical method based on an extra-binomial model to address the over-dispersion and apply it to pooled case-control data. We demonstrate that our model provides a better fit to the data than either a standard binomial model or a traditional extra-binomial model proposed by Williams and can analyse both rare and common variants with lower or more variable pool depths compared to the other methods. Availability: Package ‘extraBinomial’ is on http://cran.r-project.org/ Contact: chris.wallace@cimr.cam.ac.uk Supplementary information: Supplementary data are available at Bioinformatics Online. PMID:22976083

Multiplicity distributions of charged hadrons produced in (anti)neutrino-deuterium charged- and neutral-current interactions

International Nuclear Information System (INIS)

Jongejans, B.; Tenner, A.G.; Apeldoorn, G.W. van

1989-01-01

Results are presented on the multiplicity distributions of charged hadrons produced in νn, νp, antiνn and antiνp charged-current interactions for the hadronic energy range 2GeV ≤ W ≤ 14GeV (corresponding approximately to the neutrino energy range 5GeV ≤ E ≤ 150GeV). The experimental distributions are analysed in terms of binomial distributions. With increasing hadronic energy it is found a smooth transition from an ordinary binomial via Poissonian to the negative binomial function. KNO scaling holds approximately for the multiplicity distribution for the whole phase space. Data on the multiplicity distributions for neutral-current interactions are also presented

Adjusted Wald Confidence Interval for a Difference of Binomial Proportions Based on Paired Data

Science.gov (United States)

Bonett, Douglas G.; Price, Robert M.

2012-01-01

Adjusted Wald intervals for binomial proportions in one-sample and two-sample designs have been shown to perform about as well as the best available methods. The adjusted Wald intervals are easy to compute and have been incorporated into introductory statistics courses. An adjusted Wald interval for paired binomial proportions is proposed here and…

Variability in results from negative binomial models for Lyme disease measured at different spatial scales.

Science.gov (United States)

Tran, Phoebe; Waller, Lance

2015-01-01

Lyme disease has been the subject of many studies due to increasing incidence rates year after year and the severe complications that can arise in later stages of the disease. Negative binomial models have been used to model Lyme disease in the past with some success. However, there has been little focus on the reliability and consistency of these models when they are used to study Lyme disease at multiple spatial scales. This study seeks to explore how sensitive/consistent negative binomial models are when they are used to study Lyme disease at different spatial scales (at the regional and sub-regional levels). The study area includes the thirteen states in the Northeastern United States with the highest Lyme disease incidence during the 2002-2006 period. Lyme disease incidence at county level for the period of 2002-2006 was linked with several previously identified key landscape and climatic variables in a negative binomial regression model for the Northeastern region and two smaller sub-regions (the New England sub-region and the Mid-Atlantic sub-region). This study found that negative binomial models, indeed, were sensitive/inconsistent when used at different spatial scales. We discuss various plausible explanations for such behavior of negative binomial models. Further investigation of the inconsistency and sensitivity of negative binomial models when used at different spatial scales is important for not only future Lyme disease studies and Lyme disease risk assessment/management but any study that requires use of this model type in a spatial context. Copyright © 2014 Elsevier Inc. All rights reserved.

A New Extension of the Binomial Error Model for Responses to Items of Varying Difficulty in Educational Testing and Attitude Surveys.

Directory of Open Access Journals (Sweden)

James A Wiley

Full Text Available We put forward a new item response model which is an extension of the binomial error model first introduced by Keats and Lord. Like the binomial error model, the basic latent variable can be interpreted as a probability of responding in a certain way to an arbitrarily specified item. For a set of dichotomous items, this model gives predictions that are similar to other single parameter IRT models (such as the Rasch model but has certain advantages in more complex cases. The first is that in specifying a flexible two-parameter Beta distribution for the latent variable, it is easy to formulate models for randomized experiments in which there is no reason to believe that either the latent variable or its distribution vary over randomly composed experimental groups. Second, the elementary response function is such that extensions to more complex cases (e.g., polychotomous responses, unfolding scales are straightforward. Third, the probability metric of the latent trait allows tractable extensions to cover a wide variety of stochastic response processes.

Jump-and-return sandwiches: A new family of binomial-like selective inversion sequences with improved performance

Science.gov (United States)

Brenner, Tom; Chen, Johnny; Stait-Gardner, Tim; Zheng, Gang; Matsukawa, Shingo; Price, William S.

2018-03-01

A new family of binomial-like inversion sequences, named jump-and-return sandwiches (JRS), has been developed by inserting a binomial-like sequence into a standard jump-and-return sequence, discovered through use of a stochastic Genetic Algorithm optimisation. Compared to currently used binomial-like inversion sequences (e.g., 3-9-19 and W5), the new sequences afford wider inversion bands and narrower non-inversion bands with an equal number of pulses. As an example, two jump-and-return sandwich 10-pulse sequences achieved 95% inversion at offsets corresponding to 9.4% and 10.3% of the non-inversion band spacing, compared to 14.7% for the binomial-like W5 inversion sequence, i.e., they afforded non-inversion bands about two thirds the width of the W5 non-inversion band.

Improved binomial charts for monitoring high-quality processes

NARCIS (Netherlands)

Albers, Willem/Wim

2009-01-01

For processes concerning attribute data with (very) small failure rate p, often negative binomial control charts are used. The decision whether to stop or continue is made each time r failures have occurred, for some r≥1. Finding the optimal r for detecting a given increase of p first requires

Application of Negative Binomial Regression for Assessing Public ...

African Journals Online (AJOL)

Because the variance was nearly two times greater than the mean, the negative binomial regression model provided an improved fit to the data and accounted better for overdispersion than the Poisson regression model, which assumed that the mean and variance are the same. The level of education and race were found

Fat suppression in MR imaging with binomial pulse sequences

International Nuclear Information System (INIS)

Baudovin, C.J.; Bryant, D.J.; Bydder, G.M.; Young, I.R.

1989-01-01

This paper reports on a study to develop pulse sequences allowing suppression of fat signal on MR images without eliminating signal from other tissues with short T1. They have developed such a technique involving selective excitation of protons in water, based on a binomial pulse sequence. Imaging is performed at 0.15 T. Careful shimming is performed to maximize separation of fat and water peaks. A spin-echo 1,500/80 sequence is used, employing 90 degrees pulse with transit frequency optimized for water with null excitation of 20 H offset, followed by a section-selective 180 degrees pulse. With use of the binomial sequence for imagining, reduction in fat signal is seen on images of the pelvis and legs of volunteers. Patient studies show dramatic improvement in visualization of prostatic carcinoma compared with standard sequences

A Neutrosophic Binomial Factorial Theorem with their Refrains

Directory of Open Access Journals (Sweden)

Huda E. Khalid

2016-12-01

Full Text Available The Neutrosophic Precalculus and the Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the method used to deal with such indeterminacy. This article is innovative since the form of neutrosophic binomial factorial theorem was constructed in addition to its refrains.

Pricing American Asian options with higher moments in the underlying distribution

Science.gov (United States)

Lo, Keng-Hsin; Wang, Kehluh; Hsu, Ming-Feng

2009-01-01

We develop a modified Edgeworth binomial model with higher moment consideration for pricing American Asian options. With lognormal underlying distribution for benchmark comparison, our algorithm is as precise as that of Chalasani et al. [P. Chalasani, S. Jha, F. Egriboyun, A. Varikooty, A refined binomial lattice for pricing American Asian options, Rev. Derivatives Res. 3 (1) (1999) 85-105] if the number of the time steps increases. If the underlying distribution displays negative skewness and leptokurtosis as often observed for stock index returns, our estimates can work better than those in Chalasani et al. [P. Chalasani, S. Jha, F. Egriboyun, A. Varikooty, A refined binomial lattice for pricing American Asian options, Rev. Derivatives Res. 3 (1) (1999) 85-105] and are very similar to the benchmarks in Hull and White [J. Hull, A. White, Efficient procedures for valuing European and American path-dependent options, J. Derivatives 1 (Fall) (1993) 21-31]. The numerical analysis shows that our modified Edgeworth binomial model can value American Asian options with greater accuracy and speed given higher moments in their underlying distribution.

Flare stars and Pascal distribution

International Nuclear Information System (INIS)

Muradian, R.

1994-07-01

Observed statistics of stellar flares are described by Pascal or Negative Binomial Distribution. The analogy with other classes of chaotic production mechanisms such as hadronic particle multiplicity distributions and photoelectron counts from thermal sources is noticed. (author). 12 refs

Determination of finite-difference weights using scaled binomial windows

KAUST Repository

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties. © 2012 Society of Exploration Geophysicists.

Determination of finite-difference weights using scaled binomial windows

KAUST Repository

Chu, Chunlei

2012-05-01

The finite-difference method evaluates a derivative through a weighted summation of function values from neighboring grid nodes. Conventional finite-difference weights can be calculated either from Taylor series expansions or by Lagrange interpolation polynomials. The finite-difference method can be interpreted as a truncated convolutional counterpart of the pseudospectral method in the space domain. For this reason, we also can derive finite-difference operators by truncating the convolution series of the pseudospectral method. Various truncation windows can be employed for this purpose and they result in finite-difference operators with different dispersion properties. We found that there exists two families of scaled binomial windows that can be used to derive conventional finite-difference operators analytically. With a minor change, these scaled binomial windows can also be used to derive optimized finite-difference operators with enhanced dispersion properties. © 2012 Society of Exploration Geophysicists.

Standardized binomial models for risk or prevalence ratios and differences.

Science.gov (United States)

Richardson, David B; Kinlaw, Alan C; MacLehose, Richard F; Cole, Stephen R

2015-10-01

Epidemiologists often analyse binary outcomes in cohort and cross-sectional studies using multivariable logistic regression models, yielding estimates of adjusted odds ratios. It is widely known that the odds ratio closely approximates the risk or prevalence ratio when the outcome is rare, and it does not do so when the outcome is common. Consequently, investigators may decide to directly estimate the risk or prevalence ratio using a log binomial regression model. We describe the use of a marginal structural binomial regression model to estimate standardized risk or prevalence ratios and differences. We illustrate the proposed approach using data from a cohort study of coronary heart disease status in Evans County, Georgia, USA. The approach reduces problems with model convergence typical of log binomial regression by shifting all explanatory variables except the exposures of primary interest from the linear predictor of the outcome regression model to a model for the standardization weights. The approach also facilitates evaluation of departures from additivity in the joint effects of two exposures. Epidemiologists should consider reporting standardized risk or prevalence ratios and differences in cohort and cross-sectional studies. These are readily-obtained using the SAS, Stata and R statistical software packages. The proposed approach estimates the exposure effect in the total population. © The Author 2015; all rights reserved. Published by Oxford University Press on behalf of the International Epidemiological Association.

Football goal distributions and extremal statistics

Science.gov (United States)

Greenhough, J.; Birch, P. C.; Chapman, S. C.; Rowlands, G.

2002-12-01

We analyse the distributions of the number of goals scored by home teams, away teams, and the total scored in the match, in domestic football games from 169 countries between 1999 and 2001. The probability density functions (PDFs) of goals scored are too heavy-tailed to be fitted over their entire ranges by Poisson or negative binomial distributions which would be expected for uncorrelated processes. Log-normal distributions cannot include zero scores and here we find that the PDFs are consistent with those arising from extremal statistics. In addition, we show that it is sufficient to model English top division and FA Cup matches in the seasons of 1970/71-2000/01 on Poisson or negative binomial distributions, as reported in analyses of earlier seasons, and that these are not consistent with extremal statistics.

Calculation of generalized secant integral using binomial coefficients

International Nuclear Information System (INIS)

Guseinov, I.I.; Mamedov, B.A.

2004-01-01

A single series expansion relation is derived for the generalized secant (GS) integral in terms of binomial coefficients, exponential integrals and incomplete gamma functions. The convergence of the series is tested by the concrete cases of parameters. The formulas given in this study for the evaluation of GS integral show good rate of convergence and numerical stability

Ecological effects of the invasive giant madagascar day gecko on endemic mauritian geckos: applications of binomial-mixture and species distribution models.

Science.gov (United States)

Buckland, Steeves; Cole, Nik C; Aguirre-Gutiérrez, Jesús; Gallagher, Laura E; Henshaw, Sion M; Besnard, Aurélien; Tucker, Rachel M; Bachraz, Vishnu; Ruhomaun, Kevin; Harris, Stephen

2014-01-01

The invasion of the giant Madagascar day gecko Phelsuma grandis has increased the threats to the four endemic Mauritian day geckos (Phelsuma spp.) that have survived on mainland Mauritius. We had two main aims: (i) to predict the spatial distribution and overlap of P. grandis and the endemic geckos at a landscape level; and (ii) to investigate the effects of P. grandis on the abundance and risks of extinction of the endemic geckos at a local scale. An ensemble forecasting approach was used to predict the spatial distribution and overlap of P. grandis and the endemic geckos. We used hierarchical binomial mixture models and repeated visual estimate surveys to calculate the abundance of the endemic geckos in sites with and without P. grandis. The predicted range of each species varied from 85 km2 to 376 km2. Sixty percent of the predicted range of P. grandis overlapped with the combined predicted ranges of the four endemic geckos; 15% of the combined predicted ranges of the four endemic geckos overlapped with P. grandis. Levin's niche breadth varied from 0.140 to 0.652 between P. grandis and the four endemic geckos. The abundance of endemic geckos was 89% lower in sites with P. grandis compared to sites without P. grandis, and the endemic geckos had been extirpated at four of ten sites we surveyed with P. grandis. Species Distribution Modelling, together with the breadth metrics, predicted that P. grandis can partly share the equivalent niche with endemic species and survive in a range of environmental conditions. We provide strong evidence that smaller endemic geckos are unlikely to survive in sympatry with P. grandis. This is a cause of concern in both Mauritius and other countries with endemic species of Phelsuma.

Ecological effects of the invasive giant madagascar day gecko on endemic mauritian geckos: applications of binomial-mixture and species distribution models.

Directory of Open Access Journals (Sweden)

Steeves Buckland

Full Text Available The invasion of the giant Madagascar day gecko Phelsuma grandis has increased the threats to the four endemic Mauritian day geckos (Phelsuma spp. that have survived on mainland Mauritius. We had two main aims: (i to predict the spatial distribution and overlap of P. grandis and the endemic geckos at a landscape level; and (ii to investigate the effects of P. grandis on the abundance and risks of extinction of the endemic geckos at a local scale. An ensemble forecasting approach was used to predict the spatial distribution and overlap of P. grandis and the endemic geckos. We used hierarchical binomial mixture models and repeated visual estimate surveys to calculate the abundance of the endemic geckos in sites with and without P. grandis. The predicted range of each species varied from 85 km2 to 376 km2. Sixty percent of the predicted range of P. grandis overlapped with the combined predicted ranges of the four endemic geckos; 15% of the combined predicted ranges of the four endemic geckos overlapped with P. grandis. Levin's niche breadth varied from 0.140 to 0.652 between P. grandis and the four endemic geckos. The abundance of endemic geckos was 89% lower in sites with P. grandis compared to sites without P. grandis, and the endemic geckos had been extirpated at four of ten sites we surveyed with P. grandis. Species Distribution Modelling, together with the breadth metrics, predicted that P. grandis can partly share the equivalent niche with endemic species and survive in a range of environmental conditions. We provide strong evidence that smaller endemic geckos are unlikely to survive in sympatry with P. grandis. This is a cause of concern in both Mauritius and other countries with endemic species of Phelsuma.

Growth Estimators and Confidence Intervals for the Mean of Negative Binomial Random Variables with Unknown Dispersion

Directory of Open Access Journals (Sweden)

David Shilane

2013-01-01

Full Text Available The negative binomial distribution becomes highly skewed under extreme dispersion. Even at moderately large sample sizes, the sample mean exhibits a heavy right tail. The standard normal approximation often does not provide adequate inferences about the data's expected value in this setting. In previous work, we have examined alternative methods of generating confidence intervals for the expected value. These methods were based upon Gamma and Chi Square approximations or tail probability bounds such as Bernstein's inequality. We now propose growth estimators of the negative binomial mean. Under high dispersion, zero values are likely to be overrepresented in the data. A growth estimator constructs a normal-style confidence interval by effectively removing a small, predetermined number of zeros from the data. We propose growth estimators based upon multiplicative adjustments of the sample mean and direct removal of zeros from the sample. These methods do not require estimating the nuisance dispersion parameter. We will demonstrate that the growth estimators' confidence intervals provide improved coverage over a wide range of parameter values and asymptotically converge to the sample mean. Interestingly, the proposed methods succeed despite adding both bias and variance to the normal approximation.

Currency lookback options and observation frequency: A binomial approach

NARCIS (Netherlands)

T.H.F. Cheuk; A.C.F. Vorst (Ton)

1997-01-01

textabstractIn the last decade, interest in exotic options has been growing, especially in the over-the-counter currency market. In this paper we consider Iookback currency options, which are path-dependent. We show that a one-state variable binomial model for currency Iookback options can

Binomial confidence intervals for testing non-inferiority or superiority: a practitioner's dilemma.

Science.gov (United States)

Pradhan, Vivek; Evans, John C; Banerjee, Tathagata

2016-08-01

In testing for non-inferiority or superiority in a single arm study, the confidence interval of a single binomial proportion is frequently used. A number of such intervals are proposed in the literature and implemented in standard software packages. Unfortunately, use of different intervals leads to conflicting conclusions. Practitioners thus face a serious dilemma in deciding which one to depend on. Is there a way to resolve this dilemma? We address this question by investigating the performances of ten commonly used intervals of a single binomial proportion, in the light of two criteria, viz., coverage and expected length of the interval. © The Author(s) 2013.

Spatial modeling of rat bites and prediction of rat infestation in Peshawar valley using binomial kriging with logistic regression.

Science.gov (United States)

Ali, Asad; Zaidi, Farrah; Fatima, Syeda Hira; Adnan, Muhammad; Ullah, Saleem

2018-03-24

In this study, we propose to develop a geostatistical computational framework to model the distribution of rat bite infestation of epidemic proportion in Peshawar valley, Pakistan. Two species Rattus norvegicus and Rattus rattus are suspected to spread the infestation. The framework combines strengths of maximum entropy algorithm and binomial kriging with logistic regression to spatially model the distribution of infestation and to determine the individual role of environmental predictors in modeling the distribution trends. Our results demonstrate the significance of a number of social and environmental factors in rat infestations such as (I) high human population density; (II) greater dispersal ability of rodents due to the availability of better connectivity routes such as roads, and (III) temperature and precipitation influencing rodent fecundity and life cycle.

Difference of Sums Containing Products of Binomial Coefficients and Their Logarithms

National Research Council Canada - National Science Library

Miller, Allen R; Moskowitz, Ira S

2005-01-01

Properties of the difference of two sums containing products of binomial coefficients and their logarithms which arise in the application of Shannon's information theory to a certain class of covert channels are deduced...

Difference of Sums Containing Products of Binomial Coefficients and their Logarithms

National Research Council Canada - National Science Library

Miller, Allen R; Moskowitz, Ira S

2004-01-01

Properties of the difference of two sums containing products of binomial coefficients and their logarithms which arise in the application of Shannon's information theory to a certain class of covert channels are deduced...

e+-e- hadronic multiplicity distributions

International Nuclear Information System (INIS)

Carruthers, P.; Shih, C.C.

1986-01-01

The 29 GeV multiplicity data have been analyzed for e + -e - → hadrons using the partially coherent laser distribution (PCLD). The latter interpolates between the negative binomial and Poisson distributions as the ratio S/N of coherent/incoherent multiplcity varies from zero to infinity. The negative binomial gives an excellent fit for rather large values of the cell parameter k. Equally good fits (for full and partial rapidity range, and for the forward/backward 2 jet correlation) are obtained for the mostly coherent (almost Poissonian) PCLD with small values of k (equal to the number of jets). The reasons for the existence of this tradeoff are explained in detail. The existence of the resulting ambiguity is traced to the insensitivity of the probability distribution to phase information in the hadronic density matrix. The study of higher order correlations (intensity interferometry) among like sign-particles is recommended to resolve this question

Geographically weighted negative binomial regression applied to zonal level safety performance models.

Science.gov (United States)

Gomes, Marcos José Timbó Lima; Cunto, Flávio; da Silva, Alan Ricardo

2017-09-01

Generalized Linear Models (GLM) with negative binomial distribution for errors, have been widely used to estimate safety at the level of transportation planning. The limited ability of this technique to take spatial effects into account can be overcome through the use of local models from spatial regression techniques, such as Geographically Weighted Poisson Regression (GWPR). Although GWPR is a system that deals with spatial dependency and heterogeneity and has already been used in some road safety studies at the planning level, it fails to account for the possible overdispersion that can be found in the observations on road-traffic crashes. Two approaches were adopted for the Geographically Weighted Negative Binomial Regression (GWNBR) model to allow discrete data to be modeled in a non-stationary form and to take note of the overdispersion of the data: the first examines the constant overdispersion for all the traffic zones and the second includes the variable for each spatial unit. This research conducts a comparative analysis between non-spatial global crash prediction models and spatial local GWPR and GWNBR at the level of traffic zones in Fortaleza/Brazil. A geographic database of 126 traffic zones was compiled from the available data on exposure, network characteristics, socioeconomic factors and land use. The models were calibrated by using the frequency of injury crashes as a dependent variable and the results showed that GWPR and GWNBR achieved a better performance than GLM for the average residuals and likelihood as well as reducing the spatial autocorrelation of the residuals, and the GWNBR model was more able to capture the spatial heterogeneity of the crash frequency. Copyright © 2017 Elsevier Ltd. All rights reserved.

A Bayesian non-inferiority test for two independent binomial proportions.

Science.gov (United States)

Kawasaki, Yohei; Miyaoka, Etsuo

2013-01-01

In drug development, non-inferiority tests are often employed to determine the difference between two independent binomial proportions. Many test statistics for non-inferiority are based on the frequentist framework. However, research on non-inferiority in the Bayesian framework is limited. In this paper, we suggest a new Bayesian index τ = P(π₁  > π₂-Δ₀|X₁, X₂), where X₁ and X₂ denote binomial random variables for trials n1 and n₂, and parameters π₁ and π₂ , respectively, and the non-inferiority margin is Δ₀> 0. We show two calculation methods for τ, an approximate method that uses normal approximation and an exact method that uses an exact posterior PDF. We compare the approximate probability with the exact probability for τ. Finally, we present the results of actual clinical trials to show the utility of index τ. Copyright © 2013 John Wiley & Sons, Ltd.

Detection of progression of glaucomatous visual field damage using the point-wise method with the binomial test.

Science.gov (United States)

Karakawa, Ayako; Murata, Hiroshi; Hirasawa, Hiroyo; Mayama, Chihiro; Asaoka, Ryo

2013-01-01

To compare the performance of newly proposed point-wise linear regression (PLR) with the binomial test (binomial PLR) against mean deviation (MD) trend analysis and permutation analyses of PLR (PoPLR), in detecting global visual field (VF) progression in glaucoma. 15 VFs (Humphrey Field Analyzer, SITA standard, 24-2) were collected from 96 eyes of 59 open angle glaucoma patients (6.0 ± 1.5 [mean ± standard deviation] years). Using the total deviation of each point on the 2(nd) to 16(th) VFs (VF2-16), linear regression analysis was carried out. The numbers of VF test points with a significant trend at various probability levels (pbinomial test (one-side). A VF series was defined as "significant" if the median p-value from the binomial test was binomial PLR method (0.14 to 0.86) was significantly higher than MD trend analysis (0.04 to 0.89) and PoPLR (0.09 to 0.93). The PIS of the proposed method (0.0 to 0.17) was significantly lower than the MD approach (0.0 to 0.67) and PoPLR (0.07 to 0.33). The PBNS of the three approaches were not significantly different. The binomial BLR method gives more consistent results than MD trend analysis and PoPLR, hence it will be helpful as a tool to 'flag' possible VF deterioration.

Hits per trial: Basic analysis of binomial data

International Nuclear Information System (INIS)

Atwood, C.L.

1994-09-01

This report presents simple statistical methods for analyzing binomial data, such as the number of failures in some number of demands. It gives point estimates, confidence intervals, and Bayesian intervals for the failure probability. It shows how to compare subsets of the data, both graphically and by statistical tests, and how to look for trends in time. It presents a compound model when the failure probability varies randomly. Examples and SAS programs are given

Hits per trial: Basic analysis of binomial data

Energy Technology Data Exchange (ETDEWEB)

Atwood, C.L.

1994-09-01

This report presents simple statistical methods for analyzing binomial data, such as the number of failures in some number of demands. It gives point estimates, confidence intervals, and Bayesian intervals for the failure probability. It shows how to compare subsets of the data, both graphically and by statistical tests, and how to look for trends in time. It presents a compound model when the failure probability varies randomly. Examples and SAS programs are given.

Analysis of railroad tank car releases using a generalized binomial model.

Science.gov (United States)

Liu, Xiang; Hong, Yili

2015-11-01

The United States is experiencing an unprecedented boom in shale oil production, leading to a dramatic growth in petroleum crude oil traffic by rail. In 2014, U.S. railroads carried over 500,000 tank carloads of petroleum crude oil, up from 9500 in 2008 (a 5300% increase). In light of continual growth in crude oil by rail, there is an urgent national need to manage this emerging risk. This need has been underscored in the wake of several recent crude oil release incidents. In contrast to highway transport, which usually involves a tank trailer, a crude oil train can carry a large number of tank cars, having the potential for a large, multiple-tank-car release incident. Previous studies exclusively assumed that railroad tank car releases in the same train accident are mutually independent, thereby estimating the number of tank cars releasing given the total number of tank cars derailed based on a binomial model. This paper specifically accounts for dependent tank car releases within a train accident. We estimate the number of tank cars releasing given the number of tank cars derailed based on a generalized binomial model. The generalized binomial model provides a significantly better description for the empirical tank car accident data through our numerical case study. This research aims to provide a new methodology and new insights regarding the further development of risk management strategies for improving railroad crude oil transportation safety. Copyright © 2015 Elsevier Ltd. All rights reserved.

The Compound Binomial Risk Model with Randomly Charging Premiums and Paying Dividends to Shareholders

Directory of Open Access Journals (Sweden)

Xiong Wang

2013-01-01

Full Text Available Based on characteristics of the nonlife joint-stock insurance company, this paper presents a compound binomial risk model that randomizes the premium income on unit time and sets the threshold for paying dividends to shareholders. In this model, the insurance company obtains the insurance policy in unit time with probability and pays dividends to shareholders with probability when the surplus is no less than . We then derive the recursive formulas of the expected discounted penalty function and the asymptotic estimate for it. And we will derive the recursive formulas and asymptotic estimates for the ruin probability and the distribution function of the deficit at ruin. The numerical examples have been shown to illustrate the accuracy of the asymptotic estimations.

Some Instructional Issues in Hypergeometric Distribution

Directory of Open Access Journals (Sweden)

Anwar H. Joarder

2012-07-01

Full Text Available 800x600 Normal 0 false false false EN-US X-NONE X-NONE A brief introduction to sampling without replacement is presented. We represent the probability of a sample outcome in sampling without replacement from a finite population by three equivalent forms involving permutation and combination. Then it is used to calculate the probability of any number of successes in a given sample. The resulting forms are equivalent to the well known mass function of the hypergeometric distribution. Vandermonde’s identity readily justifies different forms of the mass function. One of the new form of the mass function embodies binomial coefficient showing much resemblance to that of binomial distribution. It also yields some interesting identities. Some other related issues are discussed.

Binomial Distribution Sample Confidence Intervals Estimation 7. Absolute Risk Reduction and ARR-like Expressions

Directory of Open Access Journals (Sweden)

Andrei ACHIMAŞ CADARIU

2004-08-01

Full Text Available Assessments of a controlled clinical trial suppose to interpret some key parameters as the controlled event rate, experimental event date, relative risk, absolute risk reduction, relative risk reduction, number needed to treat when the effect of the treatment are dichotomous variables. Defined as the difference in the event rate between treatment and control groups, the absolute risk reduction is the parameter that allowed computing the number needed to treat. The absolute risk reduction is compute when the experimental treatment reduces the risk for an undesirable outcome/event. In medical literature when the absolute risk reduction is report with its confidence intervals, the method used is the asymptotic one, even if it is well know that may be inadequate. The aim of this paper is to introduce and assess nine methods of computing confidence intervals for absolute risk reduction and absolute risk reduction – like function.Computer implementations of the methods use the PHP language. Methods comparison uses the experimental errors, the standard deviations, and the deviation relative to the imposed significance level for specified sample sizes. Six methods of computing confidence intervals for absolute risk reduction and absolute risk reduction-like functions were assessed using random binomial variables and random sample sizes.The experiments shows that the ADAC, and ADAC1 methods obtains the best overall performance of computing confidence intervals for absolute risk reduction.

Possibility and challenges of conversion of current virus species names to Linnaean binomials

Science.gov (United States)

Thomas, Postler; Clawson, Anna N.; Amarasinghe, Gaya K.; Basler, Christopher F.; Bavari, Sina; Benko, Maria; Blasdell, Kim R.; Briese, Thomas; Buchmeier, Michael J.; Bukreyev, Alexander; Calisher, Charles H.; Chandran, Kartik; Charrel, Remi; Clegg, Christopher S.; Collins, Peter L.; De la Torre, Juan Carlos; DeRisi, Joseph L.; Dietzgen, Ralf G.; Dolnik, Olga; Durrwald, Ralf; Dye, John M.; Easton, Andrew J.; Emonet, Sebastian; Formenty, Pierre; Fouchier, Ron A. M.; Ghedin, Elodie; Gonzalez, Jean-Paul; Harrach, Balazs; Hewson, Roger; Horie, Masayuki; Jiang, Daohong; Kobinger, Gary P.; Kondo, Hideki; Kropinski, Andrew; Krupovic, Mart; Kurath, Gael; Lamb, Robert A.; Leroy, Eric M.; Lukashevich, Igor S.; Maisner, Andrea; Mushegian, Arcady; Netesov, Sergey V.; Nowotny, Norbert; Patterson, Jean L.; Payne, Susan L.; Paweska, Janusz T.; Peters, C.J.; Radoshitzky, Sheli; Rima, Bertus K.; Romanowski, Victor; Rubbenstroth, Dennis; Sabanadzovic, Sead; Sanfacon, Helene; Salvato , Maria; Schwemmle, Martin; Smither, Sophie J.; Stenglein, Mark; Stone, D.M.; Takada , Ayato; Tesh, Robert B.; Tomonaga, Keizo; Tordo, N.; Towner, Jonathan S.; Vasilakis, Nikos; Volchkov, Victor E.; Jensen, Victoria; Walker, Peter J.; Wang, Lin-Fa; Varsani, Arvind; Whitfield , Anna E.; Zerbini, Francisco Murilo; Kuhn, Jens H.

2017-01-01

Botanical, mycological, zoological, and prokaryotic species names follow the Linnaean format, consisting of an italicized Latinized binomen with a capitalized genus name and a lower case species epithet (e.g., Homo sapiens). Virus species names, however, do not follow a uniform format, and, even when binomial, are not Linnaean in style. In this thought exercise, we attempted to convert all currently official names of species included in the virus family Arenaviridae and the virus order Mononegavirales to Linnaean binomials, and to identify and address associated challenges and concerns. Surprisingly, this endeavor was not as complicated or time-consuming as even the authors of this article expected when conceiving the experiment.

Modeling and Predistortion of Envelope Tracking Power Amplifiers using a Memory Binomial Model

DEFF Research Database (Denmark)

Tafuri, Felice Francesco; Sira, Daniel; Larsen, Torben

2013-01-01

. The model definition is based on binomial series, hence the name of memory binomial model (MBM). The MBM is here applied to measured data-sets acquired from an ET measurement set-up. When used as a PA model the MBM showed an NMSE (Normalized Mean Squared Error) as low as −40dB and an ACEPR (Adjacent Channel...... Error Power Ratio) below −51 dB. The simulated predistortion results showed that the MBM can improve the compensation of distortion in the adjacent channel of 5.8 dB and 5.7 dB compared to a memory polynomial predistorter (MPPD). The predistortion performance in the time domain showed an NMSE...

Time evolution of negative binomial optical field in a diffusion channel

International Nuclear Information System (INIS)

Liu Tang-Kun; Wu Pan-Pan; Shan Chuan-Jia; Liu Ji-Bing; Fan Hong-Yi

2015-01-01

We find the time evolution law of a negative binomial optical field in a diffusion channel. We reveal that by adjusting the diffusion parameter, the photon number can be controlled. Therefore, the diffusion process can be considered a quantum controlling scheme through photon addition. (paper)

Adaptive multiresolution Hermite-Binomial filters for image edge and texture analysis

NARCIS (Netherlands)

Gu, Y.H.; Katsaggelos, A.K.

1994-01-01

A new multiresolution image analysis approach using adaptive Hermite-Binomial filters is presented in this paper. According to the local image structural and textural properties, the analysis filter kernels are made adaptive both in their scales and orders. Applications of such an adaptive filtering

Fermat’s Little Theorem via Divisibility of Newton’s Binomial

Directory of Open Access Journals (Sweden)

Ziobro Rafał

2015-09-01

Full Text Available Solving equations in integers is an important part of the number theory [29]. In many cases it can be conducted by the factorization of equation’s elements, such as the Newton’s binomial. The article introduces several simple formulas, which may facilitate this process. Some of them are taken from relevant books [28], [14].

Learning Binomial Probability Concepts with Simulation, Random Numbers and a Spreadsheet

Science.gov (United States)

Rochowicz, John A., Jr.

2005-01-01

This paper introduces the reader to the concepts of binomial probability and simulation. A spreadsheet is used to illustrate these concepts. Random number generators are great technological tools for demonstrating the concepts of probability. Ideas of approximation, estimation, and mathematical usefulness provide numerous ways of learning…

On a saddlepoint approximation to the Markov binomial distribution

DEFF Research Database (Denmark)

Jensen, Jens Ledet

A nonstandard saddlepoint approximation to the distribution of a sum of Markov dependent trials is introduced. The relative error of the approximation is studied, not only for the number of summands tending to infinity, but also for the parameter approaching the boundary of its definition range...

Modelling the Frequency of Operational Risk Losses under the Basel II Capital Accord: A Comparative study of Poisson and Negative Binomial Distributions

OpenAIRE

Silver, Toni O.

2013-01-01

2013 dissertation for MSc in Finance and Risk Management. Selected by academic staff as a good example of a masters level dissertation. \\ud \\ud This study investigated the two major methods of modelling the frequency of\\ud operational losses under the BCBS Accord of 1998 known as Basel II Capital\\ud Accord. It compared the Poisson method of modelling the frequency of\\ud losses to that of the Negative Binomial. The frequency of operational losses\\ud was investigated using a cross section of se...

Joint Analysis of Binomial and Continuous Traits with a Recursive Model

DEFF Research Database (Denmark)

Varona, Louis; Sorensen, Daniel

2014-01-01

This work presents a model for the joint analysis of a binomial and a Gaussian trait using a recursive parametrization that leads to a computationally efficient implementation. The model is illustrated in an analysis of mortality and litter size in two breeds of Danish pigs, Landrace and Yorkshir...

Binomial Coefficients Modulo a Prime--A Visualization Approach to Undergraduate Research

Science.gov (United States)

Bardzell, Michael; Poimenidou, Eirini

2011-01-01

In this article we present, as a case study, results of undergraduate research involving binomial coefficients modulo a prime "p." We will discuss how undergraduates were involved in the project, even with a minimal mathematical background beforehand. There are two main avenues of exploration described to discover these binomial…

A binomial random sum of present value models in investment analysis

OpenAIRE

Βουδούρη, Αγγελική; Ντζιαχρήστος, Ευάγγελος

1997-01-01

Stochastic present value models have been widely adopted in financial theory and practice and play a very important role in capital budgeting and profit planning. The purpose of this paper is to introduce a binomial random sum of stochastic present value models and offer an application in investment analysis.

Using the Binomial Series to Prove the Arithmetic Mean-Geometric Mean Inequality

Science.gov (United States)

Persky, Ronald L.

2003-01-01

In 1968, Leon Gerber compared (1 + x)[superscript a] to its kth partial sum as a binomial series. His result is stated and, as an application of this result, a proof of the arithmetic mean-geometric mean inequality is presented.

Experimental investigation of statistical models describing distribution of counts

International Nuclear Information System (INIS)

Salma, I.; Zemplen-Papp, E.

1992-01-01

The binomial, Poisson and modified Poisson models which are used for describing the statistical nature of the distribution of counts are compared theoretically, and conclusions for application are considered. The validity of the Poisson and the modified Poisson statistical distribution for observing k events in a short time interval is investigated experimentally for various measuring times. The experiments to measure the influence of the significant radioactive decay were performed with 89 Y m (T 1/2 =16.06 s), using a multichannel analyser (4096 channels) in the multiscaling mode. According to the results, Poisson statistics describe the counting experiment for short measuring times (up to T=0.5T 1/2 ) and its application is recommended. However, analysis of the data demonstrated, with confidence, that for long measurements (T≥T 1/2 ) Poisson distribution is not valid and the modified Poisson function is preferable. The practical implications in calculating uncertainties and in optimizing the measuring time are discussed. Differences between the standard deviations evaluated on the basis of the Poisson and binomial models are especially significant for experiments with long measuring time (T/T 1/2 ≥2) and/or large detection efficiency (ε>0.30). Optimization of the measuring time for paired observations yields the same solution for either the binomial or the Poisson distribution. (orig.)

Poisson and negative binomial item count techniques for surveys with sensitive question.

Science.gov (United States)

Tian, Guo-Liang; Tang, Man-Lai; Wu, Qin; Liu, Yin

2017-04-01

Although the item count technique is useful in surveys with sensitive questions, privacy of those respondents who possess the sensitive characteristic of interest may not be well protected due to a defect in its original design. In this article, we propose two new survey designs (namely the Poisson item count technique and negative binomial item count technique) which replace several independent Bernoulli random variables required by the original item count technique with a single Poisson or negative binomial random variable, respectively. The proposed models not only provide closed form variance estimate and confidence interval within [0, 1] for the sensitive proportion, but also simplify the survey design of the original item count technique. Most importantly, the new designs do not leak respondents' privacy. Empirical results show that the proposed techniques perform satisfactorily in the sense that it yields accurate parameter estimate and confidence interval.

Data analysis using the Binomial Failure Rate common cause model

International Nuclear Information System (INIS)

Atwood, C.L.

1983-09-01

This report explains how to use the Binomial Failure Rate (BFR) method to estimate common cause failure rates. The entire method is described, beginning with the conceptual model, and covering practical issues of data preparation, treatment of variation in the failure rates, Bayesian estimation of the quantities of interest, checking the model assumptions for lack of fit to the data, and the ultimate application of the answers

Estimating spatial and temporal components of variation in count data using negative binomial mixed models

Science.gov (United States)

Irwin, Brian J.; Wagner, Tyler; Bence, James R.; Kepler, Megan V.; Liu, Weihai; Hayes, Daniel B.

2013-01-01

Partitioning total variability into its component temporal and spatial sources is a powerful way to better understand time series and elucidate trends. The data available for such analyses of fish and other populations are usually nonnegative integer counts of the number of organisms, often dominated by many low values with few observations of relatively high abundance. These characteristics are not well approximated by the Gaussian distribution. We present a detailed description of a negative binomial mixed-model framework that can be used to model count data and quantify temporal and spatial variability. We applied these models to data from four fishery-independent surveys of Walleyes Sander vitreus across the Great Lakes basin. Specifically, we fitted models to gill-net catches from Wisconsin waters of Lake Superior; Oneida Lake, New York; Saginaw Bay in Lake Huron, Michigan; and Ohio waters of Lake Erie. These long-term monitoring surveys varied in overall sampling intensity, the total catch of Walleyes, and the proportion of zero catches. Parameter estimation included the negative binomial scaling parameter, and we quantified the random effects as the variations among gill-net sampling sites, the variations among sampled years, and site × year interactions. This framework (i.e., the application of a mixed model appropriate for count data in a variance-partitioning context) represents a flexible approach that has implications for monitoring programs (e.g., trend detection) and for examining the potential of individual variance components to serve as response metrics to large-scale anthropogenic perturbations or ecological changes.

e/sup +/ -e/sup -/ hadronic multiplicity distributions

International Nuclear Information System (INIS)

Carruthers, P.; Shih, C.C.

1987-01-01

The authors have analyzed the 29 GeV multiplicity data for e/sup +/ -e/sup -/ → hadrons using the partially coherent laser distribution (PCLD). The latter interpolates between the negative binomial and Poisson distributions as the ratio S/N of coherent/incoherent multiplicity varies from zero to infinity. The negative binomial gives an excellent fit for rather large values of the cell parameter κ. Equally good fits (for full and partial rapidity range, and for the forward/backward 2 jet correlation) are obtained for the mostly coherent (almost Poissonian) PCLD with small values of κ (equal to the number of jets). The reasons for the existence of this tradeoff are explained in detail. The existence of the resulting ambiguity is traced to the insensitivity of the probability distribution to phase information in the hadronic density matrix. They recommend the study of higher order correlations (intensity interferometry) among like-sign particles to resolve this question

Topology of unitary groups and the prime orders of binomial coefficients

Science.gov (United States)

Duan, HaiBao; Lin, XianZu

2017-09-01

Let $c:SU(n)\\rightarrow PSU(n)=SU(n)/\\mathbb{Z}_{n}$ be the quotient map of the special unitary group $SU(n)$ by its center subgroup $\\mathbb{Z}_{n}$. We determine the induced homomorphism $c^{\\ast}:$ $H^{\\ast}(PSU(n))\\rightarrow H^{\\ast}(SU(n))$ on cohomologies by computing with the prime orders of binomial coefficients

Poissonian and binomial models in radionuclide metrology by liquid scintillation counting

International Nuclear Information System (INIS)

Grau Malonda, A.

1990-01-01

Binomial and Poissonian models developed for calculating the counting efficiency from a free parameter is analysed in this paper. This model have been applied to liquid scintillator counting systems with two or three photomultipliers. It is mathematically demostrated that both models are equivalent and that the counting efficiencies calculated either from one or the other model are identical. (Author)

Raw and Central Moments of Binomial Random Variables via Stirling Numbers

Science.gov (United States)

Griffiths, Martin

2013-01-01

We consider here the problem of calculating the moments of binomial random variables. It is shown how formulae for both the raw and the central moments of such random variables may be obtained in a recursive manner utilizing Stirling numbers of the first kind. Suggestions are also provided as to how students might be encouraged to explore this…

Entanglement properties between two atoms in the binomial optical field interacting with two entangled atoms

International Nuclear Information System (INIS)

Liu Tang-Kun; Zhang Kang-Long; Tao Yu; Shan Chuan-Jia; Liu Ji-Bing

2016-01-01

The temporal evolution of the degree of entanglement between two atoms in a system of the binomial optical field interacting with two arbitrary entangled atoms is investigated. The influence of the strength of the dipole–dipole interaction between two atoms, probabilities of the Bernoulli trial, and particle number of the binomial optical field on the temporal evolution of the atomic entanglement are discussed. The result shows that the two atoms are always in the entanglement state. Moreover, if and only if the two atoms are initially in the maximally entangled state, the entanglement evolution is not affected by the parameters, and the degree of entanglement is always kept as 1. (paper)

[Application of negative binomial regression and modified Poisson regression in the research of risk factors for injury frequency].

Science.gov (United States)

Cao, Qingqing; Wu, Zhenqiang; Sun, Ying; Wang, Tiezhu; Han, Tengwei; Gu, Chaomei; Sun, Yehuan

2011-11-01

To Eexplore the application of negative binomial regression and modified Poisson regression analysis in analyzing the influential factors for injury frequency and the risk factors leading to the increase of injury frequency. 2917 primary and secondary school students were selected from Hefei by cluster random sampling method and surveyed by questionnaire. The data on the count event-based injuries used to fitted modified Poisson regression and negative binomial regression model. The risk factors incurring the increase of unintentional injury frequency for juvenile students was explored, so as to probe the efficiency of these two models in studying the influential factors for injury frequency. The Poisson model existed over-dispersion (P Poisson regression and negative binomial regression model, was fitted better. respectively. Both showed that male gender, younger age, father working outside of the hometown, the level of the guardian being above junior high school and smoking might be the results of higher injury frequencies. On a tendency of clustered frequency data on injury event, both the modified Poisson regression analysis and negative binomial regression analysis can be used. However, based on our data, the modified Poisson regression fitted better and this model could give a more accurate interpretation of relevant factors affecting the frequency of injury.

A note on inconsistent families of discrete multivariate distributions

KAUST Repository

Ghosh, Sugata; Dutta, Subhajit; Genton, Marc G.

2017-01-01

We construct a d-dimensional discrete multivariate distribution for which any proper subset of its components belongs to a specific family of distributions. However, the joint d-dimensional distribution fails to belong to that family and in other words, it is ‘inconsistent’ with the distribution of these subsets. We also address preservation of this ‘inconsistency’ property for the symmetric Binomial distribution, and some discrete distributions arising from the multivariate discrete normal distribution.

A note on inconsistent families of discrete multivariate distributions

KAUST Repository

Ghosh, Sugata

2017-07-05

We construct a d-dimensional discrete multivariate distribution for which any proper subset of its components belongs to a specific family of distributions. However, the joint d-dimensional distribution fails to belong to that family and in other words, it is ‘inconsistent’ with the distribution of these subsets. We also address preservation of this ‘inconsistency’ property for the symmetric Binomial distribution, and some discrete distributions arising from the multivariate discrete normal distribution.

Estimation of adjusted rate differences using additive negative binomial regression.

Science.gov (United States)

Donoghoe, Mark W; Marschner, Ian C

2016-08-15

Rate differences are an important effect measure in biostatistics and provide an alternative perspective to rate ratios. When the data are event counts observed during an exposure period, adjusted rate differences may be estimated using an identity-link Poisson generalised linear model, also known as additive Poisson regression. A problem with this approach is that the assumption of equality of mean and variance rarely holds in real data, which often show overdispersion. An additive negative binomial model is the natural alternative to account for this; however, standard model-fitting methods are often unable to cope with the constrained parameter space arising from the non-negativity restrictions of the additive model. In this paper, we propose a novel solution to this problem using a variant of the expectation-conditional maximisation-either algorithm. Our method provides a reliable way to fit an additive negative binomial regression model and also permits flexible generalisations using semi-parametric regression functions. We illustrate the method using a placebo-controlled clinical trial of fenofibrate treatment in patients with type II diabetes, where the outcome is the number of laser therapy courses administered to treat diabetic retinopathy. An R package is available that implements the proposed method. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

QNB: differential RNA methylation analysis for count-based small-sample sequencing data with a quad-negative binomial model.

Science.gov (United States)

Liu, Lian; Zhang, Shao-Wu; Huang, Yufei; Meng, Jia

2017-08-31

As a newly emerged research area, RNA epigenetics has drawn increasing attention recently for the participation of RNA methylation and other modifications in a number of crucial biological processes. Thanks to high throughput sequencing techniques, such as, MeRIP-Seq, transcriptome-wide RNA methylation profile is now available in the form of count-based data, with which it is often of interests to study the dynamics at epitranscriptomic layer. However, the sample size of RNA methylation experiment is usually very small due to its costs; and additionally, there usually exist a large number of genes whose methylation level cannot be accurately estimated due to their low expression level, making differential RNA methylation analysis a difficult task. We present QNB, a statistical approach for differential RNA methylation analysis with count-based small-sample sequencing data. Compared with previous approaches such as DRME model based on a statistical test covering the IP samples only with 2 negative binomial distributions, QNB is based on 4 independent negative binomial distributions with their variances and means linked by local regressions, and in the way, the input control samples are also properly taken care of. In addition, different from DRME approach, which relies only the input control sample only for estimating the background, QNB uses a more robust estimator for gene expression by combining information from both input and IP samples, which could largely improve the testing performance for very lowly expressed genes. QNB showed improved performance on both simulated and real MeRIP-Seq datasets when compared with competing algorithms. And the QNB model is also applicable to other datasets related RNA modifications, including but not limited to RNA bisulfite sequencing, m 1 A-Seq, Par-CLIP, RIP-Seq, etc.

Confidence Intervals for Weighted Composite Scores under the Compound Binomial Error Model

Science.gov (United States)

Kim, Kyung Yong; Lee, Won-Chan

2018-01-01

Reporting confidence intervals with test scores helps test users make important decisions about examinees by providing information about the precision of test scores. Although a variety of estimation procedures based on the binomial error model are available for computing intervals for test scores, these procedures assume that items are randomly…

Computation of Clebsch-Gordan and Gaunt coefficients using binomial coefficients

International Nuclear Information System (INIS)

Guseinov, I.I.; Oezmen, A.; Atav, Ue

1995-01-01

Using binomial coefficients the Clebsch-Gordan and Gaunt coefficients were calculated for extremely large quantum numbers. The main advantage of this approach is directly calculating these coefficients, instead of using recursion relations. Accuracy of the results is quite high for quantum numbers l 1 , and l 2 up to 100. Despite direct calculation, the CPU times are found comparable with those given in the related literature. 11 refs., 1 fig., 2 tabs

A distribución binomial como ferramenta na resolución de problemas de xenética

OpenAIRE

Ron Pedreira, Antonio Miguel de; Martínez, Ana María

1999-01-01

La distribución binomial presenta una amplia gama de campos de aplicación debido a que en situaciones cotidianas, se presenta con elevada frecuencia algún tipo de situación basada en dos hechos diferentes, alternativos, excluyentes y con probablilidades que suman 1 (cien por cien), es decir, el hecho cierto. En cuanto a la genética, pueden encontrarse supuestos que permitan la aplicación de la distribución binomial en ámbitos de la genética molecular, mendeliana, cuantitativa y genética de po...

Application of a binomial cusum control chart to monitor one drinking water indicator

Directory of Open Access Journals (Sweden)

Elisa Henning

2014-02-01

Full Text Available The aim of this study is to analyze the use of a binomial cumulative sum chart (CUSUM to monitor the presence of total coliforms, biological indicators of quality of water supplies in water treatment processes. The sample series were monthly taken from a water treatment plant and were analyzed from 2007 to 2009. The statistical treatment of the data was performed using GNU R, and routines were created for the approximation of the upper limit of the binomial CUSUM chart. Furthermore, a comparative study was conducted to investigate whether there is a significant difference in sensitivity between the use of CUSUM and the traditional Shewhart chart, the most commonly used chart in process monitoring. The results obtained demonstrate that this study was essential for making the right choice in selecting a chart for the statistical analysis of this process.

Baseline for the cumulants of net-proton distributions at STAR

International Nuclear Information System (INIS)

Luo, Xiaofeng; Mohanty, Bedangadas; Xu, Nu

2014-01-01

We present a systematic comparison between the recently measured cumulants of the net-proton distributions by STAR for 0–5% central Au + Au collisions at √(s NN )=7.7–200 GeV and two kinds of possible baseline measure, the Poisson and Binomial baselines. These baseline measures are assuming that the proton and anti-proton distributions independently follow Poisson statistics or Binomial statistics. The higher order cumulant net-proton data are observed to deviate from all the baseline measures studied at 19.6 and 27 GeV. We also compare the net-proton with net-baryon fluctuations in UrQMD and AMPT model, and convert the net-proton fluctuations to net-baryon fluctuations in AMPT model by using a set of formula

Comparison and Field Validation of Binomial Sampling Plans for Oligonychus perseae (Acari: Tetranychidae) on Hass Avocado in Southern California.

Science.gov (United States)

Lara, Jesus R; Hoddle, Mark S

2015-08-01

Oligonychus perseae Tuttle, Baker, & Abatiello is a foliar pest of 'Hass' avocados [Persea americana Miller (Lauraceae)]. The recommended action threshold is 50-100 motile mites per leaf, but this count range and other ecological factors associated with O. perseae infestations limit the application of enumerative sampling plans in the field. Consequently, a comprehensive modeling approach was implemented to compare the practical application of various binomial sampling models for decision-making of O. perseae in California. An initial set of sequential binomial sampling models were developed using three mean-proportion modeling techniques (i.e., Taylor's power law, maximum likelihood, and an empirical model) in combination with two-leaf infestation tally thresholds of either one or two mites. Model performance was evaluated using a robust mite count database consisting of >20,000 Hass avocado leaves infested with varying densities of O. perseae and collected from multiple locations. Operating characteristic and average sample number results for sequential binomial models were used as the basis to develop and validate a standardized fixed-size binomial sampling model with guidelines on sample tree and leaf selection within blocks of avocado trees. This final validated model requires a leaf sampling cost of 30 leaves and takes into account the spatial dynamics of O. perseae to make reliable mite density classifications for a 50-mite action threshold. Recommendations for implementing this fixed-size binomial sampling plan to assess densities of O. perseae in commercial California avocado orchards are discussed. © The Authors 2015. Published by Oxford University Press on behalf of Entomological Society of America. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Reducing Monte Carlo error in the Bayesian estimation of risk ratios using log-binomial regression models.

Science.gov (United States)

Salmerón, Diego; Cano, Juan A; Chirlaque, María D

2015-08-30

In cohort studies, binary outcomes are very often analyzed by logistic regression. However, it is well known that when the goal is to estimate a risk ratio, the logistic regression is inappropriate if the outcome is common. In these cases, a log-binomial regression model is preferable. On the other hand, the estimation of the regression coefficients of the log-binomial model is difficult owing to the constraints that must be imposed on these coefficients. Bayesian methods allow a straightforward approach for log-binomial regression models and produce smaller mean squared errors in the estimation of risk ratios than the frequentist methods, and the posterior inferences can be obtained using the software WinBUGS. However, Markov chain Monte Carlo methods implemented in WinBUGS can lead to large Monte Carlo errors in the approximations to the posterior inferences because they produce correlated simulations, and the accuracy of the approximations are inversely related to this correlation. To reduce correlation and to improve accuracy, we propose a reparameterization based on a Poisson model and a sampling algorithm coded in R. Copyright © 2015 John Wiley & Sons, Ltd.

A comparison of different ways of including baseline counts in negative binomial models for data from falls prevention trials.

Science.gov (United States)

Zheng, Han; Kimber, Alan; Goodwin, Victoria A; Pickering, Ruth M

2018-01-01

A common design for a falls prevention trial is to assess falling at baseline, randomize participants into an intervention or control group, and ask them to record the number of falls they experience during a follow-up period of time. This paper addresses how best to include the baseline count in the analysis of the follow-up count of falls in negative binomial (NB) regression. We examine the performance of various approaches in simulated datasets where both counts are generated from a mixed Poisson distribution with shared random subject effect. Including the baseline count after log-transformation as a regressor in NB regression (NB-logged) or as an offset (NB-offset) resulted in greater power than including the untransformed baseline count (NB-unlogged). Cook and Wei's conditional negative binomial (CNB) model replicates the underlying process generating the data. In our motivating dataset, a statistically significant intervention effect resulted from the NB-logged, NB-offset, and CNB models, but not from NB-unlogged, and large, outlying baseline counts were overly influential in NB-unlogged but not in NB-logged. We conclude that there is little to lose by including the log-transformed baseline count in standard NB regression compared to CNB for moderate to larger sized datasets. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Bayesian analysis of overdispersed chromosome aberration data with the negative binomial model

International Nuclear Information System (INIS)

Brame, R.S.; Groer, P.G.

2002-01-01

The usual assumption of a Poisson model for the number of chromosome aberrations in controlled calibration experiments implies variance equal to the mean. However, it is known that chromosome aberration data from experiments involving high linear energy transfer radiations can be overdispersed, i.e. the variance is greater than the mean. Present methods for dealing with overdispersed chromosome data rely on frequentist statistical techniques. In this paper, the problem of overdispersion is considered from a Bayesian standpoint. The Bayes Factor is used to compare Poisson and negative binomial models for two previously published calibration data sets describing the induction of dicentric chromosome aberrations by high doses of neutrons. Posterior densities for the model parameters, which characterise dose response and overdispersion are calculated and graphed. Calibrative densities are derived for unknown neutron doses from hypothetical radiation accident data to determine the impact of different model assumptions on dose estimates. The main conclusion is that an initial assumption of a negative binomial model is the conservative approach to chromosome dosimetry for high LET radiations. (author)

Spatial Distribution of Eggs of Alabama argillacea Hübner and Heliothis virescens Fabricius (Lepidoptera: Noctuidae on Bt and non-BtCotton

Directory of Open Access Journals (Sweden)

TATIANA R. RODRIGUES

2015-12-01

Full Text Available ABSTRACT Among the options to control Alabama argillacea (Hübner, 1818 and Heliothis virescens (Fabricius, 1781 on cotton, insecticide spraying and biological control have been extensively used. The GM'Bt' cotton has been introduced as an extremely viable alternative, but it is yet not known how transgenic plants affect populations of organisms that are interrelated in an agroecosystem. For this reason, it is important to know how the spatial arrangement of pests and beneficial insect are affected, which may call for changes in the methods used for sampling these species. This study was conducted with the goal to investigate the pattern of spatial distribution of eggs of A. argillacea and H. virescens in DeltaOpalTM (non-Bt and DP90BTMBt cotton cultivars. Data were collected during the agricultural year 2006/2007 in two areas of 5,000 m2, located in in the district of Nova América, Caarapó municipality. In each sampling area, comprising 100 plots of 50 m2, 15 evaluations were performed on two plants per plot. The sampling consisted in counting the eggs. The aggregation index (variance/mean ratio, Morisita index and exponent k of the negative binomial distribution and chi-square fit of the observed and expected values to the theoretical frequency distribution (Poisson, Binomial and Negative Binomial Positive, showed that in both cultivars, the eggs of these species are distributed according to the aggregate distribution model, fitting the pattern of negative binomial distribution.

Multiplicity distributions in a thermodynamical model of hadron production in e+e- collisions

International Nuclear Information System (INIS)

Becattini, F.; Giovannini, A.; Lupia, S.

1996-01-01

Predictions of a thermodynamical model of hadron production for multiplicity distributions in e + e - annihilations at LEP and PEP-PETRA centre of mass energies are shown. The production process is described as a two-step process in which primary hadrons emitted from the thermal source decay into final observable particles. The final charged track multiplicity distributions turn out to be of negative binomial type and are in quite good agreement with experimental observations. The average number of clans calculated from fitted negative binomial coincides with the average number of primary hadrons predicted by the thermodynamical model, suggesting that clans should be identified with primary hadrons. (orig.)

Determining order-up-to levels under periodic review for compound binomial (intermittent) demand

NARCIS (Netherlands)

Teunter, R. H.; Syntetos, A. A.; Babai, M. Z.

2010-01-01

We propose a new method for determining order-up-to levels for intermittent demand items in a periodic review system. Contrary to existing methods, we exploit the intermittent character of demand by modelling lead time demand as a compound binomial process. in an extensive numerical study using

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

Generalized harmonic, cyclotomic, and binomial sums, their polylogarithms and special numbers

Energy Technology Data Exchange (ETDEWEB)

Ablinger, J.; Schneider, C. [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, J. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2013-10-15

A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of special numbers. Starting with harmonic sums and polylogarithms we discuss recent extensions of these quantities as cyclotomic, generalized (cyclotomic), and binomially weighted sums, associated iterated integrals and special constants and their relations.

Generalized harmonic, cyclotomic, and binomial sums, their polylogarithms and special numbers

International Nuclear Information System (INIS)

Ablinger, J.; Schneider, C.; Bluemlein, J.

2013-10-01

A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of special numbers. Starting with harmonic sums and polylogarithms we discuss recent extensions of these quantities as cyclotomic, generalized (cyclotomic), and binomially weighted sums, associated iterated integrals and special constants and their relations.

Partitioning detectability components in populations subject to within-season temporary emigration using binomial mixture models.

Science.gov (United States)

O'Donnell, Katherine M; Thompson, Frank R; Semlitsch, Raymond D

2015-01-01

Detectability of individual animals is highly variable and nearly always binomial mixture models to account for multiple sources of variation in detectability. The state process of the hierarchical model describes ecological mechanisms that generate spatial and temporal patterns in abundance, while the observation model accounts for the imperfect nature of counting individuals due to temporary emigration and false absences. We illustrate our model's potential advantages, including the allowance of temporary emigration between sampling periods, with a case study of southern red-backed salamanders Plethodon serratus. We fit our model and a standard binomial mixture model to counts of terrestrial salamanders surveyed at 40 sites during 3-5 surveys each spring and fall 2010-2012. Our models generated similar parameter estimates to standard binomial mixture models. Aspect was the best predictor of salamander abundance in our case study; abundance increased as aspect became more northeasterly. Increased time-since-rainfall strongly decreased salamander surface activity (i.e. availability for sampling), while higher amounts of woody cover objects and rocks increased conditional detection probability (i.e. probability of capture, given an animal is exposed to sampling). By explicitly accounting for both components of detectability, we increased congruence between our statistical modeling and our ecological understanding of the system. We stress the importance of choosing survey locations and protocols that maximize species availability and conditional detection probability to increase population parameter estimate reliability.

Patterns of medicinal plant use: an examination of the Ecuadorian Shuar medicinal flora using contingency table and binomial analyses.

Science.gov (United States)

Bennett, Bradley C; Husby, Chad E

2008-03-28

Botanical pharmacopoeias are non-random subsets of floras, with some taxonomic groups over- or under-represented. Moerman [Moerman, D.E., 1979. Symbols and selectivity: a statistical analysis of Native American medical ethnobotany, Journal of Ethnopharmacology 1, 111-119] introduced linear regression/residual analysis to examine these patterns. However, regression, the commonly-employed analysis, suffers from several statistical flaws. We use contingency table and binomial analyses to examine patterns of Shuar medicinal plant use (from Amazonian Ecuador). We first analyzed the Shuar data using Moerman's approach, modified to better meet requirements of linear regression analysis. Second, we assessed the exact randomization contingency table test for goodness of fit. Third, we developed a binomial model to test for non-random selection of plants in individual families. Modified regression models (which accommodated assumptions of linear regression) reduced R(2) to from 0.59 to 0.38, but did not eliminate all problems associated with regression analyses. Contingency table analyses revealed that the entire flora departs from the null model of equal proportions of medicinal plants in all families. In the binomial analysis, only 10 angiosperm families (of 115) differed significantly from the null model. These 10 families are largely responsible for patterns seen at higher taxonomic levels. Contingency table and binomial analyses offer an easy and statistically valid alternative to the regression approach.

Estimation of component failure probability from masked binomial system testing data

International Nuclear Information System (INIS)

Tan Zhibin

2005-01-01

The component failure probability estimates from analysis of binomial system testing data are very useful because they reflect the operational failure probability of components in the field which is similar to the test environment. In practice, this type of analysis is often confounded by the problem of data masking: the status of tested components is unknown. Methods in considering this type of uncertainty are usually computationally intensive and not practical to solve the problem for complex systems. In this paper, we consider masked binomial system testing data and develop a probabilistic model to efficiently estimate component failure probabilities. In the model, all system tests are classified into test categories based on component coverage. Component coverage of test categories is modeled by a bipartite graph. Test category failure probabilities conditional on the status of covered components are defined. An EM algorithm to estimate component failure probabilities is developed based on a simple but powerful concept: equivalent failures and tests. By simulation we not only demonstrate the convergence and accuracy of the algorithm but also show that the probabilistic model is capable of analyzing systems in series, parallel and any other user defined structures. A case study illustrates an application in test case prioritization

Constrained Dynamic Optimality and Binomial Terminal Wealth

DEFF Research Database (Denmark)

Pedersen, J. L.; Peskir, G.

2018-01-01

with interest rate $r \\in {R}$). Letting $P_{t,x}$ denote a probability measure under which $X^u$ takes value $x$ at time $t,$ we study the dynamic version of the nonlinear optimal control problem $\\inf_u\\, Var{t,X_t^u}(X_T^u)$ where the infimum is taken over admissible controls $u$ subject to $X_t^u \\ge e...... a martingale method combined with Lagrange multipliers, we derive the dynamically optimal control $u_*^d$ in closed form and prove that the dynamically optimal terminal wealth $X_T^d$ can only take two values $g$ and $\\beta$. This binomial nature of the dynamically optimal strategy stands in sharp contrast...... with other known portfolio selection strategies encountered in the literature. A direct comparison shows that the dynamically optimal (time-consistent) strategy outperforms the statically optimal (time-inconsistent) strategy in the problem....

Calculation Methods for Wallenius’ Noncentral Hypergeometric Distribution

DEFF Research Database (Denmark)

Fog, Agner

2008-01-01

Two different probability distributions are both known in the literature as "the" noncentral hypergeometric distribution. Wallenius' noncentral hypergeometric distribution can be described by an urn model without replacement with bias. Fisher's noncentral hypergeometric distribution...... is the conditional distribution of independent binomial variates given their sum. No reliable calculation method for Wallenius' noncentral hypergeometric distribution has hitherto been described in the literature. Several new methods for calculating probabilities from Wallenius' noncentral hypergeometric...... distribution are derived. Range of applicability, numerical problems, and efficiency are discussed for each method. Approximations to the mean and variance are also discussed. This distribution has important applications in models of biased sampling and in models of evolutionary systems....

Multiplicity distributions in a thermodynamical model of hadron production in e{sup +}e{sup -} collisions

Energy Technology Data Exchange (ETDEWEB)

Becattini, F. [Florence Univ. (Italy)]|[Istituto Nazionale di Fisica Nucleare, Florence (Italy); Giovannini, A. [Turin Univ. (Italy). Ist. di Fisica Teorica]|[Istituto Nazionale di Fisica Nucleare, Turin (Italy); Lupia, S. [Max-Planck-Institut fuer Physik, Muenchen (Germany). Werner-Heisenberg-Institut

1996-10-01

Predictions of a thermodynamical model of hadron production for multiplicity distributions in e{sup +}e{sup -} annihilations at LEP and PEP-PETRA centre of mass energies are shown. The production process is described as a two-step process in which primary hadrons emitted from the thermal source decay into final observable particles. The final charged track multiplicity distributions turn out to be of negative binomial type and are in quite good agreement with experimental observations. The average number of clans calculated from fitted negative binomial coincides with the average number of primary hadrons predicted by the thermodynamical model, suggesting that clans should be identified with primary hadrons. (orig.)

Negative binomial mixed models for analyzing microbiome count data.

Science.gov (United States)

Zhang, Xinyan; Mallick, Himel; Tang, Zaixiang; Zhang, Lei; Cui, Xiangqin; Benson, Andrew K; Yi, Nengjun

2017-01-03

Recent advances in next-generation sequencing (NGS) technology enable researchers to collect a large volume of metagenomic sequencing data. These data provide valuable resources for investigating interactions between the microbiome and host environmental/clinical factors. In addition to the well-known properties of microbiome count measurements, for example, varied total sequence reads across samples, over-dispersion and zero-inflation, microbiome studies usually collect samples with hierarchical structures, which introduce correlation among the samples and thus further complicate the analysis and interpretation of microbiome count data. In this article, we propose negative binomial mixed models (NBMMs) for detecting the association between the microbiome and host environmental/clinical factors for correlated microbiome count data. Although having not dealt with zero-inflation, the proposed mixed-effects models account for correlation among the samples by incorporating random effects into the commonly used fixed-effects negative binomial model, and can efficiently handle over-dispersion and varying total reads. We have developed a flexible and efficient IWLS (Iterative Weighted Least Squares) algorithm to fit the proposed NBMMs by taking advantage of the standard procedure for fitting the linear mixed models. We evaluate and demonstrate the proposed method via extensive simulation studies and the application to mouse gut microbiome data. The results show that the proposed method has desirable properties and outperform the previously used methods in terms of both empirical power and Type I error. The method has been incorporated into the freely available R package BhGLM ( http://www.ssg.uab.edu/bhglm/ and http://github.com/abbyyan3/BhGLM ), providing a useful tool for analyzing microbiome data.

Robust inference in the negative binomial regression model with an application to falls data.

Science.gov (United States)

Aeberhard, William H; Cantoni, Eva; Heritier, Stephane

2014-12-01

A popular way to model overdispersed count data, such as the number of falls reported during intervention studies, is by means of the negative binomial (NB) distribution. Classical estimating methods are well-known to be sensitive to model misspecifications, taking the form of patients falling much more than expected in such intervention studies where the NB regression model is used. We extend in this article two approaches for building robust M-estimators of the regression parameters in the class of generalized linear models to the NB distribution. The first approach achieves robustness in the response by applying a bounded function on the Pearson residuals arising in the maximum likelihood estimating equations, while the second approach achieves robustness by bounding the unscaled deviance components. For both approaches, we explore different choices for the bounding functions. Through a unified notation, we show how close these approaches may actually be as long as the bounding functions are chosen and tuned appropriately, and provide the asymptotic distributions of the resulting estimators. Moreover, we introduce a robust weighted maximum likelihood estimator for the overdispersion parameter, specific to the NB distribution. Simulations under various settings show that redescending bounding functions yield estimates with smaller biases under contamination while keeping high efficiency at the assumed model, and this for both approaches. We present an application to a recent randomized controlled trial measuring the effectiveness of an exercise program at reducing the number of falls among people suffering from Parkinsons disease to illustrate the diagnostic use of such robust procedures and their need for reliable inference. © 2014, The International Biometric Society.

Comparison of robustness to outliers between robust poisson models and log-binomial models when estimating relative risks for common binary outcomes: a simulation study.

Science.gov (United States)

Chen, Wansu; Shi, Jiaxiao; Qian, Lei; Azen, Stanley P

2014-06-26

To estimate relative risks or risk ratios for common binary outcomes, the most popular model-based methods are the robust (also known as modified) Poisson and the log-binomial regression. Of the two methods, it is believed that the log-binomial regression yields more efficient estimators because it is maximum likelihood based, while the robust Poisson model may be less affected by outliers. Evidence to support the robustness of robust Poisson models in comparison with log-binomial models is very limited. In this study a simulation was conducted to evaluate the performance of the two methods in several scenarios where outliers existed. The findings indicate that for data coming from a population where the relationship between the outcome and the covariate was in a simple form (e.g. log-linear), the two models yielded comparable biases and mean square errors. However, if the true relationship contained a higher order term, the robust Poisson models consistently outperformed the log-binomial models even when the level of contamination is low. The robust Poisson models are more robust (or less sensitive) to outliers compared to the log-binomial models when estimating relative risks or risk ratios for common binary outcomes. Users should be aware of the limitations when choosing appropriate models to estimate relative risks or risk ratios.

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.

The option to expand a project: its assessment with the binomial options pricing model

Directory of Open Access Journals (Sweden)

Salvador Cruz Rambaud

Full Text Available Traditional methods of investment appraisal, like the Net Present Value, are not able to include the value of the operational flexibility of the project. In this paper, real options, and more specifically the option to expand, are assumed to be included in the project information in addition to the expected cash flows. Thus, to calculate the total value of the project, we are going to apply the methodology of the Net Present Value to the different scenarios derived from the existence of the real option to expand. Taking into account the analogy between real and financial options, the value of including an option to expand is explored by using the binomial options pricing model. In this way, estimating the value of the option to expand is a tool which facilitates the control of the uncertainty element implicit in the project. Keywords: Real options, Option to expand, Binomial options pricing model, Investment project appraisal

Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams

International Nuclear Information System (INIS)

Ablinger, Jakob; Schneider, Carsten; Bluemlein, Johannes; Raab, Clemens G.

2014-07-01

Nested sums containing binomial coefficients occur in the computation of massive operatormatrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss algorithms for converting between sum and integral representations, mainly relying on the Mellin transform. To aid the conversion we worked out dedicated rewrite rules, based on which also some general patterns emerging in the process can be obtained.

Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams

Energy Technology Data Exchange (ETDEWEB)

Ablinger, Jakob; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation (RISC); Bluemlein, Johannes; Raab, Clemens G. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

2014-07-15

Nested sums containing binomial coefficients occur in the computation of massive operatormatrix elements. Their associated iterated integrals lead to alphabets including radicals, for which we determined a suitable basis. We discuss algorithms for converting between sum and integral representations, mainly relying on the Mellin transform. To aid the conversion we worked out dedicated rewrite rules, based on which also some general patterns emerging in the process can be obtained.

Combinatorial interpretations of binomial coefficient analogues related to Lucas sequences

OpenAIRE

Sagan, Bruce; Savage, Carla

2009-01-01

Let s and t be variables. Define polynomials {n} in s, t by {0}=0, {1}=1, and {n}=s{n-1}+t{n-2} for n >= 2. If s, t are integers then the corresponding sequence of integers is called a Lucas sequence. Define an analogue of the binomial coefficients by C{n,k}={n}!/({k}!{n-k}!) where {n}!={1}{2}...{n}. It is easy to see that C{n,k} is a polynomial in s and t. The purpose of this note is to give two combinatorial interpretations for this polynomial in terms of statistics on integer partitions in...

“Micro” Phraseology in Action: A Look at Fixed Binomials

Directory of Open Access Journals (Sweden)

Dušan Gabrovšek

2011-05-01

Full Text Available Multiword items in English are a motley crew, as they are not only numerous but also structurally, semantically, and functionally diverse. The paper offers a fresh look at fixed binomials, an intriguing and unexpectedly heterogeneous phraseological type prototypically consisting of two lexical components with the coordinating conjunction and – less commonly but, or, (neither/ (nor – acting as the connecting element, as e.g. in body and soul, slowly but surely, sooner or later, neither fish nor fowl. In particular, their idiomaticity and lexicographical significance are highlighted, while the cross-linguistic perspective is only outlined.

Extending the Binomial Checkpointing Technique for Resilience

Energy Technology Data Exchange (ETDEWEB)

Walther, Andrea; Narayanan, Sri Hari Krishna

2016-10-10

In terms of computing time, adjoint methods offer a very attractive alternative to compute gradient information, re- quired, e.g., for optimization purposes. However, together with this very favorable temporal complexity result comes a memory requirement that is in essence proportional with the operation count of the underlying function, e.g., if algo- rithmic differentiation is used to provide the adjoints. For this reason, checkpointing approaches in many variants have become popular. This paper analyzes an extension of the so-called binomial approach to cover also possible failures of the computing systems. Such a measure of precaution is of special interest for massive parallel simulations and adjoint calculations where the mean time between failure of the large scale computing system is smaller than the time needed to complete the calculation of the adjoint information. We de- scribe the extensions of standard checkpointing approaches required for such resilience, provide a corresponding imple- mentation and discuss numerical results.

Using a Negative Binomial Regression Model for Early Warning at the Start of a Hand Foot Mouth Disease Epidemic in Dalian, Liaoning Province, China.

Science.gov (United States)

An, Qingyu; Wu, Jun; Fan, Xuesong; Pan, Liyang; Sun, Wei

2016-01-01

The hand foot and mouth disease (HFMD) is a human syndrome caused by intestinal viruses like that coxsackie A virus 16, enterovirus 71 and easily developed into outbreak in kindergarten and school. Scientifically and accurately early detection of the start time of HFMD epidemic is a key principle in planning of control measures and minimizing the impact of HFMD. The objective of this study was to establish a reliable early detection model for start timing of hand foot mouth disease epidemic in Dalian and to evaluate the performance of model by analyzing the sensitivity in detectability. The negative binomial regression model was used to estimate the weekly baseline case number of HFMD and identified the optimal alerting threshold between tested difference threshold values during the epidemic and non-epidemic year. Circular distribution method was used to calculate the gold standard of start timing of HFMD epidemic. From 2009 to 2014, a total of 62022 HFMD cases were reported (36879 males and 25143 females) in Dalian, Liaoning Province, China, including 15 fatal cases. The median age of the patients was 3 years. The incidence rate of epidemic year ranged from 137.54 per 100,000 population to 231.44 per 100,000population, the incidence rate of non-epidemic year was lower than 112 per 100,000 population. The negative binomial regression model with AIC value 147.28 was finally selected to construct the baseline level. The threshold value was 100 for the epidemic year and 50 for the non- epidemic year had the highest sensitivity(100%) both in retrospective and prospective early warning and the detection time-consuming was 2 weeks before the actual starting of HFMD epidemic. The negative binomial regression model could early warning the start of a HFMD epidemic with good sensitivity and appropriate detection time in Dalian.

Temporal acceleration of spatially distributed kinetic Monte Carlo simulations

International Nuclear Information System (INIS)

Chatterjee, Abhijit; Vlachos, Dionisios G.

2006-01-01

The computational intensity of kinetic Monte Carlo (KMC) simulation is a major impediment in simulating large length and time scales. In recent work, an approximate method for KMC simulation of spatially uniform systems, termed the binomial τ-leap method, was introduced [A. Chatterjee, D.G. Vlachos, M.A. Katsoulakis, Binomial distribution based τ-leap accelerated stochastic simulation, J. Chem. Phys. 122 (2005) 024112], where molecular bundles instead of individual processes are executed over coarse-grained time increments. This temporal coarse-graining can lead to significant computational savings but its generalization to spatially lattice KMC simulation has not been realized yet. Here we extend the binomial τ-leap method to lattice KMC simulations by combining it with spatially adaptive coarse-graining. Absolute stability and computational speed-up analyses for spatial systems along with simulations provide insights into the conditions where accuracy and substantial acceleration of the new spatio-temporal coarse-graining method are ensured. Model systems demonstrate that the r-time increment criterion of Chatterjee et al. obeys the absolute stability limit for values of r up to near 1

Spiritual and ceremonial plants in North America: an assessment of Moerman's ethnobotanical database comparing Residual, Binomial, Bayesian and Imprecise Dirichlet Model (IDM) analysis.

Science.gov (United States)

Turi, Christina E; Murch, Susan J

2013-07-09

Ethnobotanical research and the study of plants used for rituals, ceremonies and to connect with the spirit world have led to the discovery of many novel psychoactive compounds such as nicotine, caffeine, and cocaine. In North America, spiritual and ceremonial uses of plants are well documented and can be accessed online via the University of Michigan's Native American Ethnobotany Database. The objective of the study was to compare Residual, Bayesian, Binomial and Imprecise Dirichlet Model (IDM) analyses of ritual, ceremonial and spiritual plants in Moerman's ethnobotanical database and to identify genera that may be good candidates for the discovery of novel psychoactive compounds. The database was queried with the following format "Family Name AND Ceremonial OR Spiritual" for 263 North American botanical families. Spiritual and ceremonial flora consisted of 86 families with 517 species belonging to 292 genera. Spiritual taxa were then grouped further into ceremonial medicines and items categories. Residual, Bayesian, Binomial and IDM analysis were performed to identify over and under-utilized families. The 4 statistical approaches were in good agreement when identifying under-utilized families but large families (>393 species) were underemphasized by Binomial, Bayesian and IDM approaches for over-utilization. Residual, Binomial, and IDM analysis identified similar families as over-utilized in the medium (92-392 species) and small (<92 species) classes. The families Apiaceae, Asteraceae, Ericacea, Pinaceae and Salicaceae were identified as significantly over-utilized as ceremonial medicines in medium and large sized families. Analysis of genera within the Apiaceae and Asteraceae suggest that the genus Ligusticum and Artemisia are good candidates for facilitating the discovery of novel psychoactive compounds. The 4 statistical approaches were not consistent in the selection of over-utilization of flora. Residual analysis revealed overall trends that were supported

On a Generalisation of Uniform Distribution and its Properties

Directory of Open Access Journals (Sweden)

K. Jayakumar

2016-03-01

Full Text Available Nadarajah et al.(2013 introduced a family life time models using truncated negative binomial distribution and derived some properties of the family of distributions. It is a generalization of Marshall-Olkin family of distributions. In this paper, we introduce Generalized Uniform Distribution (GUD using the approach of Nadarajah et al.(2013. The shape properties of density function and hazard function are discussed. The expression for moments, order statistics, entropies are obtained. Estimation procedure is also discussed.The GDU introduced here is a generalization of the Marshall-Olkin extended uniform distribution studied in Jose and Krishna(2011.

Multilevel binomial logistic prediction model for malignant pulmonary nodules based on texture features of CT image

International Nuclear Information System (INIS)

Wang Huan; Guo Xiuhua; Jia Zhongwei; Li Hongkai; Liang Zhigang; Li Kuncheng; He Qian

2010-01-01

Purpose: To introduce multilevel binomial logistic prediction model-based computer-aided diagnostic (CAD) method of small solitary pulmonary nodules (SPNs) diagnosis by combining patient and image characteristics by textural features of CT image. Materials and methods: Describe fourteen gray level co-occurrence matrix textural features obtained from 2171 benign and malignant small solitary pulmonary nodules, which belongs to 185 patients. Multilevel binomial logistic model is applied to gain these initial insights. Results: Five texture features, including Inertia, Entropy, Correlation, Difference-mean, Sum-Entropy, and age of patients own aggregating character on patient-level, which are statistically different (P < 0.05) between benign and malignant small solitary pulmonary nodules. Conclusion: Some gray level co-occurrence matrix textural features are efficiently descriptive features of CT image of small solitary pulmonary nodules, which can profit diagnosis of earlier period lung cancer if combined patient-level characteristics to some extent.

A Mixed-Effects Heterogeneous Negative Binomial Model for Postfire Conifer Regeneration in Northeastern California, USA

Science.gov (United States)

Justin S. Crotteau; Martin W. Ritchie; J. Morgan. Varner

2014-01-01

Many western USA fire regimes are typified by mixed-severity fire, which compounds the variability inherent to natural regeneration densities in associated forests. Tree regeneration data are often discrete and nonnegative; accordingly, we fit a series of Poisson and negative binomial variation models to conifer seedling counts across four distinct burn severities and...

Comparing distribution models for small samples of overdispersed counts of freshwater fish

Science.gov (United States)

Vaudor, Lise; Lamouroux, Nicolas; Olivier, Jean-Michel

2011-05-01

The study of species abundance often relies on repeated abundance counts whose number is limited by logistic or financial constraints. The distribution of abundance counts is generally right-skewed (i.e. with many zeros and few high values) and needs to be modelled for statistical inference. We used an extensive dataset involving about 100,000 fish individuals of 12 freshwater fish species collected in electrofishing points (7 m 2) during 350 field surveys made in 25 stream sites, in order to compare the performance and the generality of four distribution models of counts (Poisson, negative binomial and their zero-inflated counterparts). The negative binomial distribution was the best model (Bayesian Information Criterion) for 58% of the samples (species-survey combinations) and was suitable for a variety of life histories, habitat, and sample characteristics. The performance of the models was closely related to samples' statistics such as total abundance and variance. Finally, we illustrated the consequences of a distribution assumption by calculating confidence intervals around the mean abundance, either based on the most suitable distribution assumption or on an asymptotical, distribution-free (Student's) method. Student's method generally corresponded to narrower confidence intervals, especially when there were few (≤3) non-null counts in the samples.

Constructing Binomial Trees Via Random Maps for Analysis of Financial Assets

Directory of Open Access Journals (Sweden)

Antonio Airton Carneiro de Freitas

2010-04-01

Full Text Available Random maps can be constructed from a priori knowledge of the financial assets. It is also addressed the reverse problem, i.e. from a function of an empirical stationary probability density function we set up a random map that naturally leads to an implied binomial tree, allowing the adjustment of models, including the ability to incorporate jumps. An applica- tion related to the options market is presented. It is emphasized that the quality of the model to incorporate a priori knowledge of the financial asset may be affected, for example, by the skewed vision of the analyst.

Binomial tree method for pricing a regime-switching volatility stock loans

Science.gov (United States)

Putri, Endah R. M.; Zamani, Muhammad S.; Utomo, Daryono B.

2018-03-01

Binomial model with regime switching may represents the price of stock loan which follows the stochastic process. Stock loan is one of alternative that appeal investors to get the liquidity without selling the stock. The stock loan mechanism resembles that of American call option when someone can exercise any time during the contract period. From the resembles both of mechanism, determination price of stock loan can be interpreted from the model of American call option. The simulation result shows the behavior of the price of stock loan under a regime-switching with respect to various interest rate and maturity.

Partitioning detectability components in populations subject to within-season temporary emigration using binomial mixture models.

Directory of Open Access Journals (Sweden)

Katherine M O'Donnell

Full Text Available Detectability of individual animals is highly variable and nearly always < 1; imperfect detection must be accounted for to reliably estimate population sizes and trends. Hierarchical models can simultaneously estimate abundance and effective detection probability, but there are several different mechanisms that cause variation in detectability. Neglecting temporary emigration can lead to biased population estimates because availability and conditional detection probability are confounded. In this study, we extend previous hierarchical binomial mixture models to account for multiple sources of variation in detectability. The state process of the hierarchical model describes ecological mechanisms that generate spatial and temporal patterns in abundance, while the observation model accounts for the imperfect nature of counting individuals due to temporary emigration and false absences. We illustrate our model's potential advantages, including the allowance of temporary emigration between sampling periods, with a case study of southern red-backed salamanders Plethodon serratus. We fit our model and a standard binomial mixture model to counts of terrestrial salamanders surveyed at 40 sites during 3-5 surveys each spring and fall 2010-2012. Our models generated similar parameter estimates to standard binomial mixture models. Aspect was the best predictor of salamander abundance in our case study; abundance increased as aspect became more northeasterly. Increased time-since-rainfall strongly decreased salamander surface activity (i.e. availability for sampling, while higher amounts of woody cover objects and rocks increased conditional detection probability (i.e. probability of capture, given an animal is exposed to sampling. By explicitly accounting for both components of detectability, we increased congruence between our statistical modeling and our ecological understanding of the system. We stress the importance of choosing survey locations and

Beta-Binomial Model for the Detection of Rare Mutations in Pooled Next-Generation Sequencing Experiments.

Science.gov (United States)

Jakaitiene, Audrone; Avino, Mariano; Guarracino, Mario Rosario

2017-04-01

Against diminishing costs, next-generation sequencing (NGS) still remains expensive for studies with a large number of individuals. As cost saving, sequencing genome of pools containing multiple samples might be used. Currently, there are many software available for the detection of single-nucleotide polymorphisms (SNPs). Sensitivity and specificity depend on the model used and data analyzed, indicating that all software have space for improvement. We use beta-binomial model to detect rare mutations in untagged pooled NGS experiments. We propose a multireference framework for pooled data with ability being specific up to two patients affected by neuromuscular disorders (NMD). We assessed the results comparing with The Genome Analysis Toolkit (GATK), CRISP, SNVer, and FreeBayes. Our results show that the multireference approach applying beta-binomial model is accurate in predicting rare mutations at 0.01 fraction. Finally, we explored the concordance of mutations between the model and software, checking their involvement in any NMD-related gene. We detected seven novel SNPs, for which the functional analysis produced enriched terms related to locomotion and musculature.

Distribution of apparent activation energy counterparts during thermo - And thermo-oxidative degradation of Aronia melanocarpa (black chokeberry).

Science.gov (United States)

Janković, Bojan; Marinović-Cincović, Milena; Janković, Marija

2017-09-01

Kinetics of degradation for Aronia melanocarpa fresh fruits in argon and air atmospheres were investigated. The investigation was based on probability distributions of apparent activation energy of counterparts (ε a ). Isoconversional analysis results indicated that the degradation process in an inert atmosphere was governed by decomposition reactions of esterified compounds. Also, based on same kinetics approach, it was assumed that in an air atmosphere, the primary compound in degradation pathways could be anthocyanins, which undergo rapid chemical reactions. A new model of reactivity demonstrated that, under inert atmospheres, expectation values for ε a occured at levels of statistical probability. These values corresponded to decomposition processes in which polyphenolic compounds might be involved. ε a values obeyed laws of binomial distribution. It was established that, for thermo-oxidative degradation, Poisson distribution represented a very successful approximation for ε a values where there was additional mechanistic complexity and the binomial distribution was no longer valid. Copyright © 2017 Elsevier Ltd. All rights reserved.

Confidence Intervals for True Scores Using the Skew-Normal Distribution

Science.gov (United States)

Garcia-Perez, Miguel A.

2010-01-01

A recent comparative analysis of alternative interval estimation approaches and procedures has shown that confidence intervals (CIs) for true raw scores determined with the Score method--which uses the normal approximation to the binomial distribution--have actual coverage probabilities that are closest to their nominal level. It has also recently…

Covering Resilience: A Recent Development for Binomial Checkpointing

Energy Technology Data Exchange (ETDEWEB)

Walther, Andrea; Narayanan, Sri Hari Krishna

2016-09-12

In terms of computing time, adjoint methods offer a very attractive alternative to compute gradient information, required, e.g., for optimization purposes. However, together with this very favorable temporal complexity result comes a memory requirement that is in essence proportional with the operation count of the underlying function, e.g., if algorithmic differentiation is used to provide the adjoints. For this reason, checkpointing approaches in many variants have become popular. This paper analyzes an extension of the so-called binomial approach to cover also possible failures of the computing systems. Such a measure of precaution is of special interest for massive parallel simulations and adjoint calculations where the mean time between failure of the large scale computing system is smaller than the time needed to complete the calculation of the adjoint information. We describe the extensions of standard checkpointing approaches required for such resilience, provide a corresponding implementation and discuss first numerical results.

Study on Emission Measurement of Vehicle on Road Based on Binomial Logit Model

OpenAIRE

Aly, Sumarni Hamid; Selintung, Mary; Ramli, Muhammad Isran; Sumi, Tomonori

2011-01-01

This research attempts to evaluate emission measurement of on road vehicle. In this regard, the research develops failure probability model of vehicle emission test for passenger car which utilize binomial logit model. The model focuses on failure of CO and HC emission test for gasoline cars category and Opacity emission test for diesel-fuel cars category as dependent variables, while vehicle age, engine size, brand and type of the cars as independent variables. In order to imp...

A Bayesian equivalency test for two independent binomial proportions.

Science.gov (United States)

Kawasaki, Yohei; Shimokawa, Asanao; Yamada, Hiroshi; Miyaoka, Etsuo

2016-01-01

In clinical trials, it is often necessary to perform an equivalence study. The equivalence study requires actively denoting equivalence between two different drugs or treatments. Since it is not possible to assert equivalence that is not rejected by a superiority test, statistical methods known as equivalency tests have been suggested. These methods for equivalency tests are based on the frequency framework; however, there are few such methods in the Bayesian framework. Hence, this article proposes a new index that suggests the equivalency of binomial proportions, which is constructed based on the Bayesian framework. In this study, we provide two methods for calculating the index and compare the probabilities that have been calculated by these two calculation methods. Moreover, we apply this index to the results of actual clinical trials to demonstrate the utility of the index.

Universal description of inelastic and non(single)-diffractive multiplicity distributions in pp collisions at 250, 360 and 800 GeV/c

International Nuclear Information System (INIS)

Krasznovszky, S.; Wagner, I.

1987-06-01

A distribution function is proposed for multiplicity in accordance with the stochastic number evolution. This function gives a universal description of inelastic and nondiffractive multiplicity distributions in pp collisions at 250, 360 and 800 GeV/c. The negative binomial distribution fails in the description of inelastic data. (author)

The Sequential Probability Ratio Test: An efficient alternative to exact binomial testing for Clean Water Act 303(d) evaluation.

Science.gov (United States)

Chen, Connie; Gribble, Matthew O; Bartroff, Jay; Bay, Steven M; Goldstein, Larry

2017-05-01

The United States's Clean Water Act stipulates in section 303(d) that states must identify impaired water bodies for which total maximum daily loads (TMDLs) of pollution inputs into water bodies are developed. Decision-making procedures about how to list, or delist, water bodies as impaired, or not, per Clean Water Act 303(d) differ across states. In states such as California, whether or not a particular monitoring sample suggests that water quality is impaired can be regarded as a binary outcome variable, and California's current regulatory framework invokes a version of the exact binomial test to consolidate evidence across samples and assess whether the overall water body complies with the Clean Water Act. Here, we contrast the performance of California's exact binomial test with one potential alternative, the Sequential Probability Ratio Test (SPRT). The SPRT uses a sequential testing framework, testing samples as they become available and evaluating evidence as it emerges, rather than measuring all the samples and calculating a test statistic at the end of the data collection process. Through simulations and theoretical derivations, we demonstrate that the SPRT on average requires fewer samples to be measured to have comparable Type I and Type II error rates as the current fixed-sample binomial test. Policymakers might consider efficient alternatives such as SPRT to current procedure. Copyright © 2017 Elsevier Ltd. All rights reserved.

Spatial distribution and sequential sampling plans for Tuta absoluta (Lepidoptera: Gelechiidae) in greenhouse tomato crops.

Science.gov (United States)

Cocco, Arturo; Serra, Giuseppe; Lentini, Andrea; Deliperi, Salvatore; Delrio, Gavino

2015-09-01

The within- and between-plant distribution of the tomato leafminer, Tuta absoluta (Meyrick), was investigated in order to define action thresholds based on leaf infestation and to propose enumerative and binomial sequential sampling plans for pest management applications in protected crops. The pest spatial distribution was aggregated between plants, and median leaves were the most suitable sample to evaluate the pest density. Action thresholds of 36 and 48%, 43 and 56% and 60 and 73% infested leaves, corresponding to economic thresholds of 1 and 3% damaged fruits, were defined for tomato cultivars with big, medium and small fruits respectively. Green's method was a more suitable enumerative sampling plan as it required a lower sampling effort. Binomial sampling plans needed lower average sample sizes than enumerative plans to make a treatment decision, with probabilities of error of sampling plan required 87 or 343 leaves to estimate the population density in extensive or intensive ecological studies respectively. Binomial plans would be more practical and efficient for control purposes, needing average sample sizes of 17, 20 and 14 leaves to take a pest management decision in order to avoid fruit damage higher than 1% in cultivars with big, medium and small fruits respectively. © 2014 Society of Chemical Industry.

An algorithm for sequential tail value at risk for path-independent payoffs in a binomial tree

NARCIS (Netherlands)

Roorda, Berend

2010-01-01

We present an algorithm that determines Sequential Tail Value at Risk (STVaR) for path-independent payoffs in a binomial tree. STVaR is a dynamic version of Tail-Value-at-Risk (TVaR) characterized by the property that risk levels at any moment must be in the range of risk levels later on. The

Spatial Distribution of Adult Anthonomus grandis Boheman (Coleoptera: Curculionidae) and Damage to Cotton Flower Buds Due to Feeding and Oviposition.

Science.gov (United States)

Grigolli, J F J; Souza, L A; Fernandes, M G; Busoli, A C

2017-08-01

The cotton boll weevil Anthonomus grandis Boheman (Coleoptera: Curculionidae) is the main pest in cotton crop around the world, directly affecting cotton production. In order to establish a sequential sampling plan, it is crucial to understand the spatial distribution of the pest population and the damage it causes to the crop through the different developmental stages of cotton plants. Therefore, this study aimed to investigate the spatial distribution of adults in the cultivation area and their oviposition and feeding behavior throughout the development of the cotton plants. The experiment was conducted in Maracaju, Mato Grosso do Sul, Brazil, in the 2012/2013 and 2013/2014 growing seasons, in an area of 10,000 m 2 , planted with the cotton cultivar FM 993. The experimental area was divided into 100 plots of 100 m 2 (10 × 10 m) each, and five plants per plot were sampled weekly throughout the crop cycle. The number of flower buds with feeding and oviposition punctures and of adult A. grandis was recorded throughout the crop cycle in five plants per plot. After determining the aggregation indices (variance/mean ratio, Morisita's index, exponent k of the negative binomial distribution, and Green's coefficient) and adjusting the frequencies observed in the field to the distribution of frequencies (Poisson, negative binomial, and positive binomial) using the chi-squared test, it was observed that flower buds with punctures derived from feeding, oviposition, and feeding + oviposition showed an aggregated distribution in the cultivation area until 85 days after emergence and a random distribution after this stage. The adults of A. grandis presented a random distribution in the cultivation area.

Estimating cavity tree and snag abundance using negative binomial regression models and nearest neighbor imputation methods

Science.gov (United States)

Bianca N.I. Eskelson; Hailemariam Temesgen; Tara M. Barrett

2009-01-01

Cavity tree and snag abundance data are highly variable and contain many zero observations. We predict cavity tree and snag abundance from variables that are readily available from forest cover maps or remotely sensed data using negative binomial (NB), zero-inflated NB, and zero-altered NB (ZANB) regression models as well as nearest neighbor (NN) imputation methods....

The Explicit Identities for Spectral Norms of Circulant-Type Matrices Involving Binomial Coefficients and Harmonic Numbers

Directory of Open Access Journals (Sweden)

Jianwei Zhou

2014-01-01

Full Text Available The explicit formulae of spectral norms for circulant-type matrices are investigated; the matrices are circulant matrix, skew-circulant matrix, and g-circulant matrix, respectively. The entries are products of binomial coefficients with harmonic numbers. Explicit identities for these spectral norms are obtained. Employing these approaches, some numerical tests are listed to verify the results.

CMPH: a multivariate phase-type aggregate loss distribution

Directory of Open Access Journals (Sweden)

Ren Jiandong

2017-12-01

Full Text Available We introduce a compound multivariate distribution designed for modeling insurance losses arising from different risk sources in insurance companies. The distribution is based on a discrete-time Markov Chain and generalizes the multivariate compound negative binomial distribution, which is widely used for modeling insurance losses.We derive fundamental properties of the distribution and discuss computational aspects facilitating calculations of risk measures of the aggregate loss, as well as allocations of the aggregate loss to individual types of risk sources. Explicit formulas for the joint moment generating function and the joint moments of different loss types are derived, and recursive formulas for calculating the joint distributions given. Several special cases of particular interest are analyzed. An illustrative numerical example is provided.

Microbial comparative pan-genomics using binomial mixture models

Directory of Open Access Journals (Sweden)

Ussery David W

2009-08-01

Full Text Available Abstract Background The size of the core- and pan-genome of bacterial species is a topic of increasing interest due to the growing number of sequenced prokaryote genomes, many from the same species. Attempts to estimate these quantities have been made, using regression methods or mixture models. We extend the latter approach by using statistical ideas developed for capture-recapture problems in ecology and epidemiology. Results We estimate core- and pan-genome sizes for 16 different bacterial species. The results reveal a complex dependency structure for most species, manifested as heterogeneous detection probabilities. Estimated pan-genome sizes range from small (around 2600 gene families in Buchnera aphidicola to large (around 43000 gene families in Escherichia coli. Results for Echerichia coli show that as more data become available, a larger diversity is estimated, indicating an extensive pool of rarely occurring genes in the population. Conclusion Analyzing pan-genomics data with binomial mixture models is a way to handle dependencies between genomes, which we find is always present. A bottleneck in the estimation procedure is the annotation of rarely occurring genes.

Novel formulation of the ℳ model through the Generalized-K distribution for atmospheric optical channels.

Science.gov (United States)

Garrido-Balsells, José María; Jurado-Navas, Antonio; Paris, José Francisco; Castillo-Vazquez, Miguel; Puerta-Notario, Antonio

2015-03-09

In this paper, a novel and deeper physical interpretation on the recently published Málaga or ℳ statistical distribution is provided. This distribution, which is having a wide acceptance by the scientific community, models the optical irradiance scintillation induced by the atmospheric turbulence. Here, the analytical expressions previously published are modified in order to express them by a mixture of the known Generalized-K and discrete Binomial and Negative Binomial distributions. In particular, the probability density function (pdf) of the ℳ model is now obtained as a linear combination of these Generalized-K pdf, in which the coefficients depend directly on the parameters of the ℳ distribution. In this way, the Málaga model can be physically interpreted as a superposition of different optical sub-channels each of them described by the corresponding Generalized-K fading model and weighted by the ℳ dependent coefficients. The expressions here proposed are simpler than the equations of the original ℳ model and are validated by means of numerical simulations by generating ℳ -distributed random sequences and their associated histogram. This novel interpretation of the Málaga statistical distribution provides a valuable tool for analyzing the performance of atmospheric optical channels for every turbulence condition.

Risk indicators of oral health status among young adults aged 18 years analyzed by negative binomial regression.

Science.gov (United States)

Lu, Hai-Xia; Wong, May Chun Mei; Lo, Edward Chin Man; McGrath, Colman

2013-08-19

Limited information on oral health status for young adults aged 18 year-olds is known, and no available data exists in Hong Kong. The aims of this study were to investigate the oral health status and its risk indicators among young adults in Hong Kong using negative binomial regression. A survey was conducted in a representative sample of Hong Kong young adults aged 18 years. Clinical examinations were taken to assess oral health status using DMFT index and Community Periodontal Index (CPI) according to WHO criteria. Negative binomial regressions for DMFT score and the number of sextants with healthy gums were performed to identify the risk indicators of oral health status. A total of 324 young adults were examined. Prevalence of dental caries experience among the subjects was 59% and the overall mean DMFT score was 1.4. Most subjects (95%) had a score of 2 as their highest CPI score. Negative binomial regression analyses revealed that subjects who had a dental visit within 3 years had significantly higher DMFT scores (IRR = 1.68, p < 0.001). Subjects who brushed their teeth more frequently (IRR = 1.93, p < 0.001) and those with better dental knowledge (IRR = 1.09, p = 0.002) had significantly more sextants with healthy gums. Dental caries experience of the young adults aged 18 years in Hong Kong was not high but their periodontal condition was unsatisfactory. Their oral health status was related to their dental visit behavior, oral hygiene habit, and oral health knowledge.

Forms and genesis of species abundance distributions

Directory of Open Access Journals (Sweden)

Evans O. Ochiaga

2015-12-01

Full Text Available Species abundance distribution (SAD is one of the most important metrics in community ecology. SAD curves take a hollow or hyperbolic shape in a histogram plot with many rare species and only a few common species. In general, the shape of SAD is largely log-normally distributed, although the mechanism behind this particular SAD shape still remains elusive. Here, we aim to review four major parametric forms of SAD and three contending mechanisms that could potentially explain this highly skewed form of SAD. The parametric forms reviewed here include log series, negative binomial, lognormal and geometric distributions. The mechanisms reviewed here include the maximum entropy theory of ecology, neutral theory and the theory of proportionate effect.

Finding a minimally informative Dirichlet prior distribution using least squares

International Nuclear Information System (INIS)

Kelly, Dana; Atwood, Corwin

2011-01-01

In a Bayesian framework, the Dirichlet distribution is the conjugate distribution to the multinomial likelihood function, and so the analyst is required to develop a Dirichlet prior that incorporates available information. However, as it is a multiparameter distribution, choosing the Dirichlet parameters is less straightforward than choosing a prior distribution for a single parameter, such as p in the binomial distribution. In particular, one may wish to incorporate limited information into the prior, resulting in a minimally informative prior distribution that is responsive to updates with sparse data. In the case of binomial p or Poisson λ, the principle of maximum entropy can be employed to obtain a so-called constrained noninformative prior. However, even in the case of p, such a distribution cannot be written down in the form of a standard distribution (e.g., beta, gamma), and so a beta distribution is used as an approximation in the case of p. In the case of the multinomial model with parametric constraints, the approach of maximum entropy does not appear tractable. This paper presents an alternative approach, based on constrained minimization of a least-squares objective function, which leads to a minimally informative Dirichlet prior distribution. The alpha-factor model for common-cause failure, which is widely used in the United States, is the motivation for this approach, and is used to illustrate the method. In this approach to modeling common-cause failure, the alpha-factors, which are the parameters in the underlying multinomial model for common-cause failure, must be estimated from data that are often quite sparse, because common-cause failures tend to be rare, especially failures of more than two or three components, and so a prior distribution that is responsive to updates with sparse data is needed.

Distribution of chewing lice upon the polygynous peacock Pavo cristatus.

Science.gov (United States)

Stewart, I R; Clark, F; Petrie, M

1996-04-01

An opportunistic survey of louse distribution upon the peacock Pavo cristatus was undertaken following a cull of 23 birds from an English zoo. After complete skin and feather dissolution, 2 species of lice were retrieved, Goniodes pavonis and Amyrsidea minuta. The distribution of both louse species could be described by a negative binomial model. The significance of this is discussed in relation to transmission dynamics of lice in the atypical avian mating system found in the peacock, which involves no male parental care.

Inference for binomial probability based on dependent Bernoulli random variables with applications to meta‐analysis and group level studies

Science.gov (United States)

Bakbergenuly, Ilyas; Morgenthaler, Stephan

2016-01-01

We study bias arising as a result of nonlinear transformations of random variables in random or mixed effects models and its effect on inference in group‐level studies or in meta‐analysis. The findings are illustrated on the example of overdispersed binomial distributions, where we demonstrate considerable biases arising from standard log‐odds and arcsine transformations of the estimated probability p^, both for single‐group studies and in combining results from several groups or studies in meta‐analysis. Our simulations confirm that these biases are linear in ρ, for small values of ρ, the intracluster correlation coefficient. These biases do not depend on the sample sizes or the number of studies K in a meta‐analysis and result in abysmal coverage of the combined effect for large K. We also propose bias‐correction for the arcsine transformation. Our simulations demonstrate that this bias‐correction works well for small values of the intraclass correlation. The methods are applied to two examples of meta‐analyses of prevalence. PMID:27192062

SYVAC3 parameter distribution package

Energy Technology Data Exchange (ETDEWEB)

Andres, T; Skeet, A

1995-01-01

SYVAC3 (Systems Variability Analysis Code, generation 3) is a computer program that implements a method called systems variability analysis to analyze the behaviour of a system in the presence of uncertainty. This method is based on simulating the system many times to determine the variation in behaviour it can exhibit. SYVAC3 specializes in systems representing the transport of contaminants, and has several features to simplify the modelling of such systems. It provides a general tool for estimating environmental impacts from the dispersal of contaminants. This report describes a software object type (a generalization of a data type) called Parameter Distribution. This object type is used in SYVAC3, and can also be used independently. Parameter Distribution has the following subtypes: beta distribution; binomial distribution; constant distribution; lognormal distribution; loguniform distribution; normal distribution; piecewise uniform distribution; Triangular distribution; and uniform distribution. Some of these distributions can be altered by correlating two parameter distribution objects. This report provides complete specifications for parameter distributions, and also explains how to use them. It should meet the needs of casual users, reviewers, and programmers who wish to add their own subtypes. (author). 30 refs., 75 tabs., 56 figs.

Finding a Minimally Informative Dirichlet Prior Distribution Using Least Squares

International Nuclear Information System (INIS)

Kelly, Dana; Atwood, Corwin

2011-01-01

In a Bayesian framework, the Dirichlet distribution is the conjugate distribution to the multinomial likelihood function, and so the analyst is required to develop a Dirichlet prior that incorporates available information. However, as it is a multiparameter distribution, choosing the Dirichlet parameters is less straight-forward than choosing a prior distribution for a single parameter, such as p in the binomial distribution. In particular, one may wish to incorporate limited information into the prior, resulting in a minimally informative prior distribution that is responsive to updates with sparse data. In the case of binomial p or Poisson, the principle of maximum entropy can be employed to obtain a so-called constrained noninformative prior. However, even in the case of p, such a distribution cannot be written down in closed form, and so an approximate beta distribution is used in the case of p. In the case of the multinomial model with parametric constraints, the approach of maximum entropy does not appear tractable. This paper presents an alternative approach, based on constrained minimization of a least-squares objective function, which leads to a minimally informative Dirichlet prior distribution. The alpha-factor model for common-cause failure, which is widely used in the United States, is the motivation for this approach, and is used to illustrate the method. In this approach to modeling common-cause failure, the alpha-factors, which are the parameters in the underlying multinomial aleatory model for common-cause failure, must be estimated from data that is often quite sparse, because common-cause failures tend to be rare, especially failures of more than two or three components, and so a prior distribution that is responsive to updates with sparse data is needed.

Sample size determination for a three-arm equivalence trial of Poisson and negative binomial responses.

Science.gov (United States)

Chang, Yu-Wei; Tsong, Yi; Zhao, Zhigen

2017-01-01

Assessing equivalence or similarity has drawn much attention recently as many drug products have lost or will lose their patents in the next few years, especially certain best-selling biologics. To claim equivalence between the test treatment and the reference treatment when assay sensitivity is well established from historical data, one has to demonstrate both superiority of the test treatment over placebo and equivalence between the test treatment and the reference treatment. Thus, there is urgency for practitioners to derive a practical way to calculate sample size for a three-arm equivalence trial. The primary endpoints of a clinical trial may not always be continuous, but may be discrete. In this paper, the authors derive power function and discuss sample size requirement for a three-arm equivalence trial with Poisson and negative binomial clinical endpoints. In addition, the authors examine the effect of the dispersion parameter on the power and the sample size by varying its coefficient from small to large. In extensive numerical studies, the authors demonstrate that required sample size heavily depends on the dispersion parameter. Therefore, misusing a Poisson model for negative binomial data may easily lose power up to 20%, depending on the value of the dispersion parameter.

Predicting expressway crash frequency using a random effect negative binomial model: A case study in China.

Science.gov (United States)

Ma, Zhuanglin; Zhang, Honglu; Chien, Steven I-Jy; Wang, Jin; Dong, Chunjiao

2017-01-01

To investigate the relationship between crash frequency and potential influence factors, the accident data for events occurring on a 50km long expressway in China, including 567 crash records (2006-2008), were collected and analyzed. Both the fixed-length and the homogeneous longitudinal grade methods were applied to divide the study expressway section into segments. A negative binomial (NB) model and a random effect negative binomial (RENB) model were developed to predict crash frequency. The parameters of both models were determined using the maximum likelihood (ML) method, and the mixed stepwise procedure was applied to examine the significance of explanatory variables. Three explanatory variables, including longitudinal grade, road width, and ratio of longitudinal grade and curve radius (RGR), were found as significantly affecting crash frequency. The marginal effects of significant explanatory variables to the crash frequency were analyzed. The model performance was determined by the relative prediction error and the cumulative standardized residual. The results show that the RENB model outperforms the NB model. It was also found that the model performance with the fixed-length segment method is superior to that with the homogeneous longitudinal grade segment method. Copyright © 2016. Published by Elsevier Ltd.

Deteksi Dini Kasus Demam Berdarah Dengue Berdasarkan Faktor Cuaca di DKI Jakarta Menggunakan Metode Zero Truncated Negative Binomial

Directory of Open Access Journals (Sweden)

Robert Kurniawan

2017-11-01

Full Text Available AbstractThe incidence rates of DHF in Jakarta in 2010 to 2014 are always higher than that of the national rates. Therefore, this study aims to find the effect of weather parameter on DHF cases. Weather is chosen because it can be observed daily and can be predicted so that it can be used as earlydetection in estimating the number of DHF cases. Data use includes DHF cases which is collected daily and weather data including lowest and highest temperatures and rainfall. Data analysis used is zero-truncated negative binomial analysis at 10% significance level. Based on the periodic dataof selected variables from January 1st 2015 until May 31st 2015, the study revealed that weather factors consisting of highest temperature, lowest temperature, and rainfall rate were significant enough to predict the number of DHF patients in DKI Jakarta. The three variables had positiveeffects in influencing the number of DHF patients in the same period. However, the weather factors cannot be controlled by humans, so that appropriate preventions are required whenever weather’s predictions indicate the increasing number of DHF cases in DKI Jakarta.Keywords: Dengue Hemorrhagic Fever, zero truncated negative binomial, early warning.AbstrakAngka kesakitan DBD pada tahun 2010 hingga 2014 selalu lebih tinggi dibandingkan dengan angka kesakitan DBD nasional. Oleh karena itu, penelitian ini bertujuan untuk mencari pengaruh faktor cuaca terhadap kasus DBD. Faktor cuaca dipilih karena dapat diamati setiap harinya dan dapat diprediksi sehingga dapat dijadikan deteksi dini dalam perkiraan jumlah penderita DBD. Data yang digunakan dalam penelitian ini adalah data jumlah penderita DBD di DKI Jakarta per hari dan data cuaca yang meliputi suhu terendah, suhu tertinggi dan curah hujan. Untuk mengetahui pengaruh faktor cuaca tersebut terhadap jumlah penderita DBD di DKI Jakarta digunakan metode analisis zero-truncated negative binomial. Berdasarkan data periode 1 Januari 2015 hingga

Measurements of the charged particle multiplicity distribution in restricted rapidity intervals

CERN Document Server

Buskulic, Damir; De Bonis, I; Décamp, D; Ghez, P; Goy, C; Lees, J P; Lucotte, A; Minard, M N; Odier, P; Pietrzyk, B; Ariztizabal, F; Chmeissani, M; Crespo, J M; Efthymiopoulos, I; Fernández, E; Fernández-Bosman, M; Gaitan, V; Garrido, L; Martínez, M; Orteu, S; Pacheco, A; Padilla, C; Palla, Fabrizio; Pascual, A; Perlas, J A; Sánchez, F; Teubert, F; Colaleo, A; Creanza, D; De Palma, M; Farilla, A; Gelao, G; Girone, M; Iaselli, Giuseppe; Maggi, G; Maggi, M; Marinelli, N; Natali, S; Nuzzo, S; Ranieri, A; Raso, G; Romano, F; Ruggieri, F; Selvaggi, G; Silvestris, L; Tempesta, P; Zito, G; Huang, X; Lin, J; Ouyang, Q; Wang, T; Xie, Y; Xu, R; Xue, S; Zhang, J; Zhang, L; Zhao, W; Bonvicini, G; Cattaneo, M; Comas, P; Coyle, P; Drevermann, H; Engelhardt, A; Forty, Roger W; Frank, M; Hagelberg, R; Harvey, J; Jacobsen, R; Janot, P; Jost, B; Knobloch, J; Lehraus, Ivan; Markou, C; Martin, E B; Mato, P; Meinhard, H; Minten, Adolf G; Miquel, R; Oest, T; Palazzi, P; Pater, J R; Pusztaszeri, J F; Ranjard, F; Rensing, P E; Rolandi, Luigi; Schlatter, W D; Schmelling, M; Schneider, O; Tejessy, W; Tomalin, I R; Venturi, A; Wachsmuth, H W; Wiedenmann, W; Wildish, T; Witzeling, W; Wotschack, J; Ajaltouni, Ziad J; Bardadin-Otwinowska, Maria; Barrès, A; Boyer, C; Falvard, A; Gay, P; Guicheney, C; Henrard, P; Jousset, J; Michel, B; Monteil, S; Montret, J C; Pallin, D; Perret, P; Podlyski, F; Proriol, J; Rossignol, J M; Saadi, F; Fearnley, Tom; Hansen, J B; Hansen, J D; Hansen, J R; Hansen, P H; Nilsson, B S; Kyriakis, A; Simopoulou, Errietta; Siotis, I; Vayaki, Anna; Zachariadou, K; Blondel, A; Bonneaud, G R; Brient, J C; Bourdon, P; Passalacqua, L; Rougé, A; Rumpf, M; Tanaka, R; Valassi, Andrea; Verderi, M; Videau, H L; Candlin, D J; Parsons, M I; Focardi, E; Parrini, G; Corden, M; Delfino, M C; Georgiopoulos, C H; Jaffe, D E; Antonelli, A; Bencivenni, G; Bologna, G; Bossi, F; Campana, P; Capon, G; Chiarella, V; Felici, G; Laurelli, P; Mannocchi, G; Murtas, F; Murtas, G P; Pepé-Altarelli, M; Dorris, S J; Halley, A W; ten Have, I; Knowles, I G; Lynch, J G; Morton, W T; O'Shea, V; Raine, C; Reeves, P; Scarr, J M; Smith, K; Smith, M G; Thompson, A S; Thomson, F; Thorn, S; Turnbull, R M; Becker, U; Braun, O; Geweniger, C; Graefe, G; Hanke, P; Hepp, V; Kluge, E E; Putzer, A; Rensch, B; Schmidt, M; Sommer, J; Stenzel, H; Tittel, K; Werner, S; Wunsch, M; Beuselinck, R; Binnie, David M; Cameron, W; Colling, D J; Dornan, Peter J; Konstantinidis, N P; Moneta, L; Moutoussi, A; Nash, J; San Martin, G; Sedgbeer, J K; Stacey, A M; Dissertori, G; Girtler, P; Kneringer, E; Kuhn, D; Rudolph, G; Bowdery, C K; Brodbeck, T J; Colrain, P; Crawford, G; Finch, A J; Foster, F; Hughes, G; Sloan, Terence; Whelan, E P; Williams, M I; Galla, A; Greene, A M; Kleinknecht, K; Quast, G; Raab, J; Renk, B; Sander, H G; Wanke, R; Zeitnitz, C; Aubert, Jean-Jacques; Bencheikh, A M; Benchouk, C; Bonissent, A; Bujosa, G; Calvet, D; Carr, J; Diaconu, C A; Etienne, F; Thulasidas, M; Nicod, D; Payre, P; Rousseau, D; Talby, M; Abt, I; Assmann, R W; Bauer, C; Blum, Walter; Brown, D; Dietl, H; Dydak, Friedrich; Ganis, G; Gotzhein, C; Jakobs, K; Kroha, H; Lütjens, G; Lutz, Gerhard; Männer, W; Moser, H G; Richter, R H; Rosado-Schlosser, A; Settles, Ronald; Seywerd, H C J; Stierlin, U; Saint-Denis, R; Wolf, G; Alemany, R; Boucrot, J; Callot, O; Cordier, A; Courault, F; Davier, M; Duflot, L; Grivaz, J F; Jacquet, M; Kim, D W; Le Diberder, F R; Lefrançois, J; Lutz, A M; Musolino, G; Nikolic, I A; Park, H J; Park, I C; Schune, M H; Simion, S; Veillet, J J; Videau, I; Abbaneo, D; Azzurri, P; Bagliesi, G; Batignani, G; Bettarini, S; Bozzi, C; Calderini, G; Carpinelli, M; Ciocci, M A; Ciulli, V; Dell'Orso, R; Fantechi, R; Ferrante, I; Foà, L; Forti, F; Giassi, A; Giorgi, M A; Gregorio, A; Ligabue, F; Lusiani, A; Marrocchesi, P S; Messineo, A; Rizzo, G; Sanguinetti, G; Sciabà, A; Spagnolo, P; Steinberger, Jack; Tenchini, Roberto; Tonelli, G; Triggiani, G; Vannini, C; Verdini, P G; Walsh, J; Betteridge, A P; Blair, G A; Bryant, L M; Cerutti, F; Gao, Y; Green, M G; Johnson, D L; Medcalf, T; Mir, M; Perrodo, P; Strong, J A; Bertin, V; Botterill, David R; Clifft, R W; Edgecock, T R; Haywood, S; Edwards, M; Maley, P; Norton, P R; Thompson, J C; Bloch-Devaux, B; Colas, P; Duarte, H; Emery, S; Kozanecki, Witold; Lançon, E; Lemaire, M C; Locci, E; Marx, B; Pérez, P; Rander, J; Renardy, J F; Rosowsky, A; Roussarie, A; Schuller, J P; Schwindling, J; Si Mohand, D; Trabelsi, A; Vallage, B; Johnson, R P; Kim, H Y; Litke, A M; McNeil, M A; Taylor, G; Beddall, A; Booth, C N; Boswell, R; Cartwright, S L; Combley, F; Dawson, I; Köksal, A; Letho, M; Newton, W M; Rankin, C; Thompson, L F; Böhrer, A; Brandt, S; Cowan, G D; Feigl, E; Grupen, Claus; Lutters, G; Minguet-Rodríguez, J A; Rivera, F; Saraiva, P; Smolik, L; Stephan, F; Apollonio, M; Bosisio, L; Della Marina, R; Giannini, G; Gobbo, B; Ragusa, F; Rothberg, J E; Wasserbaech, S R; Armstrong, S R; Bellantoni, L; Elmer, P; Feng, Z; Ferguson, D P S; Gao, Y S; González, S; Grahl, J; Harton, J L; Hayes, O J; Hu, H; McNamara, P A; Nachtman, J M; Orejudos, W; Pan, Y B; Saadi, Y; Schmitt, M; Scott, I J; Sharma, V; Turk, J; Walsh, A M; Wu Sau Lan; Wu, X; Yamartino, J M; Zheng, M; Zobernig, G

1995-01-01

Charged particle multiplicity distributions have been measured with the ALEPH detector in restricted rapidity intervals |Y| \\leq 0.5,1.0, 1.5,2.0\\/ along the thrust axis and also without restriction on rapidity. The distribution for the full range can be parametrized by a log-normal distribution. For smaller windows one finds a more complicated structure, which is understood to arise from perturbative effects. The negative-binomial distribution fails to describe the data both with and without the restriction on rapidity. The JETSET model is found to describe all aspects of the data while the width predicted by HERWIG is in significant disagreement.

Spatial distribution of single-nucleotide polymorphisms related to fungicide resistance and implications for sampling.

Science.gov (United States)

Van der Heyden, H; Dutilleul, P; Brodeur, L; Carisse, O

2014-06-01

Spatial distribution of single-nucleotide polymorphisms (SNPs) related to fungicide resistance was studied for Botrytis cinerea populations in vineyards and for B. squamosa populations in onion fields. Heterogeneity in this distribution was characterized by performing geostatistical analyses based on semivariograms and through the fitting of discrete probability distributions. Two SNPs known to be responsible for boscalid resistance (H272R and H272Y), both located on the B subunit of the succinate dehydrogenase gene, and one SNP known to be responsible for dicarboximide resistance (I365S) were chosen for B. cinerea in grape. For B. squamosa in onion, one SNP responsible for dicarboximide resistance (I365S homologous) was chosen. One onion field was sampled in 2009 and another one was sampled in 2010 for B. squamosa, and two vineyards were sampled in 2011 for B. cinerea, for a total of four sampled sites. Cluster sampling was carried on a 10-by-10 grid, each of the 100 nodes being the center of a 10-by-10-m quadrat. In each quadrat, 10 samples were collected and analyzed by restriction fragment length polymorphism polymerase chain reaction (PCR) or allele specific PCR. Mean SNP incidence varied from 16 to 68%, with an overall mean incidence of 43%. In the geostatistical analyses, omnidirectional variograms showed spatial autocorrelation characterized by ranges of 21 to 1 m. Various levels of anisotropy were detected, however, with variograms computed in four directions (at 0°, 45°, 90°, and 135° from the within-row direction used as reference), indicating that spatial autocorrelation was prevalent or characterized by a longer range in one direction. For all eight data sets, the β-binomial distribution was found to fit the data better than the binomial distribution. This indicates local aggregation of fungicide resistance among sampling units, as supported by estimates of the parameter θ of the β-binomial distribution of 0.09 to 0.23 (overall median value = 0

Semiparametric Allelic Tests for Mapping Multiple Phenotypes: Binomial Regression and Mahalanobis Distance.

Science.gov (United States)

Majumdar, Arunabha; Witte, John S; Ghosh, Saurabh

2015-12-01

Binary phenotypes commonly arise due to multiple underlying quantitative precursors and genetic variants may impact multiple traits in a pleiotropic manner. Hence, simultaneously analyzing such correlated traits may be more powerful than analyzing individual traits. Various genotype-level methods, e.g., MultiPhen (O'Reilly et al. []), have been developed to identify genetic factors underlying a multivariate phenotype. For univariate phenotypes, the usefulness and applicability of allele-level tests have been investigated. The test of allele frequency difference among cases and controls is commonly used for mapping case-control association. However, allelic methods for multivariate association mapping have not been studied much. In this article, we explore two allelic tests of multivariate association: one using a Binomial regression model based on inverted regression of genotype on phenotype (Binomial regression-based Association of Multivariate Phenotypes [BAMP]), and the other employing the Mahalanobis distance between two sample means of the multivariate phenotype vector for two alleles at a single-nucleotide polymorphism (Distance-based Association of Multivariate Phenotypes [DAMP]). These methods can incorporate both discrete and continuous phenotypes. Some theoretical properties for BAMP are studied. Using simulations, the power of the methods for detecting multivariate association is compared with the genotype-level test MultiPhen's. The allelic tests yield marginally higher power than MultiPhen for multivariate phenotypes. For one/two binary traits under recessive mode of inheritance, allelic tests are found to be substantially more powerful. All three tests are applied to two different real data and the results offer some support for the simulation study. We propose a hybrid approach for testing multivariate association that implements MultiPhen when Hardy-Weinberg Equilibrium (HWE) is violated and BAMP otherwise, because the allelic approaches assume HWE

Criterios sobre el uso de la distribución normal para aproximar la distribución binomial

OpenAIRE

Ortiz Pinilla, Jorge; Castro, Amparo; Neira, Tito; Torres, Pedro; Castañeda, Javier

2012-01-01

Las dos reglas empíricas más conocidas para aceptar la aproximación normal de la distribución binomial carecen de regularidad en el control del margen de error cometido al utilizar la aproximación normal. Se propone un criterio y algunas fórmulas para controlarlo cerca de algunos valores escogidos para el error máximo.

Spatial distribution of adult Anthonomus grandis Boheman (Coleoptera: Curculionidae and buds with feeding punctures on conventional and Bt cottonDistribuição espacial de adultos e botões com orifício de alimentação de Anthonomus grandis Boheman (Coleoptera: Curculionidae em algodoeiro convencional e Bt

Directory of Open Access Journals (Sweden)

Paulo Rogerio Beltramin da Fonseca

2013-06-01

Full Text Available O conhecimento dos arranjos de dispersão para adultos e botões com orifício de alimentação de Anthonomus grandis em cultivares de algodoeiro é necessário para aperfeiçoar o monitoramento e controle da praga. Esta pesquisa teve por objetivo realizar análises probabilísticas dos padrões de distribuição espacial dos adultos e botões com orifícios de alimentação de A. grandis em duas cultivares de algodão Bt e não Bt. O estudo foi conduzido a campo em duas áreas experimentais, cada uma composta por 100 parcelas de sete linhas de sete metros de comprimento. Em 16 amostragens avaliaram-se cinco plantas por parcela através da contagem dos adultos e dos botões com orifício de alimentaçãoentre janeiro e maio de 2010. Foram calculados os índices de dispersão (razão variância/média, índice de Morisita e Expoente k da Distribuição Binomial Negativa e as distribuições teóricas de freqüência (Poisson, Binomial Negativa e Binomial Positiva. Não houve diferença estatística entre as cultivares avaliadas. A distribuição espacial dos adultos de A. grandis, nas cultivares Bt e não Bt, ajustou-se nos arranjos probabilísticos de distribuição binomial negativa (agregado e distribuição binomial positiva (uniforme, conforme os dias após a emergência do algodoeiro. As análises de dispersão para os botões com orifícios de alimentação nas culturas Bt e convencional mostraram os modelos espaciais de Poisson (aleatório, distribuição binomial negativa (agregado e distribuição binomial positiva (uniforme, em seqüência, durante o ciclo da cultura.Dispersion patterns of Anthonomus grandis adults and damaged squares with their feeding punctures are important to enhance pest monitoring and control on cotton. In this research we performed probabilistic analyses of the distribution patterns of adults and squares with feeding punctures of A. grandis on two cotton genotypes, Bt and non-Bt near isogenic lines. We conducted

Multiparticle distributions in limited rapidity intervals and the violation of asymptotic KNO scaling

International Nuclear Information System (INIS)

De Dias Deus, J.

1986-03-01

A simple model independent analysis of UA5 collaboration pantip collider data on rapidity cut charged particle distributions strongly suggests: i) independent particle emission from sources or clusters; ii) exact negative binomial multiparticle distributions. The violation of asymptotic KNO scaling is shown to arise from the fast growth with energy of the reduced correlations C K (O)/C 1 k (0). A comparison with recently published e + e - √s = 29 GeV data is presented

Interrelationships Between Receiver/Relative Operating Characteristics Display, Binomial, Logit, and Bayes' Rule Probability of Detection Methodologies

Science.gov (United States)

Generazio, Edward R.

2014-01-01

Unknown risks are introduced into failure critical systems when probability of detection (POD) capabilities are accepted without a complete understanding of the statistical method applied and the interpretation of the statistical results. The presence of this risk in the nondestructive evaluation (NDE) community is revealed in common statements about POD. These statements are often interpreted in a variety of ways and therefore, the very existence of the statements identifies the need for a more comprehensive understanding of POD methodologies. Statistical methodologies have data requirements to be met, procedures to be followed, and requirements for validation or demonstration of adequacy of the POD estimates. Risks are further enhanced due to the wide range of statistical methodologies used for determining the POD capability. Receiver/Relative Operating Characteristics (ROC) Display, simple binomial, logistic regression, and Bayes' rule POD methodologies are widely used in determining POD capability. This work focuses on Hit-Miss data to reveal the framework of the interrelationships between Receiver/Relative Operating Characteristics Display, simple binomial, logistic regression, and Bayes' Rule methodologies as they are applied to POD. Knowledge of these interrelationships leads to an intuitive and global understanding of the statistical data, procedural and validation requirements for establishing credible POD estimates.

Football fever: goal distributions and non-Gaussian statistics

Science.gov (United States)

Bittner, E.; Nußbaumer, A.; Janke, W.; Weigel, M.

2009-02-01

Analyzing football score data with statistical techniques, we investigate how the not purely random, but highly co-operative nature of the game is reflected in averaged properties such as the probability distributions of scored goals for the home and away teams. As it turns out, especially the tails of the distributions are not well described by the Poissonian or binomial model resulting from the assumption of uncorrelated random events. Instead, a good effective description of the data is provided by less basic distributions such as the negative binomial one or the probability densities of extreme value statistics. To understand this behavior from a microscopical point of view, however, no waiting time problem or extremal process need be invoked. Instead, modifying the Bernoulli random process underlying the Poissonian model to include a simple component of self-affirmation seems to describe the data surprisingly well and allows to understand the observed deviation from Gaussian statistics. The phenomenological distributions used before can be understood as special cases within this framework. We analyzed historical football score data from many leagues in Europe as well as from international tournaments, including data from all past tournaments of the “FIFA World Cup” series, and found the proposed models to be applicable rather universally. In particular, here we analyze the results of the German women’s premier football league and consider the two separate German men’s premier leagues in the East and West during the cold war times as well as the unified league after 1990 to see how scoring in football and the component of self-affirmation depend on cultural and political circumstances.

Multiplicity distributions in small phase-space domains in central nucleus-nucleus collisions

International Nuclear Information System (INIS)

Baechler, J.; Hoffmann, M.; Runge, K.; Schmoetten, E.; Bartke, J.; Gladysz, E.; Kowalski, M.; Stefanski, P.; Bialkowska, H.; Bock, R.; Brockmann, R.; Sandoval, A.; Buncic, P.; Ferenc, D.; Kadija, K.; Ljubicic, A. Jr.; Vranic, D.; Chase, S.I.; Harris, J.W.; Odyniec, G.; Pugh, H.G.; Rai, G.; Teitelbaum, L.; Tonse, S.; Derado, I.; Eckardt, V.; Gebauer, H.J.; Rauch, W.; Schmitz, N.; Seyboth, P.; Seyerlein, J.; Vesztergombi, G.; Eschke, J.; Heck, W.; Kabana, S.; Kuehmichel, A.; Lahanas, M.; Lee, Y.; Le Vine, M.; Margetis, S.; Renfordt, R.; Roehrich, D.; Rothard, H.; Schmidt, E.; Schneider, I.; Stock, R.; Stroebele, H.; Wenig, S.; Fleischmann, B.; Fuchs, M.; Gazdzicki, M.; Kosiec, J.; Skrzypczak, E.; Keidel, R.; Piper, A.; Puehlhofer, F.; Nappi, E.; Posa, F.; Paic, G.; Panagiotou, A.D.; Petridis, A.; Vassileiadis, G.; Pfenning, J.; Wosiek, B.

1992-10-01

Multiplicity distributions of negatively charged particles have been studied in restricted phase space intervals for central S + S, O + Au and S + Au collisions at 200 GeV/nucleon. It is shown that multiplicity distributions are well described by a negative binomial form irrespectively of the size and dimensionality of phase space domain. A clan structure analysis reveals interesting similarities between complex nuclear collisions and a simple partonic shower. The lognormal distribution agrees reasonably well with the multiplicity data in large domains, but fails in the case of small intervals. No universal scaling function was found to describe the shape of multiplicity distributions in phase space intervals of varying size. (orig.)

New distributions of the statistical time delay of electrical breakdown in nitrogen

International Nuclear Information System (INIS)

Markovic, V Lj; Gocic, S R; Stamenkovic, S N

2006-01-01

Two new distributions of the statistical time delay of electrical breakdown in nitrogen are reported in this paper. The Gaussian and Gauss-exponential distributions of statistical time delay have been obtained on the basis of thousands of time delay measurements on a gas tube with a plane-parallel electrode system. Distributions of the statistical time delay are theoretically founded on binomial distribution for the occurrence of initiating electrons and described by using simple analytical and numerical models. The shapes of distributions depend on the electron yields in the interelectrode space originating from residual states. It is shown that a distribution of the statistical time delay changes from exponential and Gauss-exponential to Gaussian distribution due to the influence of residual ionization

Inference for binomial probability based on dependent Bernoulli random variables with applications to meta-analysis and group level studies.

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Bakbergenuly, Ilyas; Kulinskaya, Elena; Morgenthaler, Stephan

2016-07-01

We study bias arising as a result of nonlinear transformations of random variables in random or mixed effects models and its effect on inference in group-level studies or in meta-analysis. The findings are illustrated on the example of overdispersed binomial distributions, where we demonstrate considerable biases arising from standard log-odds and arcsine transformations of the estimated probability p̂, both for single-group studies and in combining results from several groups or studies in meta-analysis. Our simulations confirm that these biases are linear in ρ, for small values of ρ, the intracluster correlation coefficient. These biases do not depend on the sample sizes or the number of studies K in a meta-analysis and result in abysmal coverage of the combined effect for large K. We also propose bias-correction for the arcsine transformation. Our simulations demonstrate that this bias-correction works well for small values of the intraclass correlation. The methods are applied to two examples of meta-analyses of prevalence. © 2016 The Authors. Biometrical Journal Published by Wiley-VCH Verlag GmbH & Co. KGaA.

Co-Infestation and Spatial Distribution of Bactrocera carambolae and Anastrepha spp. (Diptera: Tephritidae) in Common Guava in the Eastern Amazon

Science.gov (United States)

Deus, E. G.; Godoy, W. A. C.; Sousa, M. S. M.; Lopes, G. N.; Jesus-Barros, C. R.; Silva, J. G.; Adaime, R.

2016-01-01

Field infestation and spatial distribution of introduced Bactrocera carambolae Drew and Hancock and native species of Anastrepha in common guavas [Psidium guajava (L.)] were investigated in the eastern Amazon. Fruit sampling was carried out in the municipalities of Calçoene and Oiapoque in the state of Amapá, Brazil. The frequency distribution of larvae in fruit was fitted to the negative binomial distribution. Anastrepha striata was more abundant in both sampled areas in comparison to Anastrepha fraterculus (Wiedemann) and B. carambolae. The frequency distribution analysis of adults revealed an aggregated pattern for B. carambolae as well as for A. fraterculus and Anastrepha striata Schiner, described by the negative binomial distribution. Although the populations of Anastrepha spp. may have suffered some impact due to the presence of B. carambolae, the results are still not robust enough to indicate effective reduction in the abundance of Anastrepha spp. caused by B. carambolae in a general sense. The high degree of aggregation observed for both species suggests interspecific co-occurrence with the simultaneous presence of both species in the analysed fruit. Moreover, a significant fraction of uninfested guavas also indicated absence of competitive displacement. PMID:27638949

A flexible mixed-effect negative binomial regression model for detecting unusual increases in MRI lesion counts in individual multiple sclerosis patients.

Science.gov (United States)

Kondo, Yumi; Zhao, Yinshan; Petkau, John

2015-06-15

We develop a new modeling approach to enhance a recently proposed method to detect increases of contrast-enhancing lesions (CELs) on repeated magnetic resonance imaging, which have been used as an indicator for potential adverse events in multiple sclerosis clinical trials. The method signals patients with unusual increases in CEL activity by estimating the probability of observing CEL counts as large as those observed on a patient's recent scans conditional on the patient's CEL counts on previous scans. This conditional probability index (CPI), computed based on a mixed-effect negative binomial regression model, can vary substantially depending on the choice of distribution for the patient-specific random effects. Therefore, we relax this parametric assumption to model the random effects with an infinite mixture of beta distributions, using the Dirichlet process, which effectively allows any form of distribution. To our knowledge, no previous literature considers a mixed-effect regression for longitudinal count variables where the random effect is modeled with a Dirichlet process mixture. As our inference is in the Bayesian framework, we adopt a meta-analytic approach to develop an informative prior based on previous clinical trials. This is particularly helpful at the early stages of trials when less data are available. Our enhanced method is illustrated with CEL data from 10 previous multiple sclerosis clinical trials. Our simulation study shows that our procedure estimates the CPI more accurately than parametric alternatives when the patient-specific random effect distribution is misspecified and that an informative prior improves the accuracy of the CPI estimates. Copyright © 2015 John Wiley & Sons, Ltd.

Superclusters and hadronic multiplicity distributions

International Nuclear Information System (INIS)

Shih, C.C.; Carruthers, P.

1986-01-01

The multiplicity distribution is expressed in terms of supercluster production in hadronic processes at high energy. This process creates unstable clusters at intermediate stages and hadrons in final stage. It includes Poisson-transform distributions (with the partially coherent distribution as a special case) and is very flexible for phenomenological analyses. The associated Koba, Nielson, and Olesen limit and the behavior of cumulant moments are analyzed in detail for finite and/or infinite cluster size and particle size per cluster. In general, a supercluster distribution does not need to be equivalent to a negative binomial distribution to fit experimental data well. Furthermore, the requirement of such equivalence leads to many solutions, in which the average size of the cluster is not logarithmic: e.g., it may show a power behavior instead. Superclustering is defined as a two-or multi-stage process underlying observed global multiplicity distributions. At the first stage of the production process, individual clusters are produced according to a given statistical law. For example, the clustering distribution may be described by partially coherent (oreven sub-Poissonian distribution models. At the second stage, the clusters are considered as the sources of particle production. The corresponding distribution may then be as general as the clustering distribution just mentioned. 8 refs

Finding the Right Distribution for Highly Skewed Zero-inflated Clinical Data

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Resmi Gupta

2013-03-01

Full Text Available Discrete, highly skewed distributions with excess numbers of zeros often result in biased estimates and misleading inferences if the zeros are not properly addressed. A clinical example of children with electrophysiologic disorders in which many of the children are treated without surgery is provided. The purpose of the current study was to identify the optimal modeling strategy for highly skewed, zeroinflated data often observed in the clinical setting by: (a simulating skewed, zero-inflated count data; (b fitting simulated data with Poisson, Negative Binomial, Zero-Inflated Poisson (ZIP and Zero-inflated Negative Binomial (ZINB models; and, (c applying the aforementioned models to actual, highlyskewed, clinical data of children with an EP disorder. The ZIP model was observed to be the optimal model based on traditional fit statistics as well as estimates of bias, mean-squared error, and coverage.  

proportion: A comprehensive R package for inference on single Binomial proportion and Bayesian computations

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M. Subbiah

2017-01-01

Full Text Available Extensive statistical practice has shown the importance and relevance of the inferential problem of estimating probability parameters in a binomial experiment; especially on the issues of competing intervals from frequentist, Bayesian, and Bootstrap approaches. The package written in the free R environment and presented in this paper tries to take care of the issues just highlighted, by pooling a number of widely available and well-performing methods and apporting on them essential variations. A wide range of functions helps users with differing skills to estimate, evaluate, summarize, numerically and graphically, various measures adopting either the frequentist or the Bayesian paradigm.

A Flexible, Efficient Binomial Mixed Model for Identifying Differential DNA Methylation in Bisulfite Sequencing Data

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Lea, Amanda J.

2015-01-01

Identifying sources of variation in DNA methylation levels is important for understanding gene regulation. Recently, bisulfite sequencing has become a popular tool for investigating DNA methylation levels. However, modeling bisulfite sequencing data is complicated by dramatic variation in coverage across sites and individual samples, and because of the computational challenges of controlling for genetic covariance in count data. To address these challenges, we present a binomial mixed model and an efficient, sampling-based algorithm (MACAU: Mixed model association for count data via data augmentation) for approximate parameter estimation and p-value computation. This framework allows us to simultaneously account for both the over-dispersed, count-based nature of bisulfite sequencing data, as well as genetic relatedness among individuals. Using simulations and two real data sets (whole genome bisulfite sequencing (WGBS) data from Arabidopsis thaliana and reduced representation bisulfite sequencing (RRBS) data from baboons), we show that our method provides well-calibrated test statistics in the presence of population structure. Further, it improves power to detect differentially methylated sites: in the RRBS data set, MACAU detected 1.6-fold more age-associated CpG sites than a beta-binomial model (the next best approach). Changes in these sites are consistent with known age-related shifts in DNA methylation levels, and are enriched near genes that are differentially expressed with age in the same population. Taken together, our results indicate that MACAU is an efficient, effective tool for analyzing bisulfite sequencing data, with particular salience to analyses of structured populations. MACAU is freely available at www.xzlab.org/software.html. PMID:26599596

Charged multiplicity distributions and correlations in e+e- annihilation at PETRA energies

International Nuclear Information System (INIS)

Braunschweig, W.; Gerhards, R.; Kirschfink, F.J.; Martyn, H.U.; Kolanoski, H.; Bowler, M.G.; Burrows, P.N.; Veitch, M.E.; Brandt, S.; Holder, M.; Caldwell, A.; Muller, D.; Ritz, S.; Strom, D.; Takashima, M.; Wu Saulan; Zobernig, G.

1989-01-01

We report on an analysis of the multiplicity distributions of charged particles produced in e + e - annihilation into hadrons at c.m. energies between 14 and 46.8 GeV. The charged multiplicity distributions of the whole event and single hemisphere deviate significantly from the Poisson distribution but follow approximate KNO scaling. We have also studied the multiplicity distributions in various rapidity intervals and found that they can be well described by the negative binomial distribution only for small central intervals. We have also analysed forward-backward multiplicity correlations for different energies and selections of particle charge and shown that they can be understood in terms of the fragmentation properties of the different quark flavours and by the production and decay of resonances. These correlations are well reproduced by the Lund string model. (orig.)

Temporary disaster debris management site identification using binomial cluster analysis and GIS.

Science.gov (United States)

Grzeda, Stanislaw; Mazzuchi, Thomas A; Sarkani, Shahram

2014-04-01

An essential component of disaster planning and preparation is the identification and selection of temporary disaster debris management sites (DMS). However, since DMS identification is a complex process involving numerous variable constraints, many regional, county and municipal jurisdictions initiate this process during the post-disaster response and recovery phases, typically a period of severely stressed resources. Hence, a pre-disaster approach in identifying the most likely sites based on the number of locational constraints would significantly contribute to disaster debris management planning. As disasters vary in their nature, location and extent, an effective approach must facilitate scalability, flexibility and adaptability to variable local requirements, while also being generalisable to other regions and geographical extents. This study demonstrates the use of binomial cluster analysis in potential DMS identification in a case study conducted in Hamilton County, Indiana. © 2014 The Author(s). Disasters © Overseas Development Institute, 2014.

Entanglement and Other Nonclassical Properties of Two Two-Level Atoms Interacting with a Two-Mode Binomial Field: Constant and Intensity-Dependent Coupling Regimes

International Nuclear Information System (INIS)

Tavassoly, M.K.; Hekmatara, H.

2015-01-01

In this paper, we consider the interaction between two two-level atoms and a two-mode binomial field with a general intensity-dependent coupling regime. The outlined dynamical problem has explicit analytical solution, by which we can evaluate a few of its physical features of interest. To achieve the purpose of the paper, after choosing a particular nonlinearity function, we investigate the quantum statistics, atomic population inversion and at last the linear entropy of the atom-field system which is a good measure for the degree of entanglement. In detail, the effects of binomial field parameters, in addition to different initial atomic states on the temporal behavior of the mentioned quantities have been analyzed. The results show that, the values of binomial field parameters and the initial state of the two atoms influence on the nonclassical effects in the obtained states through which one can tune the nonclassicality criteria appropriately. Setting intensity-dependent coupling function equal to 1 reduces the results to the constant coupling case. By comparing the latter case with the nonlinear regime, we will observe that the nonlinearity disappears the pattern of collapse-revival phenomenon in the evolution of Mandel parameter and population inversion (which can be seen in the linear case with constant coupling), however, more typical collapse-revivals will be appeared for the cross-correlation function in the nonlinear case. Finally, in both linear and nonlinear regime, the entropy remains less than (but close to) 0.5. In other words the particular chosen nonlinearity does not critically affect on the entropy of the system. (paper)

The binomial work-health in the transit of Curitiba city.

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Tokars, Eunice; Moro, Antonio Renato Pereira; Cruz, Roberto Moraes

2012-01-01

The working activity in traffic of the big cities complex interacts with the environment is often in unsafe and unhealthy imbalance favoring the binomial work - health. The aim of this paper was to analyze the relationship between work and health of taxi drivers in Curitiba, Brazil. This cross-sectional observational study with 206 individuals used a questionnaire on the organization's profile and perception of the environment and direct observation of work. It was found that the majority are male, aged between 26 and 49 years and has a high school degree. They are sedentary, like making a journey from 8 to 12 hours. They consider a stressful profession, related low back pain and are concerned about safety and accidents. 40% are smokers and consume alcoholic drink and 65% do not have or do not use devices of comfort. Risk factors present in the daily taxi constraints cause physical, cognitive and organizational and can affect your performance. It is concluded that the taxi drivers must change the unhealthy lifestyle, requiring a more efficient management of government authorities for this work is healthy and safe for all involved.

Dynamic prediction of cumulative incidence functions by direct binomial regression.

Science.gov (United States)

Grand, Mia K; de Witte, Theo J M; Putter, Hein

2018-03-25

In recent years there have been a series of advances in the field of dynamic prediction. Among those is the development of methods for dynamic prediction of the cumulative incidence function in a competing risk setting. These models enable the predictions to be updated as time progresses and more information becomes available, for example when a patient comes back for a follow-up visit after completing a year of treatment, the risk of death, and adverse events may have changed since treatment initiation. One approach to model the cumulative incidence function in competing risks is by direct binomial regression, where right censoring of the event times is handled by inverse probability of censoring weights. We extend the approach by combining it with landmarking to enable dynamic prediction of the cumulative incidence function. The proposed models are very flexible, as they allow the covariates to have complex time-varying effects, and we illustrate how to investigate possible time-varying structures using Wald tests. The models are fitted using generalized estimating equations. The method is applied to bone marrow transplant data and the performance is investigated in a simulation study. © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Producing Distribution Maps for a Spatially-Explicit Ecosystem Model Using Large Monitoring and Environmental Databases and a Combination of Interpolation and Extrapolation

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Arnaud Grüss

2018-01-01

Full Text Available To be able to simulate spatial patterns of predator-prey interactions, many spatially-explicit ecosystem modeling platforms, including Atlantis, need to be provided with distribution maps defining the annual or seasonal spatial distributions of functional groups and life stages. We developed a methodology combining extrapolation and interpolation of the predictions made by statistical habitat models to produce distribution maps for the fish and invertebrates represented in the Atlantis model of the Gulf of Mexico (GOM Large Marine Ecosystem (LME (“Atlantis-GOM”. This methodology consists of: (1 compiling a large monitoring database, gathering all the fisheries-independent and fisheries-dependent data collected in the northern (U.S. GOM since 2000; (2 compiling a large environmental database, storing all the environmental parameters known to influence the spatial distribution patterns of fish and invertebrates of the GOM; (3 fitting binomial generalized additive models (GAMs to the large monitoring and environmental databases, and geostatistical binomial generalized linear mixed models (GLMMs to the large monitoring database; and (4 employing GAM predictions to infer spatial distributions in the southern GOM, and GLMM predictions to infer spatial distributions in the U.S. GOM. Thus, our methodology allows for reasonable extrapolation in the southern GOM based on a large amount of monitoring and environmental data, and for interpolation in the U.S. GOM accurately reflecting the probability of encountering fish and invertebrates in that region. We used an iterative cross-validation procedure to validate GAMs. When a GAM did not pass the validation test, we employed a GAM for a related functional group/life stage to generate distribution maps for the southern GOM. In addition, no geostatistical GLMMs were fit for the functional groups and life stages whose depth, longitudinal and latitudinal ranges within the U.S. GOM are not entirely covered by

Football fever: self-affirmation model for goal distributions

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W. Janke

2009-01-01

Full Text Available The outcome of football games, as well as matches of most other popular team sports, depends on a combination of the skills of players and coaches and a number of external factors which, due to their complex nature, are presumably best viewed as random. Such parameters include the unpredictabilities of playing the ball, the players' shape of the day or environmental conditions such as the weather and the behavior of the audience. Under such circumstances, it appears worthwhile to analyze football score data with the toolbox of mathematical statistics in order to separate deterministic from stochastic effects and see what impact the cooperative and social nature of the "agents" of the system has on the resulting stochastic observables. Considering the probability distributions of scored goals for the home and away teams, it turns out that especially the tails of the distributions are not well described by the Poissonian or binomial model resulting from the assumption of uncorrelated random events. On the contrary, some more specific probability densities such as those discussed in the context of extreme-value statistics or the so-called negative binomial distribution fit these data rather well. There seemed to be no good argument to date, however, why the simplest Poissonian model fails and, instead, the latter distributions should be observed. To fill this gap, we introduced a number of microscopic models for the scoring behavior, resulting in a Bernoulli random process with a simple component of self-affirmation. These models allow us to represent the observed probability distributions surprisingly well, and the phenomenological distributions used earlier can be understood as special cases within this framework. We analyzed historical football score data from many leagues in Europe as well as from international tournaments, including data from all past tournaments of the "FIFA World Cup" series, and found the proposed models to be applicable in

A binomial modeling approach for upscaling colloid transport under unfavorable conditions: organic prediction of extended tailing

Science.gov (United States)

Hilpert, Markus; Rasmuson, Anna; Johnson, William

2017-04-01

Transport of colloids in saturated porous media is significantly influenced by colloidal interactions with grain surfaces. Near-surface fluid domain colloids experience relatively low fluid drag and relatively strong colloidal forces that slow their down-gradient translation relative to colloids in bulk fluid. Near surface fluid domain colloids may re-enter into the bulk fluid via diffusion (nanoparticles) or expulsion at rear flow stagnation zones, they may immobilize (attach) via strong primary minimum interactions, or they may move along a grain-to-grain contact to the near surface fluid domain of an adjacent grain. We introduce a simple model that accounts for all possible permutations of mass transfer within a dual pore and grain network. The primary phenomena thereby represented in the model are mass transfer of colloids between the bulk and near-surface fluid domains and immobilization onto grain surfaces. Colloid movement is described by a sequence of trials in a series of unit cells, and the binomial distribution is used to calculate the probabilities of each possible sequence. Pore-scale simulations provide mechanistically-determined likelihoods and timescales associated with the above pore-scale colloid mass transfer processes, whereas the network-scale model employs pore and grain topology to determine probabilities of transfer from up-gradient bulk and near-surface fluid domains to down-gradient bulk and near-surface fluid domains. Inter-grain transport of colloids in the near surface fluid domain can cause extended tailing.

Measurement of Inclusive Momentum Spectra and Multiplicity Distributions of Charged Particles at {radical}s {approx} 2-5 GeV

Energy Technology Data Exchange (ETDEWEB)

Dunwoodie, William

2003-08-06

Inclusive momentum spectra and multiplicity distributions of charged particles measured with the BESII detector at center of mass energies of 2.2, 2.6, 3.0, 3.2, 4.6 and 4.8 GeV are presented. Values of the second binomial moment, R{sub 2}, obtained from the multiplicity distributions are reported. These results are compared with both experimental data from high energy e{sup +}e{sup -}, ep and p{bar p} experiments and QCD calculations.

Distribuição espacial de Aphis gossypii (Glover (Hemiptera, Aphididae e Bemisia tabaci (Gennadius biótipo B (Hemiptera, Aleyrodidae em algodoeiro Bt e não-Bt Spatial distribution of Aphis gossypii (Glover (Hemiptera, Aphididae and Bemisia tabaci (Gennadius biotype B (Hemiptera, Aleyrodidae on Bt and non-Bt cotton

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Tatiana Rojas Rodrigues

2010-03-01

Full Text Available Distribuição espacial de Aphis gossypii (Glover (Hemiptera, Aphididae e Bemisia tabaci (Gennadius biótipo B (Hemiptera, Aleyrodidae em algodoeiro Bt e não-Bt. O estudo da distribuição espacial de adultos de Bemisia tabaci e de Aphis gossypii nas culturas do algodoeiro Bt e não-Bt é fundamental para a otimização de técnicas de amostragens, além de revelar diferenças de comportamento de espécies não-alvo dessa tecnologia Bt entre as duas cultivares. Nesse sentido, o experimento buscou investigar o padrão da distribuição espacial dessas espécies de insetos no algodoeiro convencional não-Bt e no cultivar Bt. As avaliações ocorreram em dois campos de 5.000 m² cada, nos quais se realizou 14 avaliações com contagem de adultos da mosca-branca e colônias de pulgões. Foram calculados os índices de agregação (razão variância/média, índice de Morisita e Expoente k da Distribuição Binomial Negativa e realizados os testes ajustes das classes numéricas de indivíduos encontradas e esperadas às distribuições teóricas de freqüência (Poisson, Binomial Negativa e Binomial Positiva. Todas as análises mostraram que, em ambas as cultivares, a distribuição espacial de B. tabaci ajustou-se a distribuição binomial negativa durante todo o período analisado, indicando que a cultivar transgênica não influenciou o padrão de distribuição agregada desse inseto. Já com relação às análises para A. gossypii, os índices de agregação apontaram distribuição agregada nas duas cultivares, mas as distribuições de freqüência permitiram concluir a ocorrência de distribuição agregada apenas no algodoeiro convencional, pois não houve nenhum ajuste para os dados na cultivar Bt. Isso indica que o algodão Bt alterou o padrão normal de dispersão dos pulgões no cultivo.The study of spatial distribution of the adults of Bemisia tabaci and the colonies of Aphis gossypii on Bt and non-Bt cotton crop is fundamental for

Spatial distribution of parasitism on Phyllocnistis citrella Stainton, 1856 (Lepidoptera: Gracillariidae) in citrus orchards.

Science.gov (United States)

Jahnke, S M; Redaelli, L R; Diefenbach, L M G; Efrom, C F

2008-11-01

Many species of microhymenopterous parasitoids have been registered on Phyllocnistis citrella, the citrus leafminer. The present study aimed to identify the spatial distribution pattern of the native and introduced parasitoids of P. citrella in two citrus orchards in Montenegro, RS. The new shoots from 24 randomly selected trees in each orchard were inspected at the bottom (0-1.5 m) and top (1.5-2.5 m) stratum and had their position relative to the quadrants (North, South, East and West) registered at every 15 days from July/2002 to June/2003. The leaves with pupae were collected and kept isolated until the emergence of parasitoids or of the leaf miner; so, the sampling was biased towards parasitoids that emerge in the host pupal phase. The horizontal spatial distribution was evaluated testing the fitness of data to the Poisson and negative binomial distributions. In Montenegrina, there was no significant difference in the number of parasitoids and in the mean number of pupae found in the top and bottom strata (chi2 = 0.66; df = 1; P > 0.05) (chi2 = 0.27; df =1; P > 0.05), respectively. In relation to the quadrants, the highest average numbers of the leafminer pupae and of parasitoids were registered at the East quadrant (chi2 = 11.81; df = 3; P miners was registered at the North quadrant (chi2 = 19. 29; df = 3; P miners and parasitoids in the East and West quadrants would be influenced by the higher solar exposure of these quadrants. The data of the horizontal spatial distribution of the parasitism fit to the negative binomial distribution in all sampling occasions, indicating an aggregated pattern.

Spatial distribution of Diaphorina citri Kuwayama (Hemiptera: Psyllidae in citrus orchards Distribuição espacial de Diaphorina citri Kuwayama (Hemiptera: Psyllidae em pomares de citros

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Marilia Gregolin Costa

2010-10-01

Full Text Available The psyllid Diaphorina citri Kuwayama is one of the most important pests of citrus, mainly because it is the vector of the bacterium that causes huanglongbing (HLB or 'Greening' disease. To study the spatial distribution of nymphs and adults of this pest, an experiment was carried out in two 'Valencia' sweet orange orchards, four and 12 years of age, established in Matão, central area of São Paulo state, Brazil. The following dispersion indices were used to study pest aggregation in the citrus plants: variance/mean relationship (I, index of Morisita (Iδ, coefficient of Green (Cx, the exponent of negative binomial distribution, common k (c and Taylor's Power Law for each sampling. The negative binomial distribution was more representative of the spatial distribution of this psyllid, for both nymphs and adults. For most samplings, psyllid nymphs found in branches and adults caught in traps had an aggregated distribution.O psilídeo Diaphorina citri Kuwayama tornou-se nos últimos anos uma das mais importantes pragas na cultura de citros, principalmente pelos prejuízos causados às plantas por ser o transmissor da bactéria causadora da doença Huanglongbing (HLB ou 'Greening'. Com a finalidade de estudar a distribuição espacial de ninfas e adultos desta praga, instalaram-se experimentos em duas áreas de citros com histórico de ocorrência de HLB, no município de Matão (região central do Estado de São Paulo, em plantas de laranja 'Valência', com quatro e 12 anos de idade. Para estudo da agregação da população nas plantas, foram utilizados os seguintes índices de dispersão: razão variância/média (I, índice de Morisita (Iδ, coeficiente de Green (Cx e expoente da distribuição binomial negativa, k comum (c e lei da potência de Taylor para cada amostragem. A distribuição binomial negativa foi o modelo mais adequado para representar a distribuição espacial do psilídeo, tanto para ninfas como para adultos. Na maioria das

Quantifying the impact of inter-site heterogeneity on the distribution of ChIP-seq data

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Jonathan eCairns

2014-11-01

Full Text Available Chromatin Immunoprecipitation followed by sequencing (ChIP-seq is a valuable tool for epigenetic studies. Analysis of the data arising from ChIP-seq experiments often requires implicit or explicit statistical modelling of the read counts. The simple Poisson model is attractive, but does not provide a good fit to observed ChIP-seq data. Researchers therefore often either extend to a more general model (e.g. the Negative Binomial, and/or exclude regions of the genome that do not conform to the model. Since many modelling strategies employed for ChIP-seq data reduce to fitting a mixture of Poisson distributions, we explore the problem of inferring the optimal mixing distribution. We apply the Constrained Newton Method (CNM, which suggests the Negative Binomial - Negative Binomial (NB-NB mixture model as a candidate for modelling ChIP-seq data. We illustrate fitting the NB-NB model with an accelerated EM algorithm on four data sets from three species. Zero-inflated models have been suggested as an approach to improve model fit for ChIP-seq data. We show that the NB-NB mixture model requires no zero-inflation and suggest that in some cases the need for zero inflation is driven by the model's inability to cope with both artefactual large read counts and the frequently observed very low read counts.We see that the CNM-based approach is a useful diagnostic for the assessment of model fit and inference in ChIP-seq data and beyond. Use of the suggested NB-NB mixture model will be of value not only when calling peaks or otherwise modelling ChIP-seq data, but also when simulating data or constructing blacklists de novo.

The distribution of the pathogenic nematode Nematodirus battus in lambs is zero-inflated

DEFF Research Database (Denmark)

Denwood, Matthew; Stear, M J; Matthews, L

2008-01-01

Understanding the frequency distribution of parasites and parasite stages among hosts is essential for efficient experimental design and statistical analysis, and is also required for the development of sustainable methods of controlling infection. Nematodirus battus is one of the most important...... organisms that infect sheep but the distribution of parasites among hosts is unknown. An initial analysis indicated a high frequency of animals without N. battus and with zero egg counts, suggesting the possibility of a zero-inflated distribution. We developed a Bayesian analysis using Markov chain Monte...... Carlo methods to estimate the parameters of the zero-inflated negative binomial distribution. The analysis of 3000 simulated data sets indicated that this method out-performed the maximum likelihood procedure. Application of this technique to faecal egg counts from lambs in a commercial upland flock...

Asimetría y curtosis en el modelo binomial para valorar opciones reales: caso de aplicación para empresas de base tecnológica

Directory of Open Access Journals (Sweden)

Gastón Silverio Milanesi

2013-01-01

Full Text Available El trabajo propone un modelo de valoración de opciones reales con base en el modelo binomial utilizando la transformación de Edgeworth (Rubinstein, 1998 para incorporar momentos estocásticos de orden superior, especialmente para ciertos tipos de organizaciones, como empresas de base tecnológica, donde no se dispone de cartera de activos financieros gemelos, comparables de mercado y procesos estocásticos no gaussianos. Primero, se presenta el desarrollo formal del modelo, luego su aplicación sobre la valuación de spin-off tecnológico universitario, sensibilizando asimetría-curtosis y exponiendo el impacto en el valor del proyecto. Finalmente, se concluye sobre limitaciones y ventajas de la propuesta de valoración que resume la simplicidad del modelo binomial e incorporando momentos de orden superior en subyacentes con procesos no normales.

Asimetría y curtosis en el modelo binomial para valorar opciones reales: caso de aplicación para empresas de base tecnológica

Directory of Open Access Journals (Sweden)

Gastón Silverio Milanesi

2013-07-01

Full Text Available El trabajo propone un modelo de valoración de opciones reales con base en el modelo binomial utilizando la transformación de Edgeworth (Rubinstein, 1998 para incorporar momentos estocásticos de orden supe- rior, especialmente para ciertos tipos de organizaciones, como empresas de base tecnológica, donde no se dispone de cartera de activos financieros gemelos, comparables de mercado y procesos estocásticos no gaussianos. Primero, se presenta el desarrollo formal del modelo, luego su aplicación sobre la valuación de spin-off tecnológico universitario, sensibilizando asimetría-curtosis y exponiendo el impacto en el valor del proyecto. Finalmente, se concluye sobre limitaciones y ventajas de la propuesta de valoración que resume la simplicidad del modelo binomial e incorporando momentos de orden superior en subyacentes con pro- cesos no normales.

A binomial modeling approach for upscaling colloid transport under unfavorable conditions: Emergent prediction of extended tailing

Science.gov (United States)

Hilpert, Markus; Rasmuson, Anna; Johnson, William P.

2017-07-01

Colloid transport in saturated porous media is significantly influenced by colloidal interactions with grain surfaces. Near-surface fluid domain colloids experience relatively low fluid drag and relatively strong colloidal forces that slow their downgradient translation relative to colloids in bulk fluid. Near-surface fluid domain colloids may reenter into the bulk fluid via diffusion (nanoparticles) or expulsion at rear flow stagnation zones, they may immobilize (attach) via primary minimum interactions, or they may move along a grain-to-grain contact to the near-surface fluid domain of an adjacent grain. We introduce a simple model that accounts for all possible permutations of mass transfer within a dual pore and grain network. The primary phenomena thereby represented in the model are mass transfer of colloids between the bulk and near-surface fluid domains and immobilization. Colloid movement is described by a Markov chain, i.e., a sequence of trials in a 1-D network of unit cells, which contain a pore and a grain. Using combinatorial analysis, which utilizes the binomial coefficient, we derive the residence time distribution, i.e., an inventory of the discrete colloid travel times through the network and of their probabilities to occur. To parameterize the network model, we performed mechanistic pore-scale simulations in a single unit cell that determined the likelihoods and timescales associated with the above colloid mass transfer processes. We found that intergrain transport of colloids in the near-surface fluid domain can cause extended tailing, which has traditionally been attributed to hydrodynamic dispersion emanating from flow tortuosity of solute trajectories.

Application of a random effects negative binomial model to examine tram-involved crash frequency on route sections in Melbourne, Australia.

Science.gov (United States)

Naznin, Farhana; Currie, Graham; Logan, David; Sarvi, Majid

2016-07-01

Safety is a key concern in the design, operation and development of light rail systems including trams or streetcars as they impose crash risks on road users in terms of crash frequency and severity. The aim of this study is to identify key traffic, transit and route factors that influence tram-involved crash frequencies along tram route sections in Melbourne. A random effects negative binomial (RENB) regression model was developed to analyze crash frequency data obtained from Yarra Trams, the tram operator in Melbourne. The RENB modelling approach can account for spatial and temporal variations within observation groups in panel count data structures by assuming that group specific effects are randomly distributed across locations. The results identify many significant factors effecting tram-involved crash frequency including tram service frequency (2.71), tram stop spacing (-0.42), tram route section length (0.31), tram signal priority (-0.25), general traffic volume (0.18), tram lane priority (-0.15) and ratio of platform tram stops (-0.09). Findings provide useful insights on route section level tram-involved crashes in an urban tram or streetcar operating environment. The method described represents a useful planning tool for transit agencies hoping to improve safety performance. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

Multiplicity distributions of charged hadrons in vp and charged current interactions

Science.gov (United States)

Jones, G. T.; Jones, R. W. L.; Kennedy, B. W.; Morrison, D. R. O.; Mobayyen, M. M.; Wainstein, S.; Aderholz, M.; Hantke, D.; Katz, U. F.; Kern, J.; Schmitz, N.; Wittek, W.; Borner, H. P.; Myatt, G.; Radojicic, D.; Burke, S.

1992-03-01

Using data on vp andbar vp charged current interactions from a bubble chamber experiment with BEBC at CERN, the multiplicity distributions of charged hadrons are investigated. The analysis is based on ˜20000 events with incident v and ˜10000 events with incidentbar v. The invariant mass W of the total hadronic system ranges from 3 GeV to ˜14 GeV. The experimental multiplicity distributions are fitted by the binomial function (for different intervals of W and in different intervals of the rapidity y), by the Levy function and the lognormal function. All three parametrizations give acceptable values for X 2. For fixed W, forward and backward multiplicities are found to be uncorrelated. The normalized moments of the charged multiplicity distributions are measured as a function of W. They show a violation of KNO scaling.

Assessing the Option to Abandon an Investment Project by the Binomial Options Pricing Model

Directory of Open Access Journals (Sweden)

Salvador Cruz Rambaud

2016-01-01

Full Text Available Usually, traditional methods for investment project appraisal such as the net present value (hereinafter NPV do not incorporate in their values the operational flexibility offered by including a real option included in the project. In this paper, real options, and more specifically the option to abandon, are analysed as a complement to cash flow sequence which quantifies the project. In this way, by considering the existing analogy with financial options, a mathematical expression is derived by using the binomial options pricing model. This methodology provides the value of the option to abandon the project within one, two, and in general n periods. Therefore, this paper aims to be a useful tool in determining the value of the option to abandon according to its residual value, thus making easier the control of the uncertainty element within the project.

Efectos de la simulación computacional en la comprensión de la distribución binomial y la distribución de proporciones

OpenAIRE

Martínez, Johanna; Yáñez, Gabriel

2014-01-01

En este trabajo se presenta un proyecto de investigación que se basa en el enfoque instrumental para describir el efecto que tiene la simulación computacional en la comprensión de la distribución binomial y la distribución de proporciones.

Application of Binomial Model and Market Asset Declaimer Methodology for Valuation of Abandon and Expand Options. The Case Study

Directory of Open Access Journals (Sweden)

Paweł Mielcarz

2007-06-01

Full Text Available The article presents a case study of valuation of real options included in a investment project. The main goal of the article is to present the calculation and methodological issues of application the methodology for real option valuation. In order to do it there are used the binomial model and Market Asset Declaimer methodology. The project presented in the article concerns the introduction of radio station to a new market. It includes two valuable real options: to abandon the project and to expand.

Influence of kinematic cuts on the net charge distribution

Energy Technology Data Exchange (ETDEWEB)

Petersen, Hannah [Frankfurt Institute for Advanced Studies, Ruth-Moufang-Str. 1, 60438 Frankfurt am Main (Germany); Institut für Theoretische Physik, Goethe Universität, Max-von-Laue-Str. 1, 60438 Frankfurt am Main (Germany); GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstr. 1, 64291 Darmstadt (Germany); Oliinychenko, Dmytro [Frankfurt Institute for Advanced Studies, Ruth-Moufang-Str. 1, 60438 Frankfurt am Main (Germany); Bogolyubov Institute for Theoretical Physics, Kiev 03680 (Ukraine); Steinheimer, Jan [Frankfurt Institute for Advanced Studies, Ruth-Moufang-Str. 1, 60438 Frankfurt am Main (Germany); Bleicher, Marcus [Frankfurt Institute for Advanced Studies, Ruth-Moufang-Str. 1, 60438 Frankfurt am Main (Germany); Institut für Theoretische Physik, Goethe Universität, Max-von-Laue-Str. 1, 60438 Frankfurt am Main (Germany)

2016-12-15

The higher moments of the net charge distributions, e.g. the skewness and kurtosis, are studied within an infinite hadronic matter calculation in a transport approach. By dividing the box into several parts, the volume dependence of the fluctuations is investigated. After confirming that the initial distributions follow the expectations from a binomial distribution, the influence of quantum number conservation in this case the net charge in the system on the higher moments is evaluated. For this purpose, the composition of the hadron gas is adjusted and only pions and ρ mesons are simulated to investigate the charge conservation effect. In addition, the effect of imposing kinematic cuts in momentum space is analysed. The role of resonance excitations and decays on the higher moments can also be studied within this model. This work is highly relevant to understand the experimental measurements of higher moments obtained in the RHIC beam energy scan and their comparison to lattice results and other theoretical calculations assuming infinite matter.

Analytical evaluation of the plasma dispersion function for a Fermi Dirac distribution

International Nuclear Information System (INIS)

Mamedov, B.A.

2012-01-01

An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi—Dirac distribution is proposed. The new method has been developed using the binomial expansion theorem and the Gamma functions. The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function. The resulting series present better convergence rates. Several acceleration techniques are combined to further improve the efficiency. The obtained results for the plasma dispersion function are in good agreement with the known numerical data. (physics of gases, plasmas, and electric discharges)

Forecasting asthma-related hospital admissions in London using negative binomial models.

Science.gov (United States)

Soyiri, Ireneous N; Reidpath, Daniel D; Sarran, Christophe

2013-05-01

Health forecasting can improve health service provision and individual patient outcomes. Environmental factors are known to impact chronic respiratory conditions such as asthma, but little is known about the extent to which these factors can be used for forecasting. Using weather, air quality and hospital asthma admissions, in London (2005-2006), two related negative binomial models were developed and compared with a naive seasonal model. In the first approach, predictive forecasting models were fitted with 7-day averages of each potential predictor, and then a subsequent multivariable model is constructed. In the second strategy, an exhaustive search of the best fitting models between possible combinations of lags (0-14 days) of all the environmental effects on asthma admission was conducted. Three models were considered: a base model (seasonal effects), contrasted with a 7-day average model and a selected lags model (weather and air quality effects). Season is the best predictor of asthma admissions. The 7-day average and seasonal models were trivial to implement. The selected lags model was computationally intensive, but of no real value over much more easily implemented models. Seasonal factors can predict daily hospital asthma admissions in London, and there is a little evidence that additional weather and air quality information would add to forecast accuracy.

The Compound DGL/Erlang Distribution in the Collective Risk Model || La distribución compuesta DGL/Erlang en el modelo de riesgo colectivo

Directory of Open Access Journals (Sweden)

Gómez Déniz, Emilio

2013-01-01

Full Text Available In this paper the analysis of the collective risk model assuming Erlang loss, when the claim frequency follows the discrete generalized Lindley distribution, is considered. After providing some new results of this discrete model, analytical expressions for the aggregate claim size distribution in general insurance in the case that the discrete generalized Lindley distribution is assumed as the primary distribution while claim size, the secondary distribution, is modeled using an Erlang(r distribution (r = 1; 2. Comparisons with the compound Poisson and compound negative binomial are developed to explain the viability of the new compound model in two examples in automobile insurance. || En este artículo se analiza el modelo de riesgo colectivo asumiendo que la cantidad individual reclamada sigue una función de densidad Erlang y el número de reclamaciones es una variable aleatoria cuya función masa de probabilidad es la generalizada discreta Lindley. En la primera parte de este trabajo se presentan nuevas propiedades de esta distribución discreta; seguidamente, se calculan expresiones analíticas para la cantidad total reclamada en seguros generales cuando la distribución primaria es la generalizada discreta Lindley, asumiendo la densidad Erlang(r (r = 1; 2 como distribución secundaria. En la ilustración numérica, el nuevo modelo expuesto en este artículo se compara con los modelos compuestos Poisson y Binomial Negativa en dos ejemplos, en el contexto de seguros de automóviles, para mostrar su efectividad.

Elementary Bayesian biostatistics

CERN Document Server

Moyé, Lemuel A

2007-01-01

PREFACEINTRODUCTIONPROLOGUE: OPENING SALVOSBASIC PROBABILITY AND BAYES THEOREMProbability's RoleObjective and Subjective Probability Relative Frequency and Collections of EventsCounting and CombinatoricsSimple Rules in ProbabilityLaw of Total Probability and Bayes TheroemCOMPOUNDING AND THE LAW OF TOTAL PROBABILITYIntroduction The Law of Total Probability: CompoundingProportions and the Binomial DistributionNegative Binomial DistributionThe Poisson ProcessThe Uniform Distribution Exponential Distribution Proble

La distribución binominal-exponencial truncada con aplicaciones en el sector del seguro de automóviles

OpenAIRE

Gómez Déniz, Emilio; Sarabia Alegría, José María

2008-01-01

ABSTRACT. In this paper we present a new claim count distribution with overdispersion. The new distribution is obtained by mixing the p parameter in the binomial distribution with a (0,1) truncated exponential distribution. The new distribution can be considered as an alternative to the classical Poisson, binomial and geometric distributions. Some properties of the new distribution and some applications in the field of automobile insurance are given, by fitting empirical cla...

Modelling the spatio-temporal distribution of age-1 bay of biscay anchovy (Engraulis encrasicolus) at spawning time [Distribución espacio-temporal de la edad 1 de anchoa del golfo de Bizkaia (Engraulis Encrasicolus) en el momento de puesta

KAUST Repository

Ibaibarriaga, Leire; Uriarte, André s; Laconcha, Urtzi; Bernal, Miguel C.; Begoñ a Santos, Maria; Chifflet, Marina; Irigoien, Xabier

2013-01-01

during the main spawning period based on adult samples from 15 daily egg production method surveys. The proportion of age-1 individuals was modelled using generalized additive models with a binomial distribution and a logit link in relation

Design of Ultra-Wideband Tapered Slot Antenna by Using Binomial Transformer with Corrugation

Science.gov (United States)

Chareonsiri, Yosita; Thaiwirot, Wanwisa; Akkaraekthalin, Prayoot

2017-05-01

In this paper, the tapered slot antenna (TSA) with corrugation is proposed for UWB applications. The multi-section binomial transformer is used to design taper profile of the proposed TSA that does not involve using time consuming optimization. A step-by-step procedure for synthesis of the step impedance values related with step slot widths of taper profile is presented. The smooth taper can be achieved by fitting the smoothing curve to the entire step slot. The design of TSA based on this method yields results with a quite flat gain and wide impedance bandwidth covering UWB spectrum from 3.1 GHz to 10.6 GHz. To further improve the radiation characteristics, the corrugation is added on the both edges of the proposed TSA. The effects of different corrugation shapes on the improvement of antenna gain and front-to-back ratio (F-to-B ratio) are investigated. To demonstrate the validity of the design, the prototypes of TSA without and with corrugation are fabricated and measured. The results show good agreement between simulation and measurement.

The multi-class binomial failure rate model for the treatment of common-cause failures

International Nuclear Information System (INIS)

Hauptmanns, U.

1995-01-01

The impact of common cause failures (CCF) on PSA results for NPPs is in sharp contrast with the limited quality which can be achieved in their assessment. This is due to the dearth of observations and cannot be remedied in the short run. Therefore the methods employed for calculating failure rates should be devised such as to make the best use of the few available observations on CCF. The Multi-Class Binomial Failure Rate (MCBFR) Model achieves this by assigning observed failures to different classes according to their technical characteristics and applying the BFR formalism to each of these. The results are hence determined by a superposition of BFR type expressions for each class, each of them with its own coupling factor. The model thus obtained flexibly reproduces the dependence of CCF rates on failure multiplicity insinuated by the observed failure multiplicities. This is demonstrated by evaluating CCFs observed for combined impulse pilot valves in German NPPs. (orig.) [de

A semiparametric negative binomial generalized linear model for modeling over-dispersed count data with a heavy tail: Characteristics and applications to crash data.

Science.gov (United States)

Shirazi, Mohammadali; Lord, Dominique; Dhavala, Soma Sekhar; Geedipally, Srinivas Reddy

2016-06-01

Crash data can often be characterized by over-dispersion, heavy (long) tail and many observations with the value zero. Over the last few years, a small number of researchers have started developing and applying novel and innovative multi-parameter models to analyze such data. These multi-parameter models have been proposed for overcoming the limitations of the traditional negative binomial (NB) model, which cannot handle this kind of data efficiently. The research documented in this paper continues the work related to multi-parameter models. The objective of this paper is to document the development and application of a flexible NB generalized linear model with randomly distributed mixed effects characterized by the Dirichlet process (NB-DP) to model crash data. The objective of the study was accomplished using two datasets. The new model was compared to the NB and the recently introduced model based on the mixture of the NB and Lindley (NB-L) distributions. Overall, the research study shows that the NB-DP model offers a better performance than the NB model once data are over-dispersed and have a heavy tail. The NB-DP performed better than the NB-L when the dataset has a heavy tail, but a smaller percentage of zeros. However, both models performed similarly when the dataset contained a large amount of zeros. In addition to a greater flexibility, the NB-DP provides a clustering by-product that allows the safety analyst to better understand the characteristics of the data, such as the identification of outliers and sources of dispersion. Copyright © 2016 Elsevier Ltd. All rights reserved.

A Binomial Modeling Approach for Upscaling Colloid Transport Under Unfavorable Attachment Conditions: Emergent Prediction of Nonmonotonic Retention Profiles

Science.gov (United States)

Hilpert, Markus; Johnson, William P.

2018-01-01

We used a recently developed simple mathematical network model to upscale pore-scale colloid transport information determined under unfavorable attachment conditions. Classical log-linear and nonmonotonic retention profiles, both well-reported under favorable and unfavorable attachment conditions, respectively, emerged from our upscaling. The primary attribute of the network is colloid transfer between bulk pore fluid, the near-surface fluid domain (NSFD), and attachment (treated as irreversible). The network model accounts for colloid transfer to the NSFD of downgradient grains and for reentrainment to bulk pore fluid via diffusion or via expulsion at rear flow stagnation zones (RFSZs). The model describes colloid transport by a sequence of random trials in a one-dimensional (1-D) network of Happel cells, which contain a grain and a pore. Using combinatorial analysis that capitalizes on the binomial coefficient, we derived from the pore-scale information the theoretical residence time distribution of colloids in the network. The transition from log-linear to nonmonotonic retention profiles occurs when the conditions underlying classical filtration theory are not fulfilled, i.e., when an NSFD colloid population is maintained. Then, nonmonotonic retention profiles result potentially both for attached and NSFD colloids. The concentration maxima shift downgradient depending on specific parameter choice. The concentration maxima were also shown to shift downgradient temporally (with continued elution) under conditions where attachment is negligible, explaining experimentally observed downgradient transport of retained concentration maxima of adhesion-deficient bacteria. For the case of zero reentrainment, we develop closed-form, analytical expressions for the shape, and the maximum of the colloid retention profile.

Phase transition and information cascade in a voting model

Energy Technology Data Exchange (ETDEWEB)

Hisakado, M [Standard and Poor' s, Marunouchi 1-6-5, Chiyoda ku, Tokyo 100-0005 (Japan); Mori, S, E-mail: masato_hisakado@standardandpoors.co, E-mail: mori@sci.kitasato-u.ac.j [Department of Physics, School of Science, Kitasato University, Kitasato 1-15-1, Sagamihara, Kanagawa 228-8555 (Japan)

2010-08-06

In this paper, we introduce a voting model that is similar to a Keynesian beauty contest and analyse it from a mathematical point of view. There are two types of voters-copycat and independent-and two candidates. Our voting model is a binomial distribution (independent voters) doped in a beta binomial distribution (copycat voters). We find that the phase transition in this system is at the upper limit of t, where t is the time (or the number of the votes). Our model contains three phases. If copycats constitute a majority or even half of the total voters, the voting rate converges more slowly than it would in a binomial distribution. If independents constitute the majority of voters, the voting rate converges at the same rate as it would in a binomial distribution. We also study why it is difficult to estimate the conclusion of a Keynesian beauty contest when there is an information cascade.

Phase transition and information cascade in a voting model

International Nuclear Information System (INIS)

Hisakado, M; Mori, S

2010-01-01

In this paper, we introduce a voting model that is similar to a Keynesian beauty contest and analyse it from a mathematical point of view. There are two types of voters-copycat and independent-and two candidates. Our voting model is a binomial distribution (independent voters) doped in a beta binomial distribution (copycat voters). We find that the phase transition in this system is at the upper limit of t, where t is the time (or the number of the votes). Our model contains three phases. If copycats constitute a majority or even half of the total voters, the voting rate converges more slowly than it would in a binomial distribution. If independents constitute the majority of voters, the voting rate converges at the same rate as it would in a binomial distribution. We also study why it is difficult to estimate the conclusion of a Keynesian beauty contest when there is an information cascade.

Phase transition and information cascade in a voting model

Science.gov (United States)

Hisakado, M.; Mori, S.

2010-08-01

In this paper, we introduce a voting model that is similar to a Keynesian beauty contest and analyse it from a mathematical point of view. There are two types of voters—copycat and independent—and two candidates. Our voting model is a binomial distribution (independent voters) doped in a beta binomial distribution (copycat voters). We find that the phase transition in this system is at the upper limit of t, where t is the time (or the number of the votes). Our model contains three phases. If copycats constitute a majority or even half of the total voters, the voting rate converges more slowly than it would in a binomial distribution. If independents constitute the majority of voters, the voting rate converges at the same rate as it would in a binomial distribution. We also study why it is difficult to estimate the conclusion of a Keynesian beauty contest when there is an information cascade.

Modelling binary data

CERN Document Server

Collett, David

2002-01-01

INTRODUCTION Some Examples The Scope of this Book Use of Statistical Software STATISTICAL INFERENCE FOR BINARY DATA The Binomial Distribution Inference about the Success Probability Comparison of Two Proportions Comparison of Two or More Proportions MODELS FOR BINARY AND BINOMIAL DATA Statistical Modelling Linear Models Methods of Estimation Fitting Linear Models to Binomial Data Models for Binomial Response Data The Linear Logistic Model Fitting the Linear Logistic Model to Binomial Data Goodness of Fit of a Linear Logistic Model Comparing Linear Logistic Models Linear Trend in Proportions Comparing Stimulus-Response Relationships Non-Convergence and Overfitting Some other Goodness of Fit Statistics Strategy for Model Selection Predicting a Binary Response Probability BIOASSAY AND SOME OTHER APPLICATIONS The Tolerance Distribution Estimating an Effective Dose Relative Potency Natural Response Non-Linear Logistic Regression Models Applications of the Complementary Log-Log Model MODEL CHECKING Definition of Re...

Regular exercise and related factors in patients with Parkinson's disease: Applying zero-inflated negative binomial modeling of exercise count data.

Science.gov (United States)

Lee, JuHee; Park, Chang Gi; Choi, Moonki

2016-05-01

This study was conducted to identify risk factors that influence regular exercise among patients with Parkinson's disease in Korea. Parkinson's disease is prevalent in the elderly, and may lead to a sedentary lifestyle. Exercise can enhance physical and psychological health. However, patients with Parkinson's disease are less likely to exercise than are other populations due to physical disability. A secondary data analysis and cross-sectional descriptive study were conducted. A convenience sample of 106 patients with Parkinson's disease was recruited at an outpatient neurology clinic of a tertiary hospital in Korea. Demographic characteristics, disease-related characteristics (including disease duration and motor symptoms), self-efficacy for exercise, balance, and exercise level were investigated. Negative binomial regression and zero-inflated negative binomial regression for exercise count data were utilized to determine factors involved in exercise. The mean age of participants was 65.85 ± 8.77 years, and the mean duration of Parkinson's disease was 7.23 ± 6.02 years. Most participants indicated that they engaged in regular exercise (80.19%). Approximately half of participants exercised at least 5 days per week for 30 min, as recommended (51.9%). Motor symptoms were a significant predictor of exercise in the count model, and self-efficacy for exercise was a significant predictor of exercise in the zero model. Severity of motor symptoms was related to frequency of exercise. Self-efficacy contributed to the probability of exercise. Symptom management and improvement of self-efficacy for exercise are important to encourage regular exercise in patients with Parkinson's disease. Copyright © 2015 Elsevier Inc. All rights reserved.

Modelling road accident blackspots data with the discrete generalized Pareto distribution.

Science.gov (United States)

Prieto, Faustino; Gómez-Déniz, Emilio; Sarabia, José María

2014-10-01

This study shows how road traffic networks events, in particular road accidents on blackspots, can be modelled with simple probabilistic distributions. We considered the number of crashes and the number of fatalities on Spanish blackspots in the period 2003-2007, from Spanish General Directorate of Traffic (DGT). We modelled those datasets, respectively, with the discrete generalized Pareto distribution (a discrete parametric model with three parameters) and with the discrete Lomax distribution (a discrete parametric model with two parameters, and particular case of the previous model). For that, we analyzed the basic properties of both parametric models: cumulative distribution, survival, probability mass, quantile and hazard functions, genesis and rth-order moments; applied two estimation methods of their parameters: the μ and (μ+1) frequency method and the maximum likelihood method; used two goodness-of-fit tests: Chi-square test and discrete Kolmogorov-Smirnov test based on bootstrap resampling; and compared them with the classical negative binomial distribution in terms of absolute probabilities and in models including covariates. We found that those probabilistic models can be useful to describe the road accident blackspots datasets analyzed. Copyright © 2014 Elsevier Ltd. All rights reserved.

A chi-square goodness-of-fit test for non-identically distributed random variables: with application to empirical Bayes

International Nuclear Information System (INIS)

Conover, W.J.; Cox, D.D.; Martz, H.F.

1997-12-01

When using parametric empirical Bayes estimation methods for estimating the binomial or Poisson parameter, the validity of the assumed beta or gamma conjugate prior distribution is an important diagnostic consideration. Chi-square goodness-of-fit tests of the beta or gamma prior hypothesis are developed for use when the binomial sample sizes or Poisson exposure times vary. Nine examples illustrate the application of the methods, using real data from such diverse applications as the loss of feedwater flow rates in nuclear power plants, the probability of failure to run on demand and the failure rates of the high pressure coolant injection systems at US commercial boiling water reactors, the probability of failure to run on demand of emergency diesel generators in US commercial nuclear power plants, the rate of failure of aircraft air conditioners, baseball batting averages, the probability of testing positive for toxoplasmosis, and the probability of tumors in rats. The tests are easily applied in practice by means of corresponding Mathematica reg-sign computer programs which are provided

Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians

OpenAIRE

Ndayiragije, François; Van Assche, Walter

2013-01-01

Multiple Meixner polynomials are polynomials in one variable which satisfy orthogonality relations with respect to $r>1$ different negative binomial distributions (Pascal distributions). There are two kinds of multiple Meixner polynomials, depending on the selection of the parameters in the negative binomial distribution. We recall their definition and some formulas and give generating functions and explicit expressions for the coefficients in the nearest neighbor recurrence relation. Followi...

Modeling the distribution of colonial species to improve estimation of plankton concentration in ballast water

Science.gov (United States)

Rajakaruna, Harshana; VandenByllaardt, Julie; Kydd, Jocelyn; Bailey, Sarah

2018-03-01

The International Maritime Organization (IMO) has set limits on allowable plankton concentrations in ballast water discharge to minimize aquatic invasions globally. Previous guidance on ballast water sampling and compliance decision thresholds was based on the assumption that probability distributions of plankton are Poisson when spatially homogenous, or negative binomial when heterogeneous. We propose a hierarchical probability model, which incorporates distributions at the level of particles (i.e., discrete individuals plus colonies per unit volume) and also within particles (i.e., individuals per particle) to estimate the average plankton concentration in ballast water. We examined the performance of the models using data for plankton in the size class ≥ 10 μm and test ballast water compliance using the above models.

Sample size for comparing negative binomial rates in noninferiority and equivalence trials with unequal follow-up times.

Science.gov (United States)

Tang, Yongqiang

2017-05-25

We derive the sample size formulae for comparing two negative binomial rates based on both the relative and absolute rate difference metrics in noninferiority and equivalence trials with unequal follow-up times, and establish an approximate relationship between the sample sizes required for the treatment comparison based on the two treatment effect metrics. The proposed method allows the dispersion parameter to vary by treatment groups. The accuracy of these methods is assessed by simulations. It is demonstrated that ignoring the between-subject variation in the follow-up time by setting the follow-up time for all individuals to be the mean follow-up time may greatly underestimate the required size, resulting in underpowered studies. Methods are provided for back-calculating the dispersion parameter based on the published summary results.

Non-uniform approximations for sums of discrete m-dependent random variables

OpenAIRE

Vellaisamy, P.; Cekanavicius, V.

2013-01-01

Non-uniform estimates are obtained for Poisson, compound Poisson, translated Poisson, negative binomial and binomial approximations to sums of of m-dependent integer-valued random variables. Estimates for Wasserstein metric also follow easily from our results. The results are then exemplified by the approximation of Poisson binomial distribution, 2-runs and $m$-dependent $(k_1,k_2)$-events.

A binomial truncation function proposed for the second-moment approximation of tight-binding potential and application in the ternary Ni-Hf-Ti system

International Nuclear Information System (INIS)

Li, J H; Dai, X D; Wang, T L; Liu, B X

2007-01-01

We propose a two-parameter binomial truncation function for the second-moment approximation of the tight-binding (TB-SMA) interatomic potential and illustrate in detail the procedure of constructing the potentials for binary and ternary transition metal systems. For the ternary Ni-Hf-Ti system, the lattice constants, cohesion energies, elastic constants and bulk moduli of six binary compounds, i.e. L1 2 Ni 3 Hf, NiHf 3 , Ni 3 Ti, NiTi 3 , Hf 3 Ti and HfTi 3 , are firstly acquired by ab initio calculations and then employed to derive the binomial-truncated TB-SMA Ni-Hf-Ti potential. Applying the ab initio derived Ni-Hf-Ti potential, the lattice constants, cohesive energy, elastic constants and bulk moduli of another six binary compounds, i.e. D0 3 NiHf 3 , NiTi 3 HfTi 3 , and B2 NiHf, NiTi, HfTi, and two ternary compounds, i.e. C1 b NiHfTi, L2 1 Ni 2 HfTi, are calculated, respectively. It is found that, for the eight binary compounds studied, the calculated lattice constants and cohesion energies are in excellent agreement with those directly acquired from ab initio calculations and that the elastic constants and bulk moduli calculated from the potential are also qualitatively consistent with the results from ab initio calculations

Comparison of linear and zero-inflated negative binomial regression models for appraisal of risk factors associated with dental caries.

Science.gov (United States)

Batra, Manu; Shah, Aasim Farooq; Rajput, Prashant; Shah, Ishrat Aasim

2016-01-01

Dental caries among children has been described as a pandemic disease with a multifactorial nature. Various sociodemographic factors and oral hygiene practices are commonly tested for their influence on dental caries. In recent years, a recent statistical model that allows for covariate adjustment has been developed and is commonly referred zero-inflated negative binomial (ZINB) models. To compare the fit of the two models, the conventional linear regression (LR) model and ZINB model to assess the risk factors associated with dental caries. A cross-sectional survey was conducted on 1138 12-year-old school children in Moradabad Town, Uttar Pradesh during months of February-August 2014. Selected participants were interviewed using a questionnaire. Dental caries was assessed by recording decayed, missing, or filled teeth (DMFT) index. To assess the risk factor associated with dental caries in children, two approaches have been applied - LR model and ZINB model. The prevalence of caries-free subjects was 24.1%, and mean DMFT was 3.4 ± 1.8. In LR model, all the variables were statistically significant. Whereas in ZINB model, negative binomial part showed place of residence, father's education level, tooth brushing frequency, and dental visit statistically significant implying that the degree of being caries-free (DMFT = 0) increases for group of children who are living in urban, whose father is university pass out, who brushes twice a day and if have ever visited a dentist. The current study report that the LR model is a poorly fitted model and may lead to spurious conclusions whereas ZINB model has shown better goodness of fit (Akaike information criterion values - LR: 3.94; ZINB: 2.39) and can be preferred if high variance and number of an excess of zeroes are present.

Approximate solution for the reactor neutron probability distribution

International Nuclear Information System (INIS)

Ruby, L.; McSwine, T.L.

1985-01-01

Several authors have studied the Kolmogorov equation for a fission-driven chain-reacting system, written in terms of the generating function G(x,y,z,t) where x, y, and z are dummy variables referring to the neutron, delayed neutron precursor, and detector-count populations, n, m, and c, respectively. Pal and Zolotukhin and Mogil'ner have shown that if delayed neutrons are neglected, the solution is approximately negative binomial for the neutron population. Wang and Ruby have shown that if the detector effect is neglected, the solution, including the effect of delayed neutrons, is approximately negative binomial. All of the authors assumed prompt-neutron emission not exceeding two neutrons per fission. An approximate method of separating the detector effect from the statistics of the neutron and precursor populations has been proposed by Ruby. In this weak-coupling limit, it is assumed that G(x,y,z,t) = H(x,y)I(z,t). Substitution of this assumption into the Kolmogorov equation separates the latter into two equations, one for H(x,y) and the other for I(z,t). Solution of the latter then gives a generating function, which indicates that in the weak-coupling limit, the detector counts are Poisson distributed. Ruby also showed that if the detector effect is neglected in the equation for H(x,y), i.e., the detector efficiency is set to zero, then the resulting equation is identical with that considered by Wang and Ruby. The authors present here an approximate solution for H(x,y) that does not set the detector efficiency to zero

Correcting for binomial measurement error in predictors in regression with application to analysis of DNA methylation rates by bisulfite sequencing.

Science.gov (United States)

Buonaccorsi, John; Prochenka, Agnieszka; Thoresen, Magne; Ploski, Rafal

2016-09-30

Motivated by a genetic application, this paper addresses the problem of fitting regression models when the predictor is a proportion measured with error. While the problem of dealing with additive measurement error in fitting regression models has been extensively studied, the problem where the additive error is of a binomial nature has not been addressed. The measurement errors here are heteroscedastic for two reasons; dependence on the underlying true value and changing sampling effort over observations. While some of the previously developed methods for treating additive measurement error with heteroscedasticity can be used in this setting, other methods need modification. A new version of simulation extrapolation is developed, and we also explore a variation on the standard regression calibration method that uses a beta-binomial model based on the fact that the true value is a proportion. Although most of the methods introduced here can be used for fitting non-linear models, this paper will focus primarily on their use in fitting a linear model. While previous work has focused mainly on estimation of the coefficients, we will, with motivation from our example, also examine estimation of the variance around the regression line. In addressing these problems, we also discuss the appropriate manner in which to bootstrap for both inferences and bias assessment. The various methods are compared via simulation, and the results are illustrated using our motivating data, for which the goal is to relate the methylation rate of a blood sample to the age of the individual providing the sample. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Testing the anisotropy in the angular distribution of Fermi/GBM gamma-ray bursts

Science.gov (United States)

Tarnopolski, M.

2017-12-01

Gamma-ray bursts (GRBs) were confirmed to be of extragalactic origin due to their isotropic angular distribution, combined with the fact that they exhibited an intensity distribution that deviated strongly from the -3/2 power law. This finding was later confirmed with the first redshift, equal to at least z = 0.835, measured for GRB970508. Despite this result, the data from CGRO/BATSE and Swift/BAT indicate that long GRBs are indeed distributed isotropically, but the distribution of short GRBs is anisotropic. Fermi/GBM has detected 1669 GRBs up to date, and their sky distribution is examined in this paper. A number of statistical tests are applied: nearest neighbour analysis, fractal dimension, dipole and quadrupole moments of the distribution function decomposed into spherical harmonics, binomial test and the two-point angular correlation function. Monte Carlo benchmark testing of each test is performed in order to evaluate its reliability. It is found that short GRBs are distributed anisotropically in the sky, and long ones have an isotropic distribution. The probability that these results are not a chance occurrence is equal to at least 99.98 per cent and 30.68 per cent for short and long GRBs, respectively. The cosmological context of this finding and its relation to large-scale structures is discussed.

Throughput Performance Evaluation of Multiservice Multirate OCDMA in Flexible Networks

DEFF Research Database (Denmark)

Raddo, Thiago R.; Sanches, Anderson L.; Tafur Monroy, Idelfonso

2016-01-01

in the system. The bit error rate (BER) and packet correct probability expressions are derived, considering the multiple-access interference as binomially distributed. Packet throughput expressions, on the other hand, are derived considering Poisson, binomial, and Markov chain approaches for the composite......, the binomial approach proved to be more straightforward, computationally more efficient, and just as accurate as the Markov chain approach....

Multiplicity distributions of charged hadrons in νp and anti νp charged current interactions

International Nuclear Information System (INIS)

Jones, G.T.; Jones, R.W.L.; Kennedy, B.W.; Morrison, D.R.O.; Mobayyen, M.M.; Wainstein, S.; Borner, H.P.; Myatt, G.; Radojicic, D.; Burke, S.; Aderholz, M.; Hantke, D.; Katz, U.F.; Kern, J.; Schmitz, N.; Wittek, W.

1991-10-01

Using data on νp and anti νp charged current interactions from a bubble chamber experiment with BEBC at CERN, the multiplicity distributions of charged hadrons are investigated. The analysis is based on ∝ 20 000 events with incident ν and ∝ 10 000 events with incident anti ν. The invariant mass W of the total hadronic system ranges from 3 GeV to ∝ 14 GeV. The experimental multiplicity distributions are fitted by the binomial function (for different intervals of W and in different intervals of the rapidity y), by the Levy function and the lognormal function. All three parametrizations give acceptable values for χ 2 /NDF. For fixed W, forward and backward multiplicities are found to be uncorrelated. The normalized moments of the charged multiplicity distributions are measured as a function of W. They show a violation of KNO scaling. (orig.)

Multiplicity distributions of charged hadrons in νp and anti νp charged current interactions

International Nuclear Information System (INIS)

Jones, G.T.; Jones, R.W.L.; Kennedy, B.W.; Morrison, D.R.O.; Mobayyen, M.M.; Wainstein, S.; Aderholz, M.; Hantke, D.; Katz, U.F.; Kern, J.; Schmitz, N.; Wittek, W.; Borner, H.P.; Myatt, G.; Radojicic, D.; Burke, S.

1992-01-01

Using data on νp and anti νp charged current interactions from a bubble chamber experiment with BEBC at CERN, the multiplicity distributions of charged hadrons are investigated. The analysis is based on ∝20 000 events with incident ν and ∝10 000 events with incident anti ν. The invariant mass W of the total hadronic system ranges from 3 GeV to ∝14 GeV. The experimental multiplicity distributions are fitted by the binomial function (for different intervals of W and in different intervals of the rapidity y), by the Levy function and the lognormal function. All three parametrizations give acceptable values for χ 2 /NDF. For fixed W, forward and backward multiplicities are found to be uncorrelated. The normalized moments of the charged multiplicity distributions are measured as a function of W. They show a violation of KNO scaling. (orig.)

Sample Size Estimation for Negative Binomial Regression Comparing Rates of Recurrent Events with Unequal Follow-Up Time.

Science.gov (United States)

Tang, Yongqiang

2015-01-01

A sample size formula is derived for negative binomial regression for the analysis of recurrent events, in which subjects can have unequal follow-up time. We obtain sharp lower and upper bounds on the required size, which is easy to compute. The upper bound is generally only slightly larger than the required size, and hence can be used to approximate the sample size. The lower and upper size bounds can be decomposed into two terms. The first term relies on the mean number of events in each group, and the second term depends on two factors that measure, respectively, the extent of between-subject variability in event rates, and follow-up time. Simulation studies are conducted to assess the performance of the proposed method. An application of our formulae to a multiple sclerosis trial is provided.

Estimating the burden of malaria in Senegal: Bayesian zero-inflated binomial geostatistical modeling of the MIS 2008 data.

Directory of Open Access Journals (Sweden)

Federica Giardina

Full Text Available The Research Center for Human Development in Dakar (CRDH with the technical assistance of ICF Macro and the National Malaria Control Programme (NMCP conducted in 2008/2009 the Senegal Malaria Indicator Survey (SMIS, the first nationally representative household survey collecting parasitological data and malaria-related indicators. In this paper, we present spatially explicit parasitaemia risk estimates and number of infected children below 5 years. Geostatistical Zero-Inflated Binomial models (ZIB were developed to take into account the large number of zero-prevalence survey locations (70% in the data. Bayesian variable selection methods were incorporated within a geostatistical framework in order to choose the best set of environmental and climatic covariates associated with the parasitaemia risk. Model validation confirmed that the ZIB model had a better predictive ability than the standard Binomial analogue. Markov chain Monte Carlo (MCMC methods were used for inference. Several insecticide treated nets (ITN coverage indicators were calculated to assess the effectiveness of interventions. After adjusting for climatic and socio-economic factors, the presence of at least one ITN per every two household members and living in urban areas reduced the odds of parasitaemia by 86% and 81% respectively. Posterior estimates of the ORs related to the wealth index show a decreasing trend with the quintiles. Infection odds appear to be increasing with age. The population-adjusted prevalence ranges from 0.12% in Thillé-Boubacar to 13.1% in Dabo. Tambacounda has the highest population-adjusted predicted prevalence (8.08% whereas the region with the highest estimated number of infected children under the age of 5 years is Kolda (13940. The contemporary map and estimates of malaria burden identify the priority areas for future control interventions and provide baseline information for monitoring and evaluation. Zero-Inflated formulations are more appropriate

Type I error probability spending for post-market drug and vaccine safety surveillance with binomial data.

Science.gov (United States)

Silva, Ivair R

2018-01-15

Type I error probability spending functions are commonly used for designing sequential analysis of binomial data in clinical trials, but it is also quickly emerging for near-continuous sequential analysis of post-market drug and vaccine safety surveillance. It is well known that, for clinical trials, when the null hypothesis is not rejected, it is still important to minimize the sample size. Unlike in post-market drug and vaccine safety surveillance, that is not important. In post-market safety surveillance, specially when the surveillance involves identification of potential signals, the meaningful statistical performance measure to be minimized is the expected sample size when the null hypothesis is rejected. The present paper shows that, instead of the convex Type I error spending shape conventionally used in clinical trials, a concave shape is more indicated for post-market drug and vaccine safety surveillance. This is shown for both, continuous and group sequential analysis. Copyright © 2017 John Wiley & Sons, Ltd.

Distribution patterns of infection with multiple types of human papillomaviruses and their association with risk factors.

Directory of Open Access Journals (Sweden)

Sara Soto-De Leon

Full Text Available BACKGROUND: Infection with multiple types of human papillomavirus (HPV is one of the main risk factors associated with the development of cervical lesions. In this study, cervical samples collected from 1,810 women with diverse sociocultural backgrounds, who attended to their cervical screening program in different geographical regions of Colombia, were examined for the presence of cervical lesions and HPV by Papanicolau testing and DNA PCR detection, respectively. PRINCIPAL FINDINGS: The negative binomial distribution model used in this study showed differences between the observed and expected values within some risk factor categories analyzed. Particularly in the case of single infection and coinfection with more than 4 HPV types, observed frequencies were smaller than expected, while the number of women infected with 2 to 4 viral types were higher than expected. Data analysis according to a negative binomial regression showed an increase in the risk of acquiring more HPV types in women who were of indigenous ethnicity (+37.8%, while this risk decreased in women who had given birth more than 4 times (-31.1%, or were of mestizo (-24.6% or black (-40.9% ethnicity. CONCLUSIONS: According to a theoretical probability distribution, the observed number of women having either a single infection or more than 4 viral types was smaller than expected, while for those infected with 2-4 HPV types it was larger than expected. Taking into account that this study showed a higher HPV coinfection rate in the indigenous ethnicity, the role of underlying factors should be assessed in detail in future studies.

Matter density distribution in atomic nuclei as illuminated by high energy hadrons

International Nuclear Information System (INIS)

Strugalski, Z.

1991-01-01

The method is proposed for the intranuclear matter density distribution study by means of high energy strongly interacting probes. The newly recognized process - the passage of hadrons through atomic nuclei - is employed as the physical basis of the operational principle of the method; the passage is accompanied by the nucleon emission from the target nuclei. It seems that the hadronic projectile sees a definite number of nucleons at a definite impact parameter, in passing through the target nucleus, but the number of the protons among the nucleus seen fluctuates according the binomial formula; in average, this number corresponds to the neutron-proton ratio (A-Z0/Z. 21 refs.; 4 figs.; 1 tab

Deconfinement and nuclear collisions

International Nuclear Information System (INIS)

Sarma, Nataraja

1992-01-01

Expensive experiments to detect a deconfined parton phase have been done and are being planned. In these experiments it is hoped that nuclear collisions at relativistic energies will exhibit signals of this new phase. So far all the results may be interpreted in terms of independent nucleon-nucleon interactions. These elementary collisions at very high energies are therefore worth examination since each such collision produces a highly excited entity which emits a large number of hadrons. In the hadronic phase this results in the GS multiplicity distribution. In the parton phase, parton branching results in the popular negative binomial distribution. Though neither the GS nor the NB distribution alone agrees with the data beyond 200 GeV, it is fitted exceedingly well by a weighted sum of the two distributions. Since the negative binomial distribution arises from the branching of partons, we interpret the increase with energy of the negative binomial component in the weighted sum as the onset of a deconfined phase. The rising cross section for the negative binomial component parallels very closely the inclusive cross section for hadron jets which is also considered a consequence of partons branching. The consequences of this picture to nuclear collisions is discussed. (author). 8 refs., 9 figs., 3 tabs

[Monitoring microbiological safety of small systems of water distribution. Comparison of two sampling programs in a town in central Italy].

Science.gov (United States)

Papini, Paolo; Faustini, Annunziata; Manganello, Rosa; Borzacchi, Giancarlo; Spera, Domenico; Perucci, Carlo A

2005-01-01

To determine the frequency of sampling in small water distribution systems (distribution. We carried out two sampling programs to monitor the water distribution system in a town in Central Italy between July and September 1992; the Poisson distribution assumption implied 4 water samples, the assumption of negative binomial distribution implied 21 samples. Coliform organisms were used as indicators of water safety. The network consisted of two pipe rings and two wells fed by the same water source. The number of summer customers varied considerably from 3,000 to 20,000. The mean density was 2.33 coliforms/100 ml (sd= 5.29) for 21 samples and 3 coliforms/100 ml (sd= 6) for four samples. However the hypothesis of homogeneity was rejected (p-value samples (beta= 0.24) than with 21 (beta= 0.05). For this small network, determining the samples' size according to heterogeneity hypothesis strengthens the statement that water is drinkable compared with homogeneity assumption.

Asimetría y curtosis en el modelo binomial para valorar opciones reales: caso de aplicación para empresas de base tecnológica

OpenAIRE

Gastón Silverio Milanesi

2013-01-01

El trabajo propone un modelo de valoración de opciones reales con base en el modelo binomial utilizando la transformación de Edgeworth (Rubinstein, 1998) para incorporar momentos estocásticos de orden supe- rior, especialmente para ciertos tipos de organizaciones, como empresas de base tecnológica, donde no se dispone de cartera de activos financieros gemelos, comparables de mercado y procesos estocásticos no gaussianos. Primero, se presenta el desarrollo formal del modelo, luego su aplicació...

A Genetic Analysis of Mortality in Pigs

DEFF Research Database (Denmark)

Varona, Luis; Sorensen, Daniel

2010-01-01

to investigate whether there is support for genetic variation for mortality and to study the quality of fit and predictive properties of the various models. In both breeds, the model that provided the best fit to the data was the standard binomial hierarchical model. The model that performed best in terms......An analysis of mortality is undertaken in two breeds of pigs: Danish Landrace and Yorkshire. Zero-inflated and standard versions of hierarchical Poisson, binomial, and negative binomial Bayesian models were fitted using Markov chain Monte Carlo (MCMC). The objectives of the study were...... of the ability to predict the distribution of stillbirths was the hierarchical zero-inflated negative binomial model. The best fit of the binomial hierarchical model and of the zero-inflated hierarchical negative binomial model was obtained when genetic variation was included as a parameter. For the hierarchical...

Modelo binomial para la valoración de empresas y los efectos de la deuda: escudo fiscal y liquidación de la firma

OpenAIRE

Gastón Silverio Milanesi

2014-01-01

En este documento se propone un modelo binomial para valorar empresas, proyectando y condicionando escenarios de continuidad o liquidación de la firma. El modelo se basa en la Teoría de Opciones Reales para estimar el valor de la firma, que resulta de un balance explícito de las ventajas y riesgos de tomar deuda. El trabajo se estructura de la siguiente manera: Primeramente, la introducción y desarrollo del modelo teórico; luego se ilustra mediante un caso de aplicación, comparando los result...

CPO e MID: alguns resultados obtidos em meninos brancos, de 8 a 12 anos DMF and RLM: some results in white children, eight to twelve years old

Directory of Open Access Journals (Sweden)

José Maria Pacheco de Souza

1973-06-01

Full Text Available São apresentados alguns dados sobre CPO e MID (Índice de ataque ao 1° molar permanente inferior direito. São estudadas as distribuições do MID e do CPO /MID = 0, ajustando-se a binomial e binomial negativa, respectivamente, tendo o teste de aderência acusado bom ajuste em 10 casos, dos 12 testados.Data on DMF and right lower first permanent molar (RLM are presented. Binomial and negative binomial distributions are fitted to the data, and the goodness of fit test indicates good fitting in 10 out of 12 cases.

Using beta-binomial regression for high-precision differential methylation analysis in multifactor whole-genome bisulfite sequencing experiments

Science.gov (United States)

2014-01-01

Background Whole-genome bisulfite sequencing currently provides the highest-precision view of the epigenome, with quantitative information about populations of cells down to single nucleotide resolution. Several studies have demonstrated the value of this precision: meaningful features that correlate strongly with biological functions can be found associated with only a few CpG sites. Understanding the role of DNA methylation, and more broadly the role of DNA accessibility, requires that methylation differences between populations of cells are identified with extreme precision and in complex experimental designs. Results In this work we investigated the use of beta-binomial regression as a general approach for modeling whole-genome bisulfite data to identify differentially methylated sites and genomic intervals. Conclusions The regression-based analysis can handle medium- and large-scale experiments where it becomes critical to accurately model variation in methylation levels between replicates and account for influence of various experimental factors like cell types or batch effects. PMID:24962134

A new phase modulated binomial-like selective-inversion sequence for solvent signal suppression in NMR.

Science.gov (United States)

Chen, Johnny; Zheng, Gang; Price, William S

2017-02-01

A new 8-pulse Phase Modulated binomial-like selective inversion pulse sequence, dubbed '8PM', was developed by optimizing the nutation and phase angles of the constituent radio-frequency pulses so that the inversion profile resembled a target profile. Suppression profiles were obtained for both the 8PM and W5 based excitation sculpting sequences with equal inter-pulse delays. Significant distortions were observed in both profiles because of the offset effect of the radio frequency pulses. These distortions were successfully reduced by adjusting the inter-pulse delays. With adjusted inter-pulse delays, the 8PM and W5 based excitation sculpting sequences were tested on an aqueous lysozyme solution. The 8 PM based sequence provided higher suppression selectivity than the W5 based sequence. Two-dimensional nuclear Overhauser effect spectroscopy experiments were also performed on the lysozyme sample with 8PM and W5 based water signal suppression. The 8PM based suppression provided a spectrum with significantly increased (~ doubled) cross-peak intensity around the suppressed water resonance compared to the W5 based suppression. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Spatial distribution of parasitism on Phyllocnistis citrella Stainton, 1856 (Lepidoptera: Gracillariidae in citrus orchards

Directory of Open Access Journals (Sweden)

SM. Jahnke

Full Text Available Many species of microhymenopterous parasitoids have been registered on Phyllocnistis citrella, the citrus leafminer. The present study aimed to identify the spatial distribution pattern of the native and introduced parasitoids of P. citrella in two citrus orchards in Montenegro, RS. The new shoots from 24 randomly selected trees in each orchard were inspected at the bottom (0-1.5 m and top (1.5-2.5 m stratum and had their position relative to the quadrants (North, South, East and West registered at every 15 days from July/2002 to June/2003. The leaves with pupae were collected and kept isolated until the emergence of parasitoids or of the leaf miner; so, the sampling was biased towards parasitoids that emerge in the host pupal phase. The horizontal spatial distribution was evaluated testing the fitness of data to the Poisson and negative binomial distributions. In Montenegrina, there was no significant difference in the number of parasitoids and in the mean number of pupae found in the top and bottom strata (χ2 = 0.66; df = 1; P > 0.05 (χ2 = 0.27; df =1; P > 0.05, respectively. In relation to the quadrants, the highest average numbers of the leafminer pupae and of parasitoids were registered at the East quadrant (χ2 = 11.81; df = 3; P < 0.05, (χ2 = 10.36; df = 3; P < 0.05. In the Murcott orchard, a higher number of parasitoids was found at the top stratum (63.5% (χ2 = 7.24; df =1 P < 0.05, the same occurring with the average number of P. citrella pupae (62.9% (χ2 = 6.66; df = 1; P < 0.05. The highest number of parasitoids and of miners was registered at the North quadrant (χ2 = 19. 29; df = 3; P < 0.05, (χ2 = 4.39; df = 3; P < 0.05. In both orchards, there was no difference between the numbers of shoots either relative to the strata as well as to the quadrants. As the number of shoots did not varied much relative to the quadrants, it is possible that the higher number of miners and parasitoids in the East and West quadrants would be

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...

Binomial Test Method for Determining Probability of Detection Capability for Fracture Critical Applications

Science.gov (United States)

Generazio, Edward R.

2011-01-01

The capability of an inspection system is established by applications of various methodologies to determine the probability of detection (POD). One accepted metric of an adequate inspection system is that for a minimum flaw size and all greater flaw sizes, there is 0.90 probability of detection with 95% confidence (90/95 POD). Directed design of experiments for probability of detection (DOEPOD) has been developed to provide an efficient and accurate methodology that yields estimates of POD and confidence bounds for both Hit-Miss or signal amplitude testing, where signal amplitudes are reduced to Hit-Miss by using a signal threshold Directed DOEPOD uses a nonparametric approach for the analysis or inspection data that does require any assumptions about the particular functional form of a POD function. The DOEPOD procedure identifies, for a given sample set whether or not the minimum requirement of 0.90 probability of detection with 95% confidence is demonstrated for a minimum flaw size and for all greater flaw sizes (90/95 POD). The DOEPOD procedures are sequentially executed in order to minimize the number of samples needed to demonstrate that there is a 90/95 POD lower confidence bound at a given flaw size and that the POD is monotonic for flaw sizes exceeding that 90/95 POD flaw size. The conservativeness of the DOEPOD methodology results is discussed. Validated guidelines for binomial estimation of POD for fracture critical inspection are established.

Isotopic study on mechanism for skeletal isomerization of n-butane over solid acids

International Nuclear Information System (INIS)

Suzuki, Tetsuo; Okuhara, Toshio

2000-01-01

Reaction mechanism for skeletal isomerization of n-butane over typical strong solid acids were investigated by using 1,4- 13 C 2 -n-butane. We used FI MASS for the analysis of 13 C distribution to get the parent pattern. 13 C-distribution of isobutane formed at 423 K over SO 3 2- /ZrO 2 (SZ) and Cs 2.5 H 0.5 PW 12 O 40 (Cs2.5) were close to binomial distributions, indicating that the isomerization proceeded mainly via a bimolecular mechanism on these catalysts. On the other hand, at 523 K over Cs2.5, the isotopic distribution pattern in isobutane was quite different from the binomial one; the fraction of 13 C 2 -isobutane was much greater than the binomial distribution. This result demonstrates that an intramolecular (monomolecular) rearrangement became significant at 523 K over Cs2.5. The contribution of monomolecular pathway was higher on Cs2.5 than on SZ. We presumed that the contribution of mechanism is related to the acidic property and the dehydrogenation ability of the catalyst. (S.Y.)

Development of particle multiplicity distributions using a general form of the grand canonical partition function

International Nuclear Information System (INIS)

Lee, S.J.; Mekjian, A.Z.

2004-01-01

Various phenomenological models of particle multiplicity distributions are discussed using a general form of a unified model which is based on the grand canonical partition function and Feynman's path integral approach to statistical processes. These models can be written as special cases of a more general distribution which has three control parameters which are a,x,z. The relation to these parameters to various physical quantities are discussed. A connection of the parameter a with Fisher's critical exponent τ is developed. Using this grand canonical approach, moments, cumulants and combinants are discussed and a physical interpretation of the combinants are given and their behavior connected to the critical exponent τ. Various physical phenomena such as hierarchical structure, void scaling relations, Koba-Nielson-Olesen or KNO scaling features, clan variables, and branching laws are shown in terms of this general approach. Several of these features which were previously developed in terms of the negative binomial distribution are found to be more general. Both hierarchical structure and void scaling relations depend on the Fisher exponent τ. Applications of our approach to the charged particle multiplicity distribution in jets of L3 and H1 data are given

Prediction of province-level outbreaks of foot-and-mouth disease in Iran using a zero-inflated negative binomial model.

Science.gov (United States)

Jafarzadeh, S Reza; Norris, Michelle; Thurmond, Mark C

2014-08-01

To identify events that could predict province-level frequency of foot-and-mouth disease (FMD) outbreaks in Iran, 5707 outbreaks reported from April 1995 to March 2002 were studied. A zero-inflated negative binomial model was used to estimate the probability of a 'no-outbreak' status and the number of outbreaks in a province, using the number of previous occurrences of FMD for the same or adjacent provinces and season as covariates. For each province, the probability of observing no outbreak was negatively associated with the number of outbreaks in the same province in the previous month (odds ratio [OR]=0.06, 95% confidence interval [CI]: 0.01, 0.30) and in 'the second previous month' (OR=0.10, 95% CI: 0.02, 0.51), the total number of outbreaks in the second previous month in adjacent provinces (OR=0.57, 95% CI: 0.36, 0.91) and the season (winter [OR=0.18, 95% CI: 0.06, 0.55] and spring [OR=0.27, 95% CI: 0.09, 0.81], compared with summer). The expected number of outbreaks in a province was positively associated with number of outbreaks in the same province in previous month (coefficient [coef]=0.74, 95% CI: 0.66, 0.82) and in the second previous month (coef=0.23, 95% CI: 0.16, 0.31), total number of outbreaks in adjacent provinces in the previous month (coef=0.32, 95% CI: 0.22, 0.41) and season (fall [coef=0.20, 95% CI: 0.07, 0.33] and spring [coef=0.18, 95% CI: 0.05, 0.31], compared to summer); however, number of outbreaks was negatively associated with the total number of outbreaks in adjacent provinces in the second previous month (coef=-0.19, 95% CI: -0.28, -0.09). The findings indicate that the probability of an outbreak (and the expected number of outbreaks if any) may be predicted based on previous province information, which could help decision-makers allocate resources more efficiently for province-level disease control measures. Further, the study illustrates use of zero inflated negative binomial model to study diseases occurrence where disease is

Binomial model for measuring expected credit losses from trade receivables in non-financial sector entities

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Branka Remenarić

2018-01-01

Full Text Available In July 2014, the International Accounting Standards Board (IASB published International Financial Reporting Standard 9 Financial Instruments (IFRS 9. This standard introduces an expected credit loss (ECL impairment model that applies to financial instruments, including trade and lease receivables. IFRS 9 applies to annual periods beginning on or after 1 January 2018 in the European Union member states. While the main reason for amending the current model was to require major banks to recognize losses in advance of a credit event occurring, this new model also applies to all receivables, including trade receivables, lease receivables, related party loan receivables in non-financial sector entities. The new impairment model is intended to result in earlier recognition of credit losses. The previous model described in International Accounting Standard 39 Financial instruments (IAS 39 was based on incurred losses. One of the major questions now is what models to use to predict expected credit losses in non-financial sector entities. The purpose of this paper is to research the application of the current impairment model, the extent to which the current impairment model can be modified to satisfy new impairment model requirements and the applicability of the binomial model for measuring expected credit losses from accounts receivable.

Goodness-of-fit tests and model diagnostics for negative binomial regression of RNA sequencing data.

Science.gov (United States)

Mi, Gu; Di, Yanming; Schafer, Daniel W

2015-01-01

This work is about assessing model adequacy for negative binomial (NB) regression, particularly (1) assessing the adequacy of the NB assumption, and (2) assessing the appropriateness of models for NB dispersion parameters. Tools for the first are appropriate for NB regression generally; those for the second are primarily intended for RNA sequencing (RNA-Seq) data analysis. The typically small number of biological samples and large number of genes in RNA-Seq analysis motivate us to address the trade-offs between robustness and statistical power using NB regression models. One widely-used power-saving strategy, for example, is to assume some commonalities of NB dispersion parameters across genes via simple models relating them to mean expression rates, and many such models have been proposed. As RNA-Seq analysis is becoming ever more popular, it is appropriate to make more thorough investigations into power and robustness of the resulting methods, and into practical tools for model assessment. In this article, we propose simulation-based statistical tests and diagnostic graphics to address model adequacy. We provide simulated and real data examples to illustrate that our proposed methods are effective for detecting the misspecification of the NB mean-variance relationship as well as judging the adequacy of fit of several NB dispersion models.

If you like low P/sub T/ multiparticle physics, you'll love nucleus-nucleus interactions or Do E/sub T/ distributions obey KNO scaling in high energy pp and nucleus-nucleus collisions

International Nuclear Information System (INIS)

Tannenbaum, M.J.

1985-01-01

Measurements of neutral transverse energy spectra in p-p, d-d and α-α interactions at the CERN ISR are presented. The source of transverse energy is the emission of relatively low P/sub T/ particles distributed uniformly. Analysis of the αα data in terms of multiple nucleon-nucleon collisions is most convenient when Gamma distributions are used to represent the spectral shapes. This distribution bears a strong relationship to the Negative Binomial Distribution which describes multiplicity distributions in pp and p anti p interactions over the full available energy range. Extensive analysis of the data is presented in terms of Nuclear Models. However, the best fit to the pp and αα data is a single Gamma distribution scaled by the mean value. This property is also known as KNO scaling. 15 refs., 2 figs

Decision-theoretic designs for a series of trials with correlated treatment effects using the Sarmanov multivariate beta-binomial distribution.

Science.gov (United States)

Hee, Siew Wan; Parsons, Nicholas; Stallard, Nigel

2018-03-01

The motivation for the work in this article is the setting in which a number of treatments are available for evaluation in phase II clinical trials and where it may be infeasible to try them concurrently because the intended population is small. This paper introduces an extension of previous work on decision-theoretic designs for a series of phase II trials. The program encompasses a series of sequential phase II trials with interim decision making and a single two-arm phase III trial. The design is based on a hybrid approach where the final analysis of the phase III data is based on a classical frequentist hypothesis test, whereas the trials are designed using a Bayesian decision-theoretic approach in which the unknown treatment effect is assumed to follow a known prior distribution. In addition, as treatments are intended for the same population it is not unrealistic to consider treatment effects to be correlated. Thus, the prior distribution will reflect this. Data from a randomized trial of severe arthritis of the hip are used to test the application of the design. We show that the design on average requires fewer patients in phase II than when the correlation is ignored. Correspondingly, the time required to recommend an efficacious treatment for phase III is quicker. © 2017 The Author. Biometrical Journal published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded.

Science.gov (United States)

Nakagawa, Shinichi; Johnson, Paul C D; Schielzeth, Holger

2017-09-01

The coefficient of determination R 2 quantifies the proportion of variance explained by a statistical model and is an important summary statistic of biological interest. However, estimating R 2 for generalized linear mixed models (GLMMs) remains challenging. We have previously introduced a version of R 2 that we called [Formula: see text] for Poisson and binomial GLMMs, but not for other distributional families. Similarly, we earlier discussed how to estimate intra-class correlation coefficients (ICCs) using Poisson and binomial GLMMs. In this paper, we generalize our methods to all other non-Gaussian distributions, in particular to negative binomial and gamma distributions that are commonly used for modelling biological data. While expanding our approach, we highlight two useful concepts for biologists, Jensen's inequality and the delta method, both of which help us in understanding the properties of GLMMs. Jensen's inequality has important implications for biologically meaningful interpretation of GLMMs, whereas the delta method allows a general derivation of variance associated with non-Gaussian distributions. We also discuss some special considerations for binomial GLMMs with binary or proportion data. We illustrate the implementation of our extension by worked examples from the field of ecology and evolution in the R environment. However, our method can be used across disciplines and regardless of statistical environments. © 2017 The Author(s).

Statistical interpretation of the correlations between forward and backward hadrons at collider energies

International Nuclear Information System (INIS)

Carruthers, P.; Shih, C.C.

1985-01-01

Given a multiplicity distribution belonging to the class of probability distributions which are superpositions of Poisson distributions whose two components are independently (binomially) distributed, we derive joint and conditional probabilities for the two components. Specializing to the negative binomial case, we can explain the linearity and magnitude of slope and intercept of the forward-backward correlation in a way compatible with the KNO plot for the multiplicity data provided that the final particles are produced in clusters. Generalization to allow for coherent emission allows one to put limits on the amount of coherence, a result not known from high precision fits to multiplicity. (orig.)

Analysis of multiplicities in e+e- interactions using 2-jet rates from different jet algorithms

International Nuclear Information System (INIS)

Dahiya, S.; Kaur, M.; Dhamija, S.

2002-01-01

The shoulder structure of charged particle multiplicity distribution measured in full phase space in e + e - interactions at various c.m. energies from 91 to 189 GeV has been analysed in terms of weighted superposition of two negative binomial distributions associated with 2-jet and multi-jet production. The 2-jet rates have been obtained from various jet algorithms. This phenomenological parametrization reproduces the shoulder structure behaviour quantitatively and improves the agreement with the experimental distributions than the conventional negative binomial distribution. The analysis at the higher energies where the shoulder structure appears more prominently, is important for the understanding of underlying structure. (author)

Extended likelihood inference in reliability

International Nuclear Information System (INIS)

Martz, H.F. Jr.; Beckman, R.J.; Waller, R.A.

1978-10-01

Extended likelihood methods of inference are developed in which subjective information in the form of a prior distribution is combined with sampling results by means of an extended likelihood function. The extended likelihood function is standardized for use in obtaining extended likelihood intervals. Extended likelihood intervals are derived for the mean of a normal distribution with known variance, the failure-rate of an exponential distribution, and the parameter of a binomial distribution. Extended second-order likelihood methods are developed and used to solve several prediction problems associated with the exponential and binomial distributions. In particular, such quantities as the next failure-time, the number of failures in a given time period, and the time required to observe a given number of failures are predicted for the exponential model with a gamma prior distribution on the failure-rate. In addition, six types of life testing experiments are considered. For the binomial model with a beta prior distribution on the probability of nonsurvival, methods are obtained for predicting the number of nonsurvivors in a given sample size and for predicting the required sample size for observing a specified number of nonsurvivors. Examples illustrate each of the methods developed. Finally, comparisons are made with Bayesian intervals in those cases where these are known to exist

Coronary artery calcium distributions in older persons in the AGES-Reykjavik study

Science.gov (United States)

Gudmundsson, Elias Freyr; Gudnason, Vilmundur; Sigurdsson, Sigurdur; Launer, Lenore J.; Harris, Tamara B.; Aspelund, Thor

2013-01-01

Coronary Artery Calcium (CAC) is a sign of advanced atherosclerosis and an independent risk factor for cardiac events. Here, we describe CAC-distributions in an unselected aged population and compare modelling methods to characterize CAC-distribution. CAC is difficult to model because it has a skewed and zero inflated distribution with over-dispersion. Data are from the AGES-Reykjavik sample, a large population based study [2002-2006] in Iceland of 5,764 persons aged 66-96 years. Linear regressions using logarithmic- and Box-Cox transformations on CAC+1, quantile regression and a Zero-Inflated Negative Binomial model (ZINB) were applied. Methods were compared visually and with the PRESS-statistic, R2 and number of detected associations with concurrently measured variables. There were pronounced differences in CAC according to sex, age, history of coronary events and presence of plaque in the carotid artery. Associations with conventional coronary artery disease (CAD) risk factors varied between the sexes. The ZINB model provided the best results with respect to the PRESS-statistic, R2, and predicted proportion of zero scores. The ZINB model detected similar numbers of associations as the linear regression on ln(CAC+1) and usually with the same risk factors. PMID:22990371

Distinguishing between Rural and Urban Road Segment Traffic Safety Based on Zero-Inflated Negative Binomial Regression Models

Directory of Open Access Journals (Sweden)

Xuedong Yan

2012-01-01

Full Text Available In this study, the traffic crash rate, total crash frequency, and injury and fatal crash frequency were taken into consideration for distinguishing between rural and urban road segment safety. The GIS-based crash data during four and half years in Pikes Peak Area, US were applied for the analyses. The comparative statistical results show that the crash rates in rural segments are consistently lower than urban segments. Further, the regression results based on Zero-Inflated Negative Binomial (ZINB regression models indicate that the urban areas have a higher crash risk in terms of both total crash frequency and injury and fatal crash frequency, compared to rural areas. Additionally, it is found that crash frequencies increase as traffic volume and segment length increase, though the higher traffic volume lower the likelihood of severe crash occurrence; compared to 2-lane roads, the 4-lane roads have lower crash frequencies but have a higher probability of severe crash occurrence; and better road facilities with higher free flow speed can benefit from high standard design feature thus resulting in a lower total crash frequency, but they cannot mitigate the severe crash risk.

Characterization of trapped charges distribution in terms of mirror plot curve.

Science.gov (United States)

Al-Obaidi, Hassan N; Mahdi, Ali S; Khaleel, Imad H

2018-01-01

Accumulation of charges (electrons) at the specimen surface in scanning electron microscope (SEM) lead to generate an electrostatic potential. By using the method of image charges, this potential is defined in the chamber's space of such apparatus. The deduced formula is expressed in terms a general volumetric distribution which proposed to be an infinitesimal spherical extension. With aid of a binomial theorem the defined potential is expanded to a multipolar form. Then resultant formula is adopted to modify a novel mirror plot equation so as to detect the real distribution of trapped charges. Simulation results reveal that trapped charges may take a various sort of arrangement such as monopole, quadruple and octuple. But existence of any of these arrangements alone may never be take place, rather are some a formations of a mix of them. Influence of each type of these profiles depends on the distance between the incident electron and surface of a sample. Result also shows that trapped charge's amount of trapped charges can refer to a threshold for failing of point charge approximation. Copyright © 2017 Elsevier B.V. All rights reserved.

Ecological Effects of the Invasive Giant Madagascar Day Gecko on Endemic Mauritian Geckos: Applications of Binomial-Mixture and Species Distribution Models

NARCIS (Netherlands)

Buckland, S.; Cole, N.C.; Aguirre-Gutiérrez, J.; Gallagher, L.E.; Henshaw, S.M.; Besnard, A.; Tucker, R.M.; Bachraz, V.; Ruhomaun, K.; Harris, S.

2014-01-01

The invasion of the giant Madagascar day gecko Phelsuma grandis has increased the threats to the four endemic Mauritian day geckos (Phelsuma spp.) that have survived on mainland Mauritius. We had two main aims: (i) to predict the spatial distribution and overlap of P. grandis and the endemic geckos

arXiv Describing dynamical fluctuations and genuine correlations by Weibull regularity

CERN Document Server

Nayak, Ranjit K.; Sarkisyan-Grinbaum, Edward K.; Tasevsky, Marek

The Weibull parametrization of the multiplicity distribution is used to describe the multidimensional local fluctuations and genuine multiparticle correlations measured by OPAL in the large statistics $e^{+}e^{-} \\to Z^{0} \\to hadrons$ sample. The data are found to be well reproduced by the Weibull model up to higher orders. The Weibull predictions are compared to the predictions by the two other models, namely by the negative binomial and modified negative binomial distributions which mostly failed to fit the data. The Weibull regularity, which is found to reproduce the multiplicity distributions along with the genuine correlations, looks to be the optimal model to describe the multiparticle production process.

Extended moment series and the parameters of the negative binomial distribution

International Nuclear Information System (INIS)

Bowman, K.O.

1984-01-01

Recent studies indicate that, for finite sample sizes, moment estimators may be superior to maximum likelihood estimators in some regions of parameter space. In this paper a statistic based on the central moment of the sample is expanded in a Taylor series using 24 derivatives and many more terms than previous expansions. A summary algorithm is required to find meaningful approximants using the higher-order coefficients. A example is presented and a comparison between theoretical assessment and simulation results is made

5_29 - 37_Dikko et al.,_A New Generalized-Exponential-Weibull ...

African Journals Online (AJOL)

user pc

ction, survival and hazard function, order statistics of the distribution. were estimated using ... he mathematical properties eibull distribution .... 2 December, 2017. Applying binomial expansion and further simplification, equation (15) become.

Statistical considerations in NRDA studies

International Nuclear Information System (INIS)

Harner, E.G.; Parker, K.R.; Skalski, J.R.

1993-01-01

Biological, chemical, and toxicological variables are usually modeled with lognormal, Poisson, negative binomial, or binomial error distributions. Species counts and densities often have frequent zeros and overdispersion. Chemical concentrations can have frequent non-detects and a small proportion of high values. The feasibility of making adjustments to these response variables, such as zero-inflated models, are discussed. Toxicity measurements are usually modeled with the binomial distribution. A strategy for determining the most appropriate distribution is presented. Model-based methods, using concomitant variables and interactions, enhance assessment of impacts. Concomitant variable models reduce variability and also reduce bias by adjusting means to a common basis. Variable selection strategies are given for determining the most appropriate set of concomitant variables. Multi-year generalized linear models test impact-by-time interactions, possibly after adjusting for time-dependent concomitant variables. Communities are analyzed to make inferences about overall biological impact and recovery and require non-normal multivariate techniques. Partial canonical corresponding analysis is an appropriate community model for ordinating spatial and temporal shifts due to impact. The Exxon Valdez is used as a case study

Analysis of correlated count data using generalised linear mixed models exemplified by field data on aggressive behaviour of boars

Directory of Open Access Journals (Sweden)

N. Mielenz

2015-01-01

Full Text Available Population-averaged and subject-specific models are available to evaluate count data when repeated observations per subject are present. The latter are also known in the literature as generalised linear mixed models (GLMM. In GLMM repeated measures are taken into account explicitly through random animal effects in the linear predictor. In this paper the relevant GLMMs are presented based on conditional Poisson or negative binomial distribution of the response variable for given random animal effects. Equations for the repeatability of count data are derived assuming normal distribution and logarithmic gamma distribution for the random animal effects. Using count data on aggressive behaviour events of pigs (barrows, sows and boars in mixed-sex housing, we demonstrate the use of the Poisson »log-gamma intercept«, the Poisson »normal intercept« and the »normal intercept« model with negative binomial distribution. Since not all count data can definitely be seen as Poisson or negative-binomially distributed, questions of model selection and model checking are examined. Emanating from the example, we also interpret the least squares means, estimated on the link as well as the response scale. Options provided by the SAS procedure NLMIXED for estimating model parameters and for estimating marginal expected values are presented.

Parity violation and parity conservation in unstirred crystallization: Effect of first crystals

Energy Technology Data Exchange (ETDEWEB)

Szurgot, M. [Center of Mathematics and Physics, Technical University of Lodz (Poland)

2012-02-15

Statistics of nucleation of chiral forms was studied to establish the effect of the number of first crystals and their handedness on distributions of enantiomers. Various bimodal, trimodal and unimodal distributions are obtained in unstirred crystallization, depending on the number of initial crystals and growth conditions. The binomial distribution satisfactorily describes experimental distributions of enantiomeric excess and may be used to predict distributions and probabilities of nucleation of enantiomers. The first nucleated crystals determine the handedness of secondary crystals, and number of initial crystals governs statistics of chiral nucleation. According to the binomial distribution if single crystals nucleate as the first, the bimodal distributions result with D and L peaks. If LD, LL, and DD pairs are nucleated as first, trimodal distributions with D, R, and L peaks are created, and if groups of crystals of various handedness nucleate as the first the unimodal distributions of enantiomeric excess with racemate R peaks are formed. Chiral nucleation experiments on sodium bromate were the basis for the theoretical considerations and verifications of predictions resulting from binomial distributions on probabilities of the creation of L and D crystals, and racemates, and the presence of D, L, and R peaks in the distributions. Growth conditions affect the number of the first crystals and effectiveness of cloning, and as a result, the distributions of enantiomers. Formation of pure enantiomers and/or racemates proves that the conservation of chiral symmetry, and the breakage of chiral symmetry can occur in unstirred crystallization. (copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

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.

Selecting the right statistical model for analysis of insect count data by using information theoretic measures.

Science.gov (United States)

Sileshi, G

2006-10-01

Researchers and regulatory agencies often make statistical inferences from insect count data using modelling approaches that assume homogeneous variance. Such models do not allow for formal appraisal of variability which in its different forms is the subject of interest in ecology. Therefore, the objectives of this paper were to (i) compare models suitable for handling variance heterogeneity and (ii) select optimal models to ensure valid statistical inferences from insect count data. The log-normal, standard Poisson, Poisson corrected for overdispersion, zero-inflated Poisson, the negative binomial distribution and zero-inflated negative binomial models were compared using six count datasets on foliage-dwelling insects and five families of soil-dwelling insects. Akaike's and Schwarz Bayesian information criteria were used for comparing the various models. Over 50% of the counts were zeros even in locally abundant species such as Ootheca bennigseni Weise, Mesoplatys ochroptera Stål and Diaecoderus spp. The Poisson model after correction for overdispersion and the standard negative binomial distribution model provided better description of the probability distribution of seven out of the 11 insects than the log-normal, standard Poisson, zero-inflated Poisson or zero-inflated negative binomial models. It is concluded that excess zeros and variance heterogeneity are common data phenomena in insect counts. If not properly modelled, these properties can invalidate the normal distribution assumptions resulting in biased estimation of ecological effects and jeopardizing the integrity of the scientific inferences. Therefore, it is recommended that statistical models appropriate for handling these data properties be selected using objective criteria to ensure efficient statistical inference.

Multiple Meixner polynomials and non-Hermitian oscillator Hamiltonians

International Nuclear Information System (INIS)

Ndayiragije, F; Van Assche, W

2013-01-01

Multiple Meixner polynomials are polynomials in one variable which satisfy orthogonality relations with respect to r > 1 different negative binomial distributions (Pascal distributions). There are two kinds of multiple Meixner polynomials, depending on the selection of the parameters in the negative binomial distribution. We recall their definition and some formulas and give generating functions and explicit expressions for the coefficients in the nearest neighbor recurrence relation. Following a recent construction of Miki, Tsujimoto, Vinet and Zhedanov (for multiple Meixner polynomials of the first kind), we construct r > 1 non-Hermitian oscillator Hamiltonians in r dimensions which are simultaneously diagonalizable and for which the common eigenstates are expressed in terms of multiple Meixner polynomials of the second kind. (paper)

Finite-key analysis for quantum key distribution with weak coherent pulses based on Bernoulli sampling

Science.gov (United States)

Kawakami, Shun; Sasaki, Toshihiko; Koashi, Masato

2017-07-01

An essential step in quantum key distribution is the estimation of parameters related to the leaked amount of information, which is usually done by sampling of the communication data. When the data size is finite, the final key rate depends on how the estimation process handles statistical fluctuations. Many of the present security analyses are based on the method with simple random sampling, where hypergeometric distribution or its known bounds are used for the estimation. Here we propose a concise method based on Bernoulli sampling, which is related to binomial distribution. Our method is suitable for the Bennett-Brassard 1984 (BB84) protocol with weak coherent pulses [C. H. Bennett and G. Brassard, Proceedings of the IEEE Conference on Computers, Systems and Signal Processing (IEEE, New York, 1984), Vol. 175], reducing the number of estimated parameters to achieve a higher key generation rate compared to the method with simple random sampling. We also apply the method to prove the security of the differential-quadrature-phase-shift (DQPS) protocol in the finite-key regime. The result indicates that the advantage of the DQPS protocol over the phase-encoding BB84 protocol in terms of the key rate, which was previously confirmed in the asymptotic regime, persists in the finite-key regime.

Accounting for non-independent detection when estimating abundance of organisms with a Bayesian approach

Science.gov (United States)

Martin, Julien; Royle, J. Andrew; MacKenzie, Darryl I.; Edwards, Holly H.; Kery, Marc; Gardner, Beth

2011-01-01

Summary 1. Binomial mixture models use repeated count data to estimate abundance. They are becoming increasingly popular because they provide a simple and cost-effective way to account for imperfect detection. However, these models assume that individuals are detected independently of each other. This assumption may often be violated in the field. For instance, manatees (Trichechus manatus latirostris) may surface in turbid water (i.e. become available for detection during aerial surveys) in a correlated manner (i.e. in groups). However, correlated behaviour, affecting the non-independence of individual detections, may also be relevant in other systems (e.g. correlated patterns of singing in birds and amphibians). 2. We extend binomial mixture models to account for correlated behaviour and therefore to account for non-independent detection of individuals. We simulated correlated behaviour using beta-binomial random variables. Our approach can be used to simultaneously estimate abundance, detection probability and a correlation parameter. 3. Fitting binomial mixture models to data that followed a beta-binomial distribution resulted in an overestimation of abundance even for moderate levels of correlation. In contrast, the beta-binomial mixture model performed considerably better in our simulation scenarios. We also present a goodness-of-fit procedure to evaluate the fit of beta-binomial mixture models. 4. We illustrate our approach by fitting both binomial and beta-binomial mixture models to aerial survey data of manatees in Florida. We found that the binomial mixture model did not fit the data, whereas there was no evidence of lack of fit for the beta-binomial mixture model. This example helps illustrate the importance of using simulations and assessing goodness-of-fit when analysing ecological data with N-mixture models. Indeed, both the simulations and the goodness-of-fit procedure highlighted the limitations of the standard binomial mixture model for aerial

Estimation of some stochastic models used in reliability engineering

International Nuclear Information System (INIS)

Huovinen, T.

1989-04-01

The work aims to study the estimation of some stochastic models used in reliability engineering. In reliability engineering continuous probability distributions have been used as models for the lifetime of technical components. We consider here the following distributions: exponential, 2-mixture exponential, conditional exponential, Weibull, lognormal and gamma. Maximum likelihood method is used to estimate distributions from observed data which may be either complete or censored. We consider models based on homogeneous Poisson processes such as gamma-poisson and lognormal-poisson models for analysis of failure intensity. We study also a beta-binomial model for analysis of failure probability. The estimators of the parameters for three models are estimated by the matching moments method and in the case of gamma-poisson and beta-binomial models also by maximum likelihood method. A great deal of mathematical or statistical problems that arise in reliability engineering can be solved by utilizing point processes. Here we consider the statistical analysis of non-homogeneous Poisson processes to describe the failing phenomena of a set of components with a Weibull intensity function. We use the method of maximum likelihood to estimate the parameters of the Weibull model. A common cause failure can seriously reduce the reliability of a system. We consider a binomial failure rate (BFR) model as an application of the marked point processes for modelling common cause failure in a system. The parameters of the binomial failure rate model are estimated with the maximum likelihood method

Ecological Effects of the Invasive Giant Madagascar Day Gecko on Endemic Mauritian Geckos: Applications of Binomial-Mixture and Species Distribution Models

OpenAIRE

Buckland, S.; Cole, N.C.; Aguirre-Gutiérrez, J.; Gallagher, L.E.; Henshaw, S.M.; Besnard, A.; Tucker, R.M.; Bachraz, V.; Ruhomaun, K.; Harris, S.

2014-01-01

The invasion of the giant Madagascar day gecko Phelsuma grandis has increased the threats to the four endemic Mauritian day geckos (Phelsuma spp.) that have survived on mainland Mauritius. We had two main aims: (i) to predict the spatial distribution and overlap of P. grandis and the endemic geckos at a landscape level; and (ii) to investigate the effects of P. grandis on the abundance and risks of extinction of the endemic geckos at a local scale. An ensemble forecasting approach was used to...

Single-vehicle crashes along rural mountainous highways in Malaysia: An application of random parameters negative binomial model.

Science.gov (United States)

Rusli, Rusdi; Haque, Md Mazharul; King, Mark; Voon, Wong Shaw

2017-05-01

Mountainous highways generally associate with complex driving environment because of constrained road geometries, limited cross-section elements, inappropriate roadside features, and adverse weather conditions. As a result, single-vehicle (SV) crashes are overrepresented along mountainous roads, particularly in developing countries, but little attention is known about the roadway geometric, traffic and weather factors contributing to these SV crashes. As such, the main objective of the present study is to investigate SV crashes using detailed data obtained from a rigorous site survey and existing databases. The final dataset included a total of 56 variables representing road geometries including horizontal and vertical alignment, traffic characteristics, real-time weather condition, cross-sectional elements, roadside features, and spatial characteristics. To account for structured heterogeneities resulting from multiple observations within a site and other unobserved heterogeneities, the study applied a random parameters negative binomial model. Results suggest that rainfall during the crash is positively associated with SV crashes, but real-time visibility is negatively associated. The presence of a road shoulder, particularly a bitumen shoulder or wider shoulders, along mountainous highways is associated with less SV crashes. While speeding along downgrade slopes increases the likelihood of SV crashes, proper delineation decreases the likelihood. Findings of this study have significant implications for designing safer highways in mountainous areas, particularly in the context of a developing country. Copyright © 2017 Elsevier Ltd. All rights reserved.

Aplicação do modelo binomial na formação de preço de títulos de dívida corporativa no Brasil.

Directory of Open Access Journals (Sweden)

José Roberto Securato

2008-05-01

components such as call options, convertibility options, seniority and subordination to a Brazilian company. The major results consist of debt securities valuation and its comparison to secondary market prices in order to identify investments opportunities. The paper evaluated six debt securities which have secondary market prices and three of them presented prices above market, two of them were bellow market price and one of them had the same price of the market. The presented model and its adjustments to Brazilian market allow evaluating corporate debt securities and its components, evaluating the impact of new debt issues in the existing ones and comparing debt model and book values. Keywords: binomial model; corporate debt; debt components.

Robust Priority for Strategic Environmental Assessment with Incomplete Information Using Multi-Criteria Decision Making Analysis

Directory of Open Access Journals (Sweden)

Daeryong Park

2015-07-01

Full Text Available This study investigates how the priority rankings for dam construction sites vary with multi-criteria decision making (MCDM techniques and generation approaches for incomplete information. Strategic environmental assessment (SEA seeks to recommend sustainable dam construction sites based on their environmental and ecological impacts in a long-term plan for dam construction (LPDC in South Korea. However, if specific information is missing, the SEA is less useful for choosing a dam construction site. In this study, we applied AHP, ELECTRE III, PROMETHEE II and Compromise Programming as MCDM techniques, and used binomial and uniform distributions to generate missing information. We considered five dam site selection situations and compared the results as they depended on both MCDM techniques and information generation methods. The binomial generation method showed the most obvious priorities. All MCDM techniques showed similar priorities in the dam site selection results except for ELECTREE III. The results demonstrate that selecting an appropriate MCDM technique is more important than the data generation method. However, using binomial distribution to generate missing information is more effective in providing a robust priority than uniform distribution, which is a commonly used technique.

A new framework of statistical inferences based on the valid joint sampling distribution of the observed counts in an incomplete contingency table.

Science.gov (United States)

Tian, Guo-Liang; Li, Hui-Qiong

2017-08-01

Some existing confidence interval methods and hypothesis testing methods in the analysis of a contingency table with incomplete observations in both margins entirely depend on an underlying assumption that the sampling distribution of the observed counts is a product of independent multinomial/binomial distributions for complete and incomplete counts. However, it can be shown that this independency assumption is incorrect and can result in unreliable conclusions because of the under-estimation of the uncertainty. Therefore, the first objective of this paper is to derive the valid joint sampling distribution of the observed counts in a contingency table with incomplete observations in both margins. The second objective is to provide a new framework for analyzing incomplete contingency tables based on the derived joint sampling distribution of the observed counts by developing a Fisher scoring algorithm to calculate maximum likelihood estimates of parameters of interest, the bootstrap confidence interval methods, and the bootstrap testing hypothesis methods. We compare the differences between the valid sampling distribution and the sampling distribution under the independency assumption. Simulation studies showed that average/expected confidence-interval widths of parameters based on the sampling distribution under the independency assumption are shorter than those based on the new sampling distribution, yielding unrealistic results. A real data set is analyzed to illustrate the application of the new sampling distribution for incomplete contingency tables and the analysis results again confirm the conclusions obtained from the simulation studies.

The Geographic Distribution of Liver Cancer in Canada Does Not Associate with Cyanobacterial Toxin Exposure

Directory of Open Access Journals (Sweden)

Meaghan A. Labine

2015-11-01

Full Text Available Background: The incidence of liver cancer has been increasing in Canada over the past decade, as has cyanobacterial contamination of Canadian freshwater lakes and drinking water sources. Cyanotoxins released by cyanobacteria have been implicated in the pathogenesis of liver cancer. Objective: To determine whether a geographic association exists between liver cancer and surrogate markers of cyanobacterial contamination of freshwater lakes in Canada. Methods: A negative binomial regression model was employed based on previously identified risk factors for liver cancer. Results: No association existed between the geographic distribution of liver cancer and surrogate markers of cyanobacterial contamination. As predicted, significant associations existed in areas with a high prevalence of hepatitis B virus infection, large immigrant populations and urban residences. Discussion and Conclusions: The results of this study suggest that cyanobacterial contamination of freshwater lakes does not play an important role in the increasing incidence of liver cancer in Canada.

Do phase transitions survive binomial reducibility and thermal scaling?

Energy Technology Data Exchange (ETDEWEB)

Moretto, L.G.; Phair, L.; Wozniak, G.J.

1996-05-01

First order phase transitions are described in terms of the microcanonical and canonical ensemble, with special attention to finite size effects. Difficulties in interpreting a `caloric curve` are discussed. A robust parameter indicating phase coexistence (univariance) or single phase (bivariance) is extracted for charge distributions. 9 refs., 4 figs.

Predictability and interpretability of hybrid link-level crash frequency models for urban arterials compared to cluster-based and general negative binomial regression models.

Science.gov (United States)

Najaf, Pooya; Duddu, Venkata R; Pulugurtha, Srinivas S

2018-03-01

Machine learning (ML) techniques have higher prediction accuracy compared to conventional statistical methods for crash frequency modelling. However, their black-box nature limits the interpretability. The objective of this research is to combine both ML and statistical methods to develop hybrid link-level crash frequency models with high predictability and interpretability. For this purpose, M5' model trees method (M5') is introduced and applied to classify the crash data and then calibrate a model for each homogenous class. The data for 1134 and 345 randomly selected links on urban arterials in the city of Charlotte, North Carolina was used to develop and validate models, respectively. The outputs from the hybrid approach are compared with the outputs from cluster-based negative binomial regression (NBR) and general NBR models. Findings indicate that M5' has high predictability and is very reliable to interpret the role of different attributes on crash frequency compared to other developed models.

The spatial distribution of fixed mutations within genes coding for proteins

Science.gov (United States)

Holmquist, R.; Goodman, M.; Conroy, T.; Czelusniak, J.

1983-01-01

An examination has been conducted of the extensive amino acid sequence data now available for five protein families - the alpha crystallin A chain, myoglobin, alpha and beta hemoglobin, and the cytochromes c - with the goal of estimating the true spatial distribution of base substitutions within genes that code for proteins. In every case the commonly used Poisson density failed to even approximate the experimental pattern of base substitution. For the 87 species of beta hemoglobin examined, for example, the probability that the observed results were from a Poisson process was the minuscule 10 to the -44th. Analogous results were obtained for the other functional families. All the data were reasonably, but not perfectly, described by the negative binomial density. In particular, most of the data were described by one of the very simple limiting forms of this density, the geometric density. The implications of this for evolutionary inference are discussed. It is evident that most estimates of total base substitutions between genes are badly in need of revision.

Using a Simple Binomial Model to Assess Improvement in Predictive Capability: Sequential Bayesian Inference, Hypothesis Testing, and Power Analysis

Energy Technology Data Exchange (ETDEWEB)

Sigeti, David E. [Los Alamos National Laboratory; Pelak, Robert A. [Los Alamos National Laboratory

2012-09-11

We present a Bayesian statistical methodology for identifying improvement in predictive simulations, including an analysis of the number of (presumably expensive) simulations that will need to be made in order to establish with a given level of confidence that an improvement has been observed. Our analysis assumes the ability to predict (or postdict) the same experiments with legacy and new simulation codes and uses a simple binomial model for the probability, {theta}, that, in an experiment chosen at random, the new code will provide a better prediction than the old. This model makes it possible to do statistical analysis with an absolute minimum of assumptions about the statistics of the quantities involved, at the price of discarding some potentially important information in the data. In particular, the analysis depends only on whether or not the new code predicts better than the old in any given experiment, and not on the magnitude of the improvement. We show how the posterior distribution for {theta} may be used, in a kind of Bayesian hypothesis testing, both to decide if an improvement has been observed and to quantify our confidence in that decision. We quantify the predictive probability that should be assigned, prior to taking any data, to the possibility of achieving a given level of confidence, as a function of sample size. We show how this predictive probability depends on the true value of {theta} and, in particular, how there will always be a region around {theta} = 1/2 where it is highly improbable that we will be able to identify an improvement in predictive capability, although the width of this region will shrink to zero as the sample size goes to infinity. We show how the posterior standard deviation may be used, as a kind of 'plan B metric' in the case that the analysis shows that {theta} is close to 1/2 and argue that such a plan B should generally be part of hypothesis testing. All the analysis presented in the paper is done with a

Factors related to the use of antenatal care services in Ethiopia: Application of the zero-inflated negative binomial model.

Science.gov (United States)

Assefa, Enyew; Tadesse, Mekonnen

2017-08-01

The major causes for poor health in developing countries are inadequate access and under-use of modern health care services. The objective of this study was to identify and examine factors related to the use of antenatal care services using the 2011 Ethiopia Demographic and Health Survey data. The number of antenatal care visits during the last pregnancy by mothers aged 15 to 49 years (n = 7,737) was analyzed. More than 55% of the mothers did not use antenatal care (ANC) services, while more than 22% of the women used antenatal care services less than four times. More than half of the women (52%) who had access to health services had at least four antenatal care visits. The zero-inflated negative binomial model was found to be more appropriate for analyzing the data. Place of residence, age of mothers, woman's educational level, employment status, mass media exposure, religion, and access to health services were significantly associated with the use of antenatal care services. Accordingly, there should be progress toward a health-education program that enables more women to utilize ANC services, with the program targeting women in rural areas, uneducated women, and mothers with higher birth orders through appropriate media.

Response of selected binomial coefficients to varying degrees of matrix sparseness and to matrices with known data interrelationships

Science.gov (United States)

Archer, A.W.; Maples, C.G.

1989-01-01

Numerous departures from ideal relationships are revealed by Monte Carlo simulations of widely accepted binomial coefficients. For example, simulations incorporating varying levels of matrix sparseness (presence of zeros indicating lack of data) and computation of expected values reveal that not only are all common coefficients influenced by zero data, but also that some coefficients do not discriminate between sparse or dense matrices (few zero data). Such coefficients computationally merge mutually shared and mutually absent information and do not exploit all the information incorporated within the standard 2 ?? 2 contingency table; therefore, the commonly used formulae for such coefficients are more complicated than the actual range of values produced. Other coefficients do differentiate between mutual presences and absences; however, a number of these coefficients do not demonstrate a linear relationship to matrix sparseness. Finally, simulations using nonrandom matrices with known degrees of row-by-row similarities signify that several coefficients either do not display a reasonable range of values or are nonlinear with respect to known relationships within the data. Analyses with nonrandom matrices yield clues as to the utility of certain coefficients for specific applications. For example, coefficients such as Jaccard, Dice, and Baroni-Urbani and Buser are useful if correction of sparseness is desired, whereas the Russell-Rao coefficient is useful when sparseness correction is not desired. ?? 1989 International Association for Mathematical Geology.

Feasibility analysis in the expansion proposal of the nuclear power plant Laguna Verde: application of real options, binomial model; Analisis de viabilidad en la propuesta de expansion de la central nucleoelectrica Laguna Verde: aplicacion de opciones reales, modelo binomial

Energy Technology Data Exchange (ETDEWEB)

Hernandez I, S.; Ortiz C, E.; Chavez M, C., E-mail: lunitza@gmail.com [UNAM, Facultad de Ingenieria, Circuito Interior, Ciudad Universitaria, 04510 Mexico D. F. (Mexico)

2011-11-15

At the present time, is an unquestionable fact that the nuclear electrical energy is a topic of vital importance, no more because eliminates the dependence of the hydrocarbons and is friendly with the environment, but because is also a sure and reliable energy source, and represents a viable alternative before the claims in the growing demand of electricity in Mexico. Before this panorama, was intended several scenarios to elevate the capacity of electric generation of nuclear origin with a variable participation. One of the contemplated scenarios is represented by the expansion project of the nuclear power plant Laguna Verde through the addition of a third reactor that serves as detonator of an integral program that proposes the installation of more nuclear reactors in the country. Before this possible scenario, the Federal Commission of Electricity like responsible organism of supplying energy to the population should have tools that offer it the flexibility to be adapted to the possible changes that will be presented along the project and also gives a value to the risk to future. The methodology denominated Real Options, Binomial model was proposed as an evaluation tool that allows to quantify the value of the expansion proposal, demonstrating the feasibility of the project through a periodic visualization of their evolution, all with the objective of supplying a financial analysis that serves as base and justification before the evident apogee of the nuclear energy that will be presented in future years. (Author)

Stochastic evolutions and hadronization of highly excited hadronic matter

International Nuclear Information System (INIS)

Carruthers, P.

1984-01-01

Stochastic ingredients of high energy hadronic collisions are analyzed, with emphasis on multiplicity distributions. The conceptual simplicity of the k-cell negative binomial distribution is related to the evolution of probability distributions via the Fokker-Planck and related equations. The connection to underlying field theory ideas is sketched. 17 references

Estimating the transmission potential of supercritical processes based on the final size distribution of minor outbreaks.

Science.gov (United States)

Nishiura, Hiroshi; Yan, Ping; Sleeman, Candace K; Mode, Charles J

2012-02-07

Use of the final size distribution of minor outbreaks for the estimation of the reproduction numbers of supercritical epidemic processes has yet to be considered. We used a branching process model to derive the final size distribution of minor outbreaks, assuming a reproduction number above unity, and applying the method to final size data for pneumonic plague. Pneumonic plague is a rare disease with only one documented major epidemic in a spatially limited setting. Because the final size distribution of a minor outbreak needs to be normalized by the probability of extinction, we assume that the dispersion parameter (k) of the negative-binomial offspring distribution is known, and examine the sensitivity of the reproduction number to variation in dispersion. Assuming a geometric offspring distribution with k=1, the reproduction number was estimated at 1.16 (95% confidence interval: 0.97-1.38). When less dispersed with k=2, the maximum likelihood estimate of the reproduction number was 1.14. These estimates agreed with those published from transmission network analysis, indicating that the human-to-human transmission potential of the pneumonic plague is not very high. Given only minor outbreaks, transmission potential is not sufficiently assessed by directly counting the number of offspring. Since the absence of a major epidemic does not guarantee a subcritical process, the proposed method allows us to conservatively regard epidemic data from minor outbreaks as supercritical, and yield estimates of threshold values above unity. Crown Copyright © 2011. Published by Elsevier Ltd. All rights reserved.

Performance evaluation of generalized M-modeled atmospheric optical communications links

DEFF Research Database (Denmark)

Lopez-Gonzalez, Francisco J.; Garrido-Balsellss, José María; Jurado-Navas, Antonio

2016-01-01

, the behavior of the atmospheric optical channel is treated as a superposition of a finite number of Generalized-K distributed sub-channels, controlled by a discrete Negative-Binomial distribution dependent on the turbulence parameters. Unlike other studies, here, the closed-form mathematical expressions...

Packet throughput performance of multiservice, multirate OCDMA in elastic networks

DEFF Research Database (Denmark)

Raddo, Thiago R.; Sanches, Anderson L.; Tafur Monroy, Idelfonso

2016-01-01

the multiple-access interference (MAI) as binomially distributed. The packet throughput expression, by its turn, is derived considering a Poisson distribution for the composite packet arrivals. Numerical results show that the multicode technique is a good candidate for future multiservice, multirate OCDMA...

A non-linear beta-binomial regression model for mapping EORTC QLQ- C30 to the EQ-5D-3L in lung cancer patients: a comparison with existing approaches.

Science.gov (United States)

Khan, Iftekhar; Morris, Stephen

2014-11-12

The performance of the Beta Binomial (BB) model is compared with several existing models for mapping the EORTC QLQ-C30 (QLQ-C30) on to the EQ-5D-3L using data from lung cancer trials. Data from 2 separate non small cell lung cancer clinical trials (TOPICAL and SOCCAR) are used to develop and validate the BB model. Comparisons with Linear, TOBIT, Quantile, Quadratic and CLAD models are carried out. The mean prediction error, R(2), proportion predicted outside the valid range, clinical interpretation of coefficients, model fit and estimation of Quality Adjusted Life Years (QALY) are reported and compared. Monte-Carlo simulation is also used. The Beta-Binomial regression model performed 'best' among all models. For TOPICAL and SOCCAR trials, respectively, residual mean square error (RMSE) was 0.09 and 0.11; R(2) was 0.75 and 0.71; observed vs. predicted means were 0.612 vs. 0.608 and 0.750 vs. 0.749. Mean difference in QALY's (observed vs. predicted) were 0.051 vs. 0.053 and 0.164 vs. 0.162 for TOPICAL and SOCCAR respectively. Models tested on independent data show simulated 95% confidence from the BB model containing the observed mean more often (77% and 59% for TOPICAL and SOCCAR respectively) compared to the other models. All algorithms over-predict at poorer health states but the BB model was relatively better, particularly for the SOCCAR data. The BB model may offer superior predictive properties amongst mapping algorithms considered and may be more useful when predicting EQ-5D-3L at poorer health states. We recommend the algorithm derived from the TOPICAL data due to better predictive properties and less uncertainty.

Extreme temperature events affecting the electricity distribution system of the metropolitan area of Buenos Aires (1971–2013)

International Nuclear Information System (INIS)

Santágata, Daniela M.; Castesana, Paula; Rössler, Cristina E.; Gómez, Darío R.

2017-01-01

We studied the role of cold waves and heat waves on major power outages in the metropolitan area of Buenos Aires. Impacts of events occurring in the tails of distributions were assessed estimating deviations of minimum temperature, maximum temperature and hourly electricity consumption with respect to statistically derived thresholds and using three sets of data: temperature observations (1911–2013); major power outages reported in a disaster database (1971–2013) and hourly electricity consumption (2006–2013). These deviations (exceedances) proved to be adequate indicators of the stress posed by extreme temperature events to the electricity distribution system leading to major blackouts. Based on these indicators, we found that the electricity distribution system was under similar stress during cold waves or heat waves, but it was much more vulnerable to heat waves (three blackouts under cold waves against 20 under heat waves between 2006 and 2013). For heat waves, the results of a binomial regression logistic model provided an adequate description of the probability of disastrous supply interruptions in terms of exceedances in extreme temperatures and electricity consumption stress. This approach may be of use for other cities wishing to evaluate the effects of extreme temperature events on the electricity distribution infrastructure. - Highlights: • The linkage between extreme temperatures and disastrous power outages is analyzed. • Exceedance in extreme temperature and electricity consumption are stress indicators. • Extreme temperatures pose moderate to extreme impacts to electricity distribution. • Electricity distribution is more vulnerable to heat waves than cold waves.

Acceptance sampling for attributes via hypothesis testing and the hypergeometric distribution

Science.gov (United States)

Samohyl, Robert Wayne

2017-10-01

This paper questions some aspects of attribute acceptance sampling in light of the original concepts of hypothesis testing from Neyman and Pearson (NP). Attribute acceptance sampling in industry, as developed by Dodge and Romig (DR), generally follows the international standards of ISO 2859, and similarly the Brazilian standards NBR 5425 to NBR 5427 and the United States Standards ANSI/ASQC Z1.4. The paper evaluates and extends the area of acceptance sampling in two directions. First, by suggesting the use of the hypergeometric distribution to calculate the parameters of sampling plans avoiding the unnecessary use of approximations such as the binomial or Poisson distributions. We show that, under usual conditions, discrepancies can be large. The conclusion is that the hypergeometric distribution, ubiquitously available in commonly used software, is more appropriate than other distributions for acceptance sampling. Second, and more importantly, we elaborate the theory of acceptance sampling in terms of hypothesis testing rigorously following the original concepts of NP. By offering a common theoretical structure, hypothesis testing from NP can produce a better understanding of applications even beyond the usual areas of industry and commerce such as public health and political polling. With the new procedures, both sample size and sample error can be reduced. What is unclear in traditional acceptance sampling is the necessity of linking the acceptable quality limit (AQL) exclusively to the producer and the lot quality percent defective (LTPD) exclusively to the consumer. In reality, the consumer should also be preoccupied with a value of AQL, as should the producer with LTPD. Furthermore, we can also question why type I error is always uniquely associated with the producer as producer risk, and likewise, the same question arises with consumer risk which is necessarily associated with type II error. The resolution of these questions is new to the literature. The

Factores determinantes de la utilización de instrumentos públicos para la gestión del riesgo en la industria vitivinícola chilena: un modelo logit binomial

Directory of Open Access Journals (Sweden)

Germán Lobos

2008-12-01

Full Text Available The main objective of this research was to identify the determining factors of the use of public instruments to manage risk in the Chilean wine industry. A binomial logistic regression model was proposed. Based on a survey of 104 viticulture and winemaking companies, a database was constructed between January and October 2007. The model was fitted using maximum likelihood estimation. The variables that turned out to be statistically significant were: risk of the wine price, availability of external consultancy and number of permanent workers. From the Public Management point of view, the main conclusion suggests that the use of public instruments could be increased if viticulturists and winemakers had more external counseling.

Spatial distribution of psychotic disorders in an urban area of France: an ecological study.

Science.gov (United States)

Pignon, Baptiste; Schürhoff, Franck; Baudin, Grégoire; Ferchiou, Aziz; Richard, Jean-Romain; Saba, Ghassen; Leboyer, Marion; Kirkbride, James B; Szöke, Andrei

2016-05-18

Previous analyses of neighbourhood variations of non-affective psychotic disorders (NAPD) have focused mainly on incidence. However, prevalence studies provide important insights on factors associated with disease evolution as well as for healthcare resource allocation. This study aimed to investigate the distribution of prevalent NAPD cases in an urban area in France. The number of cases in each neighbourhood was modelled as a function of potential confounders and ecological variables, namely: migrant density, economic deprivation and social fragmentation. This was modelled using statistical models of increasing complexity: frequentist models (using Poisson and negative binomial regressions), and several Bayesian models. For each model, assumptions validity were checked and compared as to how this fitted to the data, in order to test for possible spatial variation in prevalence. Data showed significant overdispersion (invalidating the Poisson regression model) and residual autocorrelation (suggesting the need to use Bayesian models). The best Bayesian model was Leroux's model (i.e. a model with both strong correlation between neighbouring areas and weaker correlation between areas further apart), with economic deprivation as an explanatory variable (OR = 1.13, 95% CI [1.02-1.25]). In comparison with frequentist methods, the Bayesian model showed a better fit. The number of cases showed non-random spatial distribution and was linked to economic deprivation.

Estimation of equivalent dose and its uncertainty in the OSL SAR protocol when count numbers do not follow a Poisson distribution

International Nuclear Information System (INIS)

Bluszcz, Andrzej; Adamiec, Grzegorz; Heer, Aleksandra J.

2015-01-01

The current work focuses on the estimation of equivalent dose and its uncertainty using the single aliquot regenerative protocol in optically stimulated luminescence measurements. The authors show that the count numbers recorded with the use of photomultiplier tubes are well described by negative binomial distributions, different ones for background counts and photon induced counts. This fact is then exploited in pseudo-random count number generation and simulations of D e determination assuming a saturating exponential growth. A least squares fitting procedure is applied using different types of weights to determine whether the obtained D e 's and their error estimates are unbiased and accurate. A weighting procedure is suggested that leads to almost unbiased D e estimates. It is also shown that the assumption of Poisson distribution in D e estimation may lead to severe underestimation of the D e error. - Highlights: • Detailed analysis of statistics of count numbers in luminescence readers. • Generation of realistically scattered pseudo-random numbers of counts in luminescence measurements. • A practical guide for stringent analysis of D e values and errors assessment.

Introduction to the Monte Carlo methods

International Nuclear Information System (INIS)

Uzhinskij, V.V.

1993-01-01

Codes illustrating the use of Monte Carlo methods in high energy physics such as the inverse transformation method, the ejection method, the particle propagation through the nucleus, the particle interaction with the nucleus, etc. are presented. A set of useful algorithms of random number generators is given (the binomial distribution, the Poisson distribution, β-distribution, γ-distribution and normal distribution). 5 figs., 1 tab

A comparative empirical analysis of statistical models for evaluating highway segment crash frequency

Directory of Open Access Journals (Sweden)

Bismark R.D.K. Agbelie

2016-08-01

Full Text Available The present study conducted an empirical highway segment crash frequency analysis on the basis of fixed-parameters negative binomial and random-parameters negative binomial models. Using a 4-year data from a total of 158 highway segments, with a total of 11,168 crashes, the results from both models were presented, discussed, and compared. About 58% of the selected variables produced normally distributed parameters across highway segments, while the remaining produced fixed parameters. The presence of a noise barrier along a highway segment would increase mean annual crash frequency by 0.492 for 88.21% of the highway segments, and would decrease crash frequency for 11.79% of the remaining highway segments. Besides, the number of vertical curves per mile along a segment would increase mean annual crash frequency by 0.006 for 84.13% of the highway segments, and would decrease crash frequency for 15.87% of the remaining highway segments. Thus, constraining the parameters to be fixed across all highway segments would lead to an inaccurate conclusion. Although, the estimated parameters from both models showed consistency in direction, the magnitudes were significantly different. Out of the two models, the random-parameters negative binomial model was found to be statistically superior in evaluating highway segment crashes compared with the fixed-parameters negative binomial model. On average, the marginal effects from the fixed-parameters negative binomial model were observed to be significantly overestimated compared with those from the random-parameters negative binomial model.

Clan structure as a source of intermittency in high energy multihadron production

International Nuclear Information System (INIS)

Hove, L. van

1989-01-01

Recently the systematic study of charged hadron multiplicity distributions in high energy hadronic and leptonic collisions has revealed the general occurrence of negative binomial regularities in symmetric CM rapidity windows and of intermittency in very small windows in the central region. The negative binomial regularities imply a particular form of clustering called clan structure, which embodies all Mueller multiparticle correlations. We show that this clan structure leads to intermittency when the simplest assumptions are made on the behaviour of the clans in very small windows. (orig.)

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.

Evolution of a Modified Binomial Random Graph by Agglomeration

Science.gov (United States)

Kang, Mihyun; Pachon, Angelica; Rodríguez, Pablo M.

2018-02-01

In the classical Erdős-Rényi random graph G( n, p) there are n vertices and each of the possible edges is independently present with probability p. The random graph G( n, p) is homogeneous in the sense that all vertices have the same characteristics. On the other hand, numerous real-world networks are inhomogeneous in this respect. Such an inhomogeneity of vertices may influence the connection probability between pairs of vertices. The purpose of this paper is to propose a new inhomogeneous random graph model which is obtained in a constructive way from the Erdős-Rényi random graph G( n, p). Given a configuration of n vertices arranged in N subsets of vertices (we call each subset a super-vertex), we define a random graph with N super-vertices by letting two super-vertices be connected if and only if there is at least one edge between them in G( n, p). Our main result concerns the threshold for connectedness. We also analyze the phase transition for the emergence of the giant component and the degree distribution. Even though our model begins with G( n, p), it assumes the existence of some community structure encoded in the configuration. Furthermore, under certain conditions it exhibits a power law degree distribution. Both properties are important for real-world applications.

Media Exposure: How Models Simplify Sampling

DEFF Research Database (Denmark)

Mortensen, Peter Stendahl

1998-01-01

In media planning, the distribution of exposures to more ad spots in more media (print, TV, radio) is crucial to the evaluation of the campaign. If such information should be sampled, it would only be possible in expensive panel-studies (eg TV-meter panels). Alternatively, the distribution...... of exposures may be modelled statistically, using the Beta distribution combined with the Binomial Distribution. Examples are given....

[Homicides in the Americas region: magnitude, distribution and trends, 1999-2009].

Science.gov (United States)

Gawryszewski, Vilma Pinheiro; Sanhueza, Antonio; Martinez-Piedra, Ramon; Escamilla, José Antonio; de Souza, Maria de Fátima Marinho

2012-12-01

The scope of this study was to describe the magnitude and distribution of deaths by homicide in the Americas and to analyze the prevailing trends. Deaths by homicide (X85 to Y09 and Y35) were analyzed in 32 countries of the Americas Region from 1999 to 2009, recorded in the Mortality Information System/Pan American Health Organization. A negative binomial model was used to study the trends. There were around 121,297 homicides (89% men and 11% women) in the Americas, annually, predominantly in the 15 to 24 and 25 to 39 year age brackets. In 2009 the homicide age-adjusted mortality rate was 15.5/100,000 in the region. Countries with lower rates/100,000 were Canada (1.8), Argentina (4.4), Cuba (4.8), Chile (5.2), and the United States (5.8), whereas the highest rates/100,000 were in El Salvador (62.9), Guatemala (51.2), Colombia (42.5), Venezuela (33.2), and Puerto Rico (25.8). From 1999-2009, the homicide trend in the region was stable. They increased in nine countries: Venezuela (phomicide rates and they are on the increase.

Statistics

CERN Document Server

Hayslett, H T

1991-01-01

Statistics covers the basic principles of Statistics. The book starts by tackling the importance and the two kinds of statistics; the presentation of sample data; the definition, illustration and explanation of several measures of location; and the measures of variation. The text then discusses elementary probability, the normal distribution and the normal approximation to the binomial. Testing of statistical hypotheses and tests of hypotheses about the theoretical proportion of successes in a binomial population and about the theoretical mean of a normal population are explained. The text the

Broad distribution spectrum from Gaussian to power law appears in stochastic variations in RNA-seq data.

Science.gov (United States)

Awazu, Akinori; Tanabe, Takahiro; Kamitani, Mari; Tezuka, Ayumi; Nagano, Atsushi J

2018-05-29

Gene expression levels exhibit stochastic variations among genetically identical organisms under the same environmental conditions. In many recent transcriptome analyses based on RNA sequencing (RNA-seq), variations in gene expression levels among replicates were assumed to follow a negative binomial distribution, although the physiological basis of this assumption remains unclear. In this study, RNA-seq data were obtained from Arabidopsis thaliana under eight conditions (21-27 replicates), and the characteristics of gene-dependent empirical probability density function (ePDF) profiles of gene expression levels were analyzed. For A. thaliana and Saccharomyces cerevisiae, various types of ePDF of gene expression levels were obtained that were classified as Gaussian, power law-like containing a long tail, or intermediate. These ePDF profiles were well fitted with a Gauss-power mixing distribution function derived from a simple model of a stochastic transcriptional network containing a feedback loop. The fitting function suggested that gene expression levels with long-tailed ePDFs would be strongly influenced by feedback regulation. Furthermore, the features of gene expression levels are correlated with their functions, with the levels of essential genes tending to follow a Gaussian-like ePDF while those of genes encoding nucleic acid-binding proteins and transcription factors exhibit long-tailed ePDF.

Students' Informal Inference about the Binomial Distribution of "Bunny Hops": A Dialogic Perspective

Science.gov (United States)

Kazak, Sibel; Fujita, Taro; Wegerif, Rupert

2016-01-01

The study explores the development of 11-year-old students' informal inference about random bunny hops through student talk and use of computer simulation tools. Our aim in this paper is to draw on dialogic theory to explain how students make shifts in perspective, from intuition-based reasoning to more powerful, formal ways of using probabilistic…

Change-Point Methods for Overdispersed Count Data

National Research Council Canada - National Science Library

Wilken, Brian A

2007-01-01

.... Although the Poisson model is often used to model count data, the two-parameter gamma-Poisson mixture parameterization of the negative binomial distribution is often a more adequate model for overdispersed count data...

Deconvoluting preferences and errors: a model for binomial panel data

DEFF Research Database (Denmark)

Fosgerau, Mogens; Nielsen, Søren Feodor

2010-01-01

In many stated choice experiments researchers observe the random variables Vt, Xt, and Yt = 1{U + δxs22A4Xt + εt distributions of U and εt and also the unknown para...

Feasibility analysis in the expansion proposal of the nuclear power plant Laguna Verde: application of real options, binomial model

International Nuclear Information System (INIS)

Hernandez I, S.; Ortiz C, E.; Chavez M, C.

2011-11-01

At the present time, is an unquestionable fact that the nuclear electrical energy is a topic of vital importance, no more because eliminates the dependence of the hydrocarbons and is friendly with the environment, but because is also a sure and reliable energy source, and represents a viable alternative before the claims in the growing demand of electricity in Mexico. Before this panorama, was intended several scenarios to elevate the capacity of electric generation of nuclear origin with a variable participation. One of the contemplated scenarios is represented by the expansion project of the nuclear power plant Laguna Verde through the addition of a third reactor that serves as detonator of an integral program that proposes the installation of more nuclear reactors in the country. Before this possible scenario, the Federal Commission of Electricity like responsible organism of supplying energy to the population should have tools that offer it the flexibility to be adapted to the possible changes that will be presented along the project and also gives a value to the risk to future. The methodology denominated Real Options, Binomial model was proposed as an evaluation tool that allows to quantify the value of the expansion proposal, demonstrating the feasibility of the project through a periodic visualization of their evolution, all with the objective of supplying a financial analysis that serves as base and justification before the evident apogee of the nuclear energy that will be presented in future years. (Author)

The Detection of Signals in Impulsive Noise.

Science.gov (United States)

1983-06-01

ASSI FICATION/ DOWN GRADING SCHEOUL1E * I1S. DISTRIBUTION STATEMENT (of th0i0 Rhport) Approved for Public Release; Distribucion Unlimited * 17...has a symmetric distribution, sgn(x i) will be -1 with probability 1/2 and +1 with probability 1/2. Considering the sum of observations as 0 binomial

FluBreaks: early epidemic detection from Google flu trends.

Science.gov (United States)

Pervaiz, Fahad; Pervaiz, Mansoor; Abdur Rehman, Nabeel; Saif, Umar

2012-10-04

The Google Flu Trends service was launched in 2008 to track changes in the volume of online search queries related to flu-like symptoms. Over the last few years, the trend data produced by this service has shown a consistent relationship with the actual number of flu reports collected by the US Centers for Disease Control and Prevention (CDC), often identifying increases in flu cases weeks in advance of CDC records. However, contrary to popular belief, Google Flu Trends is not an early epidemic detection system. Instead, it is designed as a baseline indicator of the trend, or changes, in the number of disease cases. To evaluate whether these trends can be used as a basis for an early warning system for epidemics. We present the first detailed algorithmic analysis of how Google Flu Trends can be used as a basis for building a fully automated system for early warning of epidemics in advance of methods used by the CDC. Based on our work, we present a novel early epidemic detection system, called FluBreaks (dritte.org/flubreaks), based on Google Flu Trends data. We compared the accuracy and practicality of three types of algorithms: normal distribution algorithms, Poisson distribution algorithms, and negative binomial distribution algorithms. We explored the relative merits of these methods, and related our findings to changes in Internet penetration and population size for the regions in Google Flu Trends providing data. Across our performance metrics of percentage true-positives (RTP), percentage false-positives (RFP), percentage overlap (OT), and percentage early alarms (EA), Poisson- and negative binomial-based algorithms performed better in all except RFP. Poisson-based algorithms had average values of 99%, 28%, 71%, and 76% for RTP, RFP, OT, and EA, respectively, whereas negative binomial-based algorithms had average values of 97.8%, 17.8%, 60%, and 55% for RTP, RFP, OT, and EA, respectively. Moreover, the EA was also affected by the region's population size

Modelling the current distribution and predicted spread of the flea species Ctenocephalides felis infesting outdoor dogs in Spain.

Science.gov (United States)

Gálvez, Rosa; Musella, Vicenzo; Descalzo, Miguel A; Montoya, Ana; Checa, Rocío; Marino, Valentina; Martín, Oihane; Cringoli, Giuseppe; Rinaldi, Laura; Miró, Guadalupe

2017-09-19

The cat flea, Ctenocephalides felis, is the most prevalent flea species detected on dogs and cats in Europe and other world regions. The status of flea infestation today is an evident public health concern because of their cosmopolitan distribution and the flea-borne diseases transmission. This study determines the spatial distribution of the cat flea C. felis infesting dogs in Spain. Using geospatial tools, models were constructed based on entomological data collected from dogs during the period 2013-2015. Bioclimatic zones, covering broad climate and vegetation ranges, were surveyed in relation to their size. The models builded were obtained by negative binomial regression of several environmental variables to show impacts on C. felis infestation prevalence: land cover, bioclimatic zone, mean summer and autumn temperature, mean summer rainfall, distance to urban settlement and normalized difference vegetation index. In the face of climate change, we also simulated the future distributions of C. felis for the global climate model (GCM) "GFDL-CM3" and for the representative concentration pathway RCP45, which predicts their spread in the country. Predictive models for current climate conditions indicated the widespread distribution of C. felis throughout Spain, mainly across the central northernmost zone of the mainland. Under predicted conditions of climate change, the risk of spread was slightly greater, especially in the north and central peninsula, than for the current situation. The data provided will be useful for local veterinarians to design effective strategies against flea infestation and the pathogens transmitted by these arthropods.

A Statistical Treatment of Bioassay Pour Fractions

Science.gov (United States)

Barengoltz, Jack; Hughes, David W.

2014-01-01

The binomial probability distribution is used to treat the statistics of a microbiological sample that is split into two parts, with only one part evaluated for spore count. One wishes to estimate the total number of spores in the sample based on the counts obtained from the part that is evaluated (pour fraction). Formally, the binomial distribution is recharacterized as a function of the observed counts (successes), with the total number (trials) an unknown. The pour fraction is the probability of success per spore (trial). This distribution must be renormalized in terms of the total number. Finally, the new renormalized distribution is integrated and mathematically inverted to yield the maximum estimate of the total number as a function of a desired level of confidence ( P(fraction. The extension to recovery efficiency corrections is also presented. Now the product of recovery efficiency and pour fraction may be small enough that the likely value may be much larger than the usual calculation: the number of spores divided by that product. The use of this analysis would not be limited to microbiological data.

Model-based Quantile Regression for Discrete Data

KAUST Repository

Padellini, Tullia

2018-04-10

Quantile regression is a class of methods voted to the modelling of conditional quantiles. In a Bayesian framework quantile regression has typically been carried out exploiting the Asymmetric Laplace Distribution as a working likelihood. Despite the fact that this leads to a proper posterior for the regression coefficients, the resulting posterior variance is however affected by an unidentifiable parameter, hence any inferential procedure beside point estimation is unreliable. We propose a model-based approach for quantile regression that considers quantiles of the generating distribution directly, and thus allows for a proper uncertainty quantification. We then create a link between quantile regression and generalised linear models by mapping the quantiles to the parameter of the response variable, and we exploit it to fit the model with R-INLA. We extend it also in the case of discrete responses, where there is no 1-to-1 relationship between quantiles and distribution\\'s parameter, by introducing continuous generalisations of the most common discrete variables (Poisson, Binomial and Negative Binomial) to be exploited in the fitting.

Standard evaluation techniques for containment and surveillance radiation monitors

International Nuclear Information System (INIS)

Fehlau, P.E.

1982-01-01

Evaluation techniques used at Los Alamos for personnel and vehicle radiation monitors that safeguard nuclear material determine the worst-case sensitivity. An evaluation tests a monitor's lowest sensitivity regions with sources that have minimum emission rates. The result of our performance tests are analyzed as a binomial experiment. The number of trials that are required to verify the monitor's probability of detection is determined by a graph derived from the confidence limits for a binomial distribution. Our testing results are reported in a way that characterizes the monitor yet does not compromise security by revealing its routine performance for detecting process materials

Logistic quantile regression provides improved estimates for bounded avian counts: a case study of California Spotted Owl fledgling production

Science.gov (United States)

Brian S. Cade; Barry R. Noon; Rick D. Scherer; John J. Keane

2017-01-01

Counts of avian fledglings, nestlings, or clutch size that are bounded below by zero and above by some small integer form a discrete random variable distribution that is not approximated well by conventional parametric count distributions such as the Poisson or negative binomial. We developed a logistic quantile regression model to provide estimates of the empirical...

Prediction of vehicle crashes by drivers' characteristics and past traffic violations in Korea using a zero-inflated negative binomial model.

Science.gov (United States)

Kim, Dae-Hwan; Ramjan, Lucie M; Mak, Kwok-Kei

2016-01-01

Traffic safety is a significant public health challenge, and vehicle crashes account for the majority of injuries. This study aims to identify whether drivers' characteristics and past traffic violations may predict vehicle crashes in Korea. A total of 500,000 drivers were randomly selected from the 11.6 million driver records of the Ministry of Land, Transport and Maritime Affairs in Korea. Records of traffic crashes were obtained from the archives of the Korea Insurance Development Institute. After matching the past violation history for the period 2004-2005 with the number of crashes in year 2006, a total of 488,139 observations were used for the analysis. Zero-inflated negative binomial model was used to determine the incident risk ratio (IRR) of vehicle crashes by past violations of individual drivers. The included covariates were driver's age, gender, district of residence, vehicle choice, and driving experience. Drivers violating (1) a hit-and-run or drunk driving regulation at least once and (2) a signal, central line, or speed regulation more than once had a higher risk of a vehicle crash with respective IRRs of 1.06 and 1.15. Furthermore, female gender, a younger age, fewer years of driving experience, and middle-sized vehicles were all significantly associated with a higher likelihood of vehicle crashes. Drivers' demographic characteristics and past traffic violations could predict vehicle crashes in Korea. Greater resources should be assigned to the provision of traffic safety education programs for the high-risk driver groups.

Occurrence of proscopiidae in Eucalyptus spp.: analysis of the infestations and spatial distribution

Directory of Open Access Journals (Sweden)

Alexandre dos Santos

2014-12-01

Full Text Available The objective of this research was to report the occurrence of proscopiidae and to quantify its infestation and spatial distribution in one experimental plantation of eucalypt clones. The study was conducted in an experimental field with eucalypt hybrids of Eucalyptus urophylla x Eucalyptus grandis (clones GG100, Eucalyptus urophylla x Eucalyptus grandis (H13 and of Eucalyptus urophylla x Eucalyptus camaldulensis (VM01. The plantation was established in three continuous blocks with 512 plants with 3 m x 2 m, in Cáceres municipality, Mato Grosso State, Brazil. Infestation of proscopiidae insects was detected two months after planting . The insects were collected for identification. The attacked trees were geo-referenced and the injuries were quantified. The spatial pattern of proscopiidae he attack was determinated using the location information of the damaged plants, which have been submitted to a quadrats analyses using Morisita and binomial dispersion indexes. All the collected insects have been identified as Tetanorhynchus smithi Rehn, 1904 (Orthoptera, Proscopiidae. The infestation differed significantly among the three eucalypts clones and aggregated spatial pattern of attack was observed. This is the first report of this species of proscopiidae in eucalyptus in Mato Grosso State.

Binomial outcomes in dataset with some clusters of size two: can the dependence of twins be accounted for? A simulation study comparing the reliability of statistical methods based on a dataset of preterm infants.

Science.gov (United States)

Sauzet, Odile; Peacock, Janet L

2017-07-20

The analysis of perinatal outcomes often involves datasets with some multiple births. These are datasets mostly formed of independent observations and a limited number of clusters of size two (twins) and maybe of size three or more. This non-independence needs to be accounted for in the statistical analysis. Using simulated data based on a dataset of preterm infants we have previously investigated the performance of several approaches to the analysis of continuous outcomes in the presence of some clusters of size two. Mixed models have been developed for binomial outcomes but very little is known about their reliability when only a limited number of small clusters are present. Using simulated data based on a dataset of preterm infants we investigated the performance of several approaches to the analysis of binomial outcomes in the presence of some clusters of size two. Logistic models, several methods of estimation for the logistic random intercept models and generalised estimating equations were compared. The presence of even a small percentage of twins means that a logistic regression model will underestimate all parameters but a logistic random intercept model fails to estimate the correlation between siblings if the percentage of twins is too small and will provide similar estimates to logistic regression. The method which seems to provide the best balance between estimation of the standard error and the parameter for any percentage of twins is the generalised estimating equations. This study has shown that the number of covariates or the level two variance do not necessarily affect the performance of the various methods used to analyse datasets containing twins but when the percentage of small clusters is too small, mixed models cannot capture the dependence between siblings.

Binomial outcomes in dataset with some clusters of size two: can the dependence of twins be accounted for? A simulation study comparing the reliability of statistical methods based on a dataset of preterm infants

Directory of Open Access Journals (Sweden)

Odile Sauzet

2017-07-01

Full Text Available Abstract Background The analysis of perinatal outcomes often involves datasets with some multiple births. These are datasets mostly formed of independent observations and a limited number of clusters of size two (twins and maybe of size three or more. This non-independence needs to be accounted for in the statistical analysis. Using simulated data based on a dataset of preterm infants we have previously investigated the performance of several approaches to the analysis of continuous outcomes in the presence of some clusters of size two. Mixed models have been developed for binomial outcomes but very little is known about their reliability when only a limited number of small clusters are present. Methods Using simulated data based on a dataset of preterm infants we investigated the performance of several approaches to the analysis of binomial outcomes in the presence of some clusters of size two. Logistic models, several methods of estimation for the logistic random intercept models and generalised estimating equations were compared. Results The presence of even a small percentage of twins means that a logistic regression model will underestimate all parameters but a logistic random intercept model fails to estimate the correlation between siblings if the percentage of twins is too small and will provide similar estimates to logistic regression. The method which seems to provide the best balance between estimation of the standard error and the parameter for any percentage of twins is the generalised estimating equations. Conclusions This study has shown that the number of covariates or the level two variance do not necessarily affect the performance of the various methods used to analyse datasets containing twins but when the percentage of small clusters is too small, mixed models cannot capture the dependence between siblings.

Overdispersion in nuclear statistics

International Nuclear Information System (INIS)

Semkow, Thomas M.

1999-01-01

The modern statistical distribution theory is applied to the development of the overdispersion theory in ionizing-radiation statistics for the first time. The physical nuclear system is treated as a sequence of binomial processes, each depending on a characteristic probability, such as probability of decay, detection, etc. The probabilities fluctuate in the course of a measurement, and the physical reasons for that are discussed. If the average values of the probabilities change from measurement to measurement, which originates from the random Lexis binomial sampling scheme, then the resulting distribution is overdispersed. The generating functions and probability distribution functions are derived, followed by a moment analysis. The Poisson and Gaussian limits are also given. The distribution functions belong to a family of generalized hypergeometric factorial moment distributions by Kemp and Kemp, and can serve as likelihood functions for the statistical estimations. An application to radioactive decay with detection is described and working formulae are given, including a procedure for testing the counting data for overdispersion. More complex experiments in nuclear physics (such as solar neutrino) can be handled by this model, as well as distinguishing between the source and background

Empirical Bayes methods in road safety research.

NARCIS (Netherlands)

Vogelesang, R.A.W.

1997-01-01

Road safety research is a wonderful combination of counting fatal accidents and using a toolkit containing prior, posterior, overdispersed Poisson, negative binomial and Gamma distributions, together with positive and negative regression effects, shrinkage estimators and fiercy debates concerning

Research

African Journals Online (AJOL)

abp

2013-03-11

Mar 11, 2013 ... assuming a binomial distribution and a confidence level of alpha=0.05. Results: Our ... deaths per 100,000 live births [2], and has been adjusted based on ... santé communautaire (community health workers, or CHWs) were.

Fundamentals of statistics

CERN Document Server

Mulholland, Henry

1968-01-01

Fundamentals of Statistics covers topics on the introduction, fundamentals, and science of statistics. The book discusses the collection, organization and representation of numerical data; elementary probability; the binomial Poisson distributions; and the measures of central tendency. The text describes measures of dispersion for measuring the spread of a distribution; continuous distributions for measuring on a continuous scale; the properties and use of normal distribution; and tests involving the normal or student's 't' distributions. The use of control charts for sample means; the ranges

Analysis on origin of oscillation of H moment in high-energy hh collision

International Nuclear Information System (INIS)

Wu Tao; Zhou Daicui

2000-01-01

Multiplicity distributions of negative binomial distribution (NBD) and modified (NBD are obtained from a birth process model with an immigration. The ratio of factorial cumulant moment to factorial moment, i.e., H moment is calculated from different multiplicity distributions of NBD, modified NBD and the three fireball model, which shows an oscillatory behavior when there is a truncation of multiplicity. The oscillation of H moment is related to the common character of the truncated multiplicity distributions

Use of run statistics to validate tensile tests

International Nuclear Information System (INIS)

Eatherly, W.P.

1981-01-01

In tensile testing of irradiated graphites, it is difficult to assure alignment of sample and train for tensile measurements. By recording location of fractures, run (sequential) statistics can readily detect lack of randomness. The technique is based on partitioning binomial distributions

Introductory Statistics in the Garden

Science.gov (United States)

Wagaman, John C.

2017-01-01

This article describes four semesters of introductory statistics courses that incorporate service learning and gardening into the curriculum with applications of the binomial distribution, least squares regression and hypothesis testing. The activities span multiple semesters and are iterative in nature.

Bayesian Analysis for EMP Survival Probability of Solid State Relay

International Nuclear Information System (INIS)

Sun Beiyun; Zhou Hui; Cheng Xiangyue; Mao Congguang

2009-01-01

The principle to estimate the parameter p of binomial distribution by Bayesian method and the several non-informative prior are introduced. The survival probability of DC solid state relay under current injection at certain amplitude is obtained by this method. (authors)

[The binomial symptom index for the evaluation of temporal association between cardiorespiratory symptoms and gastroesophageal reflux in neonates].

Science.gov (United States)

Barriga-Rivera, Alejandro; Moya, María José; Lopez-Alonso, Manuel

2016-11-01

The evaluation of symptom association between gastroesophageal reflux and cardiorespiratory events in preterm infants remains unclear. This paper describes a conservative approach to decision-making of anti-reflux surgery through symptom association analysis. Forty-three neonates with potentially reflux-related cardiorespiratory symptoms underwent synchronized esophageal impedance-pH and cardiorespiratory monitoring. Three indices were considered to evaluate symptom association, the symptom index (SI), the symptom sensitivity index (SSI) and the symptom association probability (SAP). A conservative strategy was adopted regarding the decision of anti-reflux surgery, and therefore, patients were scheduled for laparoscopic Nissen fundoplication if the three indices showed a positive assessment of symptom association. Retrospectively, these indices and the binomial symptom index (BSI) were contrasted against the decision of anti-reflux surgery using different windows of association. Thirteen patients showed positive symptom association but only two underwent anti-reflux surgery. The SI and the SSI showed an increasing trend with the width of the window of association. The SAP was affected randomly by slightly altering the windowing parameters. The BSI showed the best performance with the two-minute window (κ =0.78) CONCLUSIONS: The pathology under study is known to improve with maturity. However, the severity of cardiorespiratory symptoms may threaten the neonate's life and therefore, in some occasions, invasive treatments must be considered to protect life. The BSI provides a good prediction of a combination of positive SI, SSI and SAP, which may improve clinical decisions. However, further clinical studies are required to prove the BSI as an optimal predictor of clinical outcomes. Copyright © 2015 Asociación Española de Pediatría. Publicado por Elsevier España, S.L.U. All rights reserved.

Intermittency in multihadron production: An analysis using stochastic theories

International Nuclear Information System (INIS)

Biyajima, M.

1989-01-01

Multiplicity data of the NA22, KLM, and UA1 collaborations are analysed by means of probability distributions derived in the framework of pure birth stochastic equations. The intermittent behaviour of the KLM and UA1 data is well reproduced by the theory. A comparison with the negative binomial distribution is also made. 19 refs., 3 figs., 1 tab. (Authors)

Statistical Methods for Unusual Count Data: Examples From Studies of Microchimerism

Science.gov (United States)

Guthrie, Katherine A.; Gammill, Hilary S.; Kamper-Jørgensen, Mads; Tjønneland, Anne; Gadi, Vijayakrishna K.; Nelson, J. Lee; Leisenring, Wendy

2016-01-01

Natural acquisition of small amounts of foreign cells or DNA, referred to as microchimerism, occurs primarily through maternal-fetal exchange during pregnancy. Microchimerism can persist long-term and has been associated with both beneficial and adverse human health outcomes. Quantitative microchimerism data present challenges for statistical analysis, including a skewed distribution, excess zero values, and occasional large values. Methods for comparing microchimerism levels across groups while controlling for covariates are not well established. We compared statistical models for quantitative microchimerism values, applied to simulated data sets and 2 observed data sets, to make recommendations for analytic practice. Modeling the level of quantitative microchimerism as a rate via Poisson or negative binomial model with the rate of detection defined as a count of microchimerism genome equivalents per total cell equivalents tested utilizes all available data and facilitates a comparison of rates between groups. We found that both the marginalized zero-inflated Poisson model and the negative binomial model can provide unbiased and consistent estimates of the overall association of exposure or study group with microchimerism detection rates. The negative binomial model remains the more accessible of these 2 approaches; thus, we conclude that the negative binomial model may be most appropriate for analyzing quantitative microchimerism data. PMID:27769989

An empirical tool to evaluate the safety of cyclists: Community based, macro-level collision prediction models using negative binomial regression.

Science.gov (United States)

Wei, Feng; Lovegrove, Gordon

2013-12-01

Today, North American governments are more willing to consider compact neighborhoods with increased use of sustainable transportation modes. Bicycling, one of the most effective modes for short trips with distances less than 5km is being encouraged. However, as vulnerable road users (VRUs), cyclists are more likely to be injured when involved in collisions. In order to create a safe road environment for them, evaluating cyclists' road safety at a macro level in a proactive way is necessary. In this paper, different generalized linear regression methods for collision prediction model (CPM) development are reviewed and previous studies on micro-level and macro-level bicycle-related CPMs are summarized. On the basis of insights gained in the exploration stage, this paper also reports on efforts to develop negative binomial models for bicycle-auto collisions at a community-based, macro-level. Data came from the Central Okanagan Regional District (CORD), of British Columbia, Canada. The model results revealed two types of statistical associations between collisions and each explanatory variable: (1) An increase in bicycle-auto collisions is associated with an increase in total lane kilometers (TLKM), bicycle lane kilometers (BLKM), bus stops (BS), traffic signals (SIG), intersection density (INTD), and arterial-local intersection percentage (IALP). (2) A decrease in bicycle collisions was found to be associated with an increase in the number of drive commuters (DRIVE), and in the percentage of drive commuters (DRP). These results support our hypothesis that in North America, with its current low levels of bicycle use (macro-level CPMs. Copyright © 2012. Published by Elsevier Ltd.

Experimental physics method

International Nuclear Information System (INIS)

Jeong, Yang Su; Oh, Byeong Seong

2010-05-01

This book introduces measurement and error, statistics of experimental data, population, sample variable, distribution function, propagation of error, mean and measurement of error, adjusting to rectilinear equation, common sense of error, experiment method, and record and statement. It also explains importance of error of estimation, systematic error, random error, treatment of single variable, significant figure, deviation, mean value, median, mode, sample mean, sample standard deviation, binomial distribution, gauss distribution, and method of least squares.

Journal of Agriculture and Social Research (JASR) Vol. 11, No. 2 ...

African Journals Online (AJOL)

MINA-LUAREL

It is reported that the k-value is influenced by plot size (P < 0.05) and depends on the ... negative binomial distribution for the determination of the cluster size of Pratylenchus penetrans an ..... Review of entomology 29:321-357. Taylor, L.R. ...

Distribution patterns of wintering sea ducks in relation to the North Atlantic Oscillation and local environmental characteristics

Science.gov (United States)

Zipkin, Elise F.; Gardner, Beth; Gilbert, Andrew T.; O'Connell, Allan F.; Royle, J. Andrew; Silverman, Emily D.

2010-01-01

Twelve species of North American sea ducks (Tribe Mergini) winter off the eastern coast of the United States and Canada. Yet, despite their seasonal proximity to urbanized areas in this region, there is limited information on patterns of wintering sea duck habitat use. It is difficult to gather information on sea ducks because of the relative inaccessibility of their offshore locations, their high degree of mobility, and their aggregated distributions. To characterize environmental conditions that affect wintering distributions, as well as their geographic ranges, we analyzed count data on five species of sea ducks (black scoters Melanitta nigra americana, surf scoters M. perspicillata, white-winged scoters M. fusca, common eiders Somateria mollissima, and long-tailed ducks Clangula hyemalis) that were collected during the Atlantic Flyway Sea Duck Survey for ten years starting in the early 1990s. We modeled count data for each species within ten-nautical-mile linear survey segments using a zero-inflated negative binomial model that included four local-scale habitat covariates (sea surface temperature, mean bottom depth, maximum bottom slope, and a variable to indicate if the segment was in a bay or not), one broad-scale covariate (the North Atlantic Oscillation), and a temporal correlation component. Our results indicate that species distributions have strong latitudinal gradients and consistency in local habitat use. The North Atlantic Oscillation was the only environmental covariate that had a significant (but variable) effect on the expected count for all five species, suggesting that broad-scale climatic conditions may be directly or indirectly important to the distributions of wintering sea ducks. Our results provide critical information on species-habitat associations, elucidate the complicated relationship between the North Atlantic Oscillation, sea surface temperature, and local sea duck abundances, and should be useful in assessing the impacts of climate

Exploiting Support Vector Machine Algorithm to Break the Secret Key

Directory of Open Access Journals (Sweden)

S. Hou

2018-04-01

Full Text Available Template attacks (TA and support vector machine (SVM are two effective methods in side channel attacks (SCAs. Almost all studies on SVM in SCAs assume the required power traces are sufficient, which also implies the number of profiling traces belonging to each class is equivalent. Indeed, in the real attack scenario, there may not be enough power traces due to various restrictions. More specifically, the Hamming Weight of the S-Box output results in 9 binomial distributed classes, which significantly reduces the performance of SVM compared with the uniformly distributed classes. In this paper, the impact of the distribution of profiling traces on the performance of SVM is first explored in detail. And also, we conduct Synthetic Minority Oversampling TEchnique (SMOTE to solve the problem caused by the binomial distributed classes. By using SMOTE, the success rate of SVM is improved in the testing phase, and SVM requires fewer power traces to recover the key. Besides, TA is selected as a comparison. In contrast to what is perceived as common knowledge in unrestricted scenarios, our results indicate that SVM with proper parameters can significantly outperform TA.

The El Niño Southern Oscillation index and wildfire prediction in British Columbia

NARCIS (Netherlands)

Xu, Zhen; Kooten, van G.C.

2014-01-01

This study investigates the potential to predict monthly wildfires and area burned in British Columbia's interior using El Niño Southern Oscillation (ENSO). The zero-inflated negative binomial (ZINB) and the generalized Pareto (GP) distributions are used, respectively, to account for uncertainty in

Sur les estimateurs du maximum de vraisemblance dans les mod& ...

African Journals Online (AJOL)

Abstract. We are interested in the existence and uniqueness of maximum likelihood estimators of parameters in the two multiplicative regression models, with Poisson or negative binomial probability distributions. Following its work on the multiplicative Poisson model with two factors without repeated measures, Haberman ...

Breeding sites of Culicoides midges in KwaZulu-Natal | Jenkins ...

African Journals Online (AJOL)

Catch numbers were correlated to site properties using the generalised linear modelling procedure on untransformed data with a negative binomial distribution and a log link function. Sites with increasing ground moisture, increasing incident radiation and increasing wetness duration were found to positively increase the ...

Variation in rank abundance replicate samples and impact of clustering

NARCIS (Netherlands)

Neuteboom, J.H.; Struik, P.C.

2005-01-01

Calculating a single-sample rank abundance curve by using the negative-binomial distribution provides a way to investigate the variability within rank abundance replicate samples and yields a measure of the degree of heterogeneity of the sampled community. The calculation of the single-sample rank

Inference of R 0 and Transmission Heterogeneity from the Size Distribution of Stuttering Chains

Science.gov (United States)

Blumberg, Seth; Lloyd-Smith, James O.

2013-01-01

For many infectious disease processes such as emerging zoonoses and vaccine-preventable diseases, and infections occur as self-limited stuttering transmission chains. A mechanistic understanding of transmission is essential for characterizing the risk of emerging diseases and monitoring spatio-temporal dynamics. Thus methods for inferring and the degree of heterogeneity in transmission from stuttering chain data have important applications in disease surveillance and management. Previous researchers have used chain size distributions to infer , but estimation of the degree of individual-level variation in infectiousness (as quantified by the dispersion parameter, ) has typically required contact tracing data. Utilizing branching process theory along with a negative binomial offspring distribution, we demonstrate how maximum likelihood estimation can be applied to chain size data to infer both and the dispersion parameter that characterizes heterogeneity. While the maximum likelihood value for is a simple function of the average chain size, the associated confidence intervals are dependent on the inferred degree of transmission heterogeneity. As demonstrated for monkeypox data from the Democratic Republic of Congo, this impacts when a statistically significant change in is detectable. In addition, by allowing for superspreading events, inference of shifts the threshold above which a transmission chain should be considered anomalously large for a given value of (thus reducing the probability of false alarms about pathogen adaptation). Our analysis of monkeypox also clarifies the various ways that imperfect observation can impact inference of transmission parameters, and highlights the need to quantitatively evaluate whether observation is likely to significantly bias results. PMID:23658504

Environmental factors prevail over dispersal constraints in determining the distribution and assembly of Trichoptera species in mountain lakes.

Science.gov (United States)

de Mendoza, Guillermo; Ventura, Marc; Catalan, Jordi

2015-07-01

Aiming to elucidate whether large-scale dispersal factors or environmental species sorting prevail in determining patterns of Trichoptera species composition in mountain lakes, we analyzed the distribution and assembly of the most common Trichoptera (Plectrocnemia laetabilis, Polycentropus flavomaculatus, Drusus rectus, Annitella pyrenaea, and Mystacides azurea) in the mountain lakes of the Pyrenees (Spain, France, Andorra) based on a survey of 82 lakes covering the geographical and environmental extremes of the lake district. Spatial autocorrelation in species composition was determined using Moran's eigenvector maps (MEM). Redundancy analysis (RDA) was applied to explore the influence of MEM variables and in-lake, and catchment environmental variables on Trichoptera assemblages. Variance partitioning analysis (partial RDA) revealed the fraction of species composition variation that could be attributed uniquely to either environmental variability or MEM variables. Finally, the distribution of individual species was analyzed in relation to specific environmental factors using binomial generalized linear models (GLM). Trichoptera assemblages showed spatial structure. However, the most relevant environmental variables in the RDA (i.e., temperature and woody vegetation in-lake catchments) were also related with spatial variables (i.e., altitude and longitude). Partial RDA revealed that the fraction of variation in species composition that was uniquely explained by environmental variability was larger than that uniquely explained by MEM variables. GLM results showed that the distribution of species with longitudinal bias is related to specific environmental factors with geographical trend. The environmental dependence found agrees with the particular traits of each species. We conclude that Trichoptera species distribution and composition in the lakes of the Pyrenees are governed predominantly by local environmental factors, rather than by dispersal constraints. For

A comparison of information functions and search strategies for sensor planning in target classification.

Science.gov (United States)

Zhang, Guoxian; Ferrari, Silvia; Cai, Chenghui

2012-02-01

This paper investigates the comparative performance of several information-driven search strategies and decision rules using a canonical target classification problem. Five sensor models are considered: one obtained from classical estimation theory and four obtained from Bernoulli, Poisson, binomial, and mixture-of-binomial distributions. A systematic approach is presented for deriving information functions that represent the expected utility of future sensor measurements from mutual information, Rènyi divergence, Kullback-Leibler divergence, information potential, quadratic entropy, and the Cauchy-Schwarz distance. The resulting information-driven strategies are compared to direct-search, alert-confirm, task-driven (TS), and log-likelihood-ratio (LLR) search strategies. Extensive numerical simulations show that quadratic entropy typically leads to the most effective search strategy with respect to correct-classification rates. In the presence of prior information, the quadratic-entropy-driven strategy also displays the lowest rate of false alarms. However, when prior information is absent or very noisy, TS and LLR strategies achieve the lowest false-alarm rates for the Bernoulli, mixture-of-binomial, and classical sensor models.

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.)

On the production of shower particles from light (Cno) and heavy (Ag Br) emulsion nuclei at Dubna energy

International Nuclear Information System (INIS)

EI-Nagdy, M.S.; Abdel-Waged, Kh; Abdel-Halim, S.M.; Khalil, E.I.

2000-01-01

The reaction cross sections for p, d, He, C, Mg and S beams with different chemical components of emulsion nuclei at 4.5 A GeV/c have been studied with high statistics, and were compared with the calculations according to Glauber model. The multiplicity distributions of shower produced particles from these interactions with light and heavy emulsion nuclei are analyzed in terms of the negative binomial and Poisson distribution laws

Random phenomena; Phenomenes aleatoires

Energy Technology Data Exchange (ETDEWEB)

Bonnet, G. [Commissariat a l' energie atomique et aux energies alternatives - CEA, C.E.N.G., Service d' Electronique, Section d' Electronique, Grenoble (France)

1963-07-01

This document gathers a set of conferences presented in 1962. A first one proposes a mathematical introduction to the analysis of random phenomena. The second one presents an axiomatic of probability calculation. The third one proposes an overview of one-dimensional random variables. The fourth one addresses random pairs, and presents basic theorems regarding the algebra of mathematical expectations. The fifth conference discusses some probability laws: binomial distribution, the Poisson distribution, and the Laplace-Gauss distribution. The last one deals with the issues of stochastic convergence and asymptotic distributions.

An extension of Krawtchouk\\'s polynomials to the contstruction of ...

African Journals Online (AJOL)

A simple method is described for the construction of a set of orthogonal polynomials for any case where the proportions of observations follow a binomial distribution. The least squares equation which fits the data is determined using the properties of orthogonal polynomials and the analysis of variance technique.

Learner-Controlled Scaffolding Linked to Open-Ended Problems in a Digital Learning Environment

Science.gov (United States)

Edson, Alden Jack

2017-01-01

This exploratory study reports on how students activated learner-controlled scaffolding and navigated through sequences of connected problems in a digital learning environment. A design experiment was completed to (re)design, iteratively develop, test, and evaluate a digital version of an instructional unit focusing on binomial distributions and…

Fulltext PDF

Indian Academy of Sciences (India)

6 Approach to Absolute Zero. 0.3 K to a Few Milli-Kelvin. 15 The Normal Distribution. From Binomial to ... The principles of thermodynamics determining the action ofthe 'Thirsty Bird' are discussed in the classroom section. Back Cover. Carl Friedrich Gauss 11777-18551. (illustration by Prema Iyerl. DEPARTMENTS. Editorial.

Studying the microlenses mass function from statistical analysis of the caustic concentration

Energy Technology Data Exchange (ETDEWEB)

Mediavilla, T; Ariza, O [Departamento de Estadistica e Investigacion Operativa, Universidad de Cadiz, Avda de Ramon Puyol, s/n 11202 Algeciras (Spain); Mediavilla, E [Instituto de Astrofisica de Canarias, Avda Via Lactea s/n, La Laguna (Spain); Munoz, J A, E-mail: teresa.mediavilla@ca.uca.es, E-mail: octavio.ariza@uca.es, E-mail: emg@iac.es [Departamento de Astrofisica y Astronomia, Universidad de Valencia, Burjassot, Valencia (Spain)

2011-09-22

The statistical distribution of caustic crossings by the images of a lensed quasar depends on the properties of the distribution of microlenses in the lens galaxy. We use a procedure based in Inverse Polygon Mapping to easily identify the critical and caustic curves generated by a distribution of stars in the lens galaxy. We analyze the statistical distributions of the number of caustic crossings by a pixel size source for several projected mass densities and different mass distributions. We compare the results of simulations with theoretical binomial distributions. Finally we apply this method to the study of the stellar mass distribution in the lens galaxy of QSO 2237+0305.

Extraction of moments of net-particle event-by-event fluctuations in the CBM experiment

Energy Technology Data Exchange (ETDEWEB)

Vovchenko, Volodymyr [Frankfurt Institute for Advanced Studies, Frankfurt am Main (Germany); Goethe University, Frankfurt am Main (Germany); Taras Shevchenko University, Kyiv (Ukraine); Kisel, Ivan [Frankfurt Institute for Advanced Studies, Frankfurt am Main (Germany); Goethe University, Frankfurt am Main (Germany); Collaboration: CBM-Collaboration

2016-07-01

The future CBM experiment at FAIR will employ high intensity beams and large acceptance detectors in order to study the properties of the strongly interacting matter produced in heavy-ion collisions at high baryon densities. The search for the conjectured critical point of QCD is one the important tasks. It is predicted from statistical physics that higher moments of event-by-event fluctuations are very sensitive to the proximity of the critical point. This argument is explicitly demonstrated with the van der Waals equation of state. Thus, it was suggested that higher moments of fluctuations of conserved charges can be used as probes for the critical behavior. The statistical convergence of cumulants of different order is explored. The extraction of scaled variance, skewness, and kurtosis of proton distribution from simulated UrQMD events is performed and the efficiency correction described by binomial distribution is accounted for. The validity of this correction is tested with different modelings of the CBM detector response: from binomial distribution with fluctuating event-by-event efficiency to a full-scale GEANT simulation. The obtained results indicate that a more elaborate efficiency correction is needed in order to accurately reconstruct moments of higher orders.

S Ramasubramanian

Indian Academy of Sciences (India)

S Ramasubramanian. Articles written in Resonance – Journal of Science Education. Volume 1 Issue 2 February 1996 pp 115-116 Book Review. Probability Theory Without Tears! S Ramasubramanian · More Details Fulltext PDF. Volume 2 Issue 6 June 1997 pp 15-24 Series Article. The Normal Distribution From Binomial to ...

Movements of adult Culicoides midges around stables in KwaZulu ...

African Journals Online (AJOL)

The catches were identified to species level and regression analysis was performed on untransformed data which followed a negative binomial distribution with a log link function. Midges were found to frequent dung heaps and the interior of stable blocks significantly more than any other site. This occurs most markedly ...

Structure of electron tracks in water. 2. Distribution of primary ionizations and excitations in water radiolysis

International Nuclear Information System (INIS)

Pimblott, S.M.; Mozumder, A.

1991-01-01

A procedure for the calculation of entity-specific ionization and excitation probabilities for water radiolysis at low linear energy transfer (LET) has been developed. The technique pays due attention to the effects of the ionization threshold and the energy dependence of the ionization efficiency. The numbers of primary ionizations and excitations are not directly proportional to the spur energy. At a given spur energy, ionization follows a binomial distribution subject to an energetically possible maximum. The excitation distribution for a spur of given energy and with a given number of ionizations is given by a geometric series. The occurrence probabilities depend upon the cross sections of ionization, excitation, and other inferior processes. Following the low-LET radiolysis of liquid water the most probable spurs contain one ionization, two ionizations, or one ionization and one excitation, while in water vapor they contain either one ionization or one excitation. In liquid water the most probable outcomes for spurs corresponding to the most probable energy loss (22 eV) and to the mean energy loss (38 eV) are one ionization and one excitation, and two ionizations and one excitation, respectively. In the vapor, the most probable energy loss is 14 eV which results in one ionization or one excitation and the mean energy loss is 34 eV for which the spur of maximum probability contains one ionization and two excitations. The total calculated primary yields for low-LET radiolysis are in approximate agreement with experiment in both phases

Inference of R(0 and transmission heterogeneity from the size distribution of stuttering chains.

Directory of Open Access Journals (Sweden)

Seth Blumberg

Full Text Available For many infectious disease processes such as emerging zoonoses and vaccine-preventable diseases, [Formula: see text] and infections occur as self-limited stuttering transmission chains. A mechanistic understanding of transmission is essential for characterizing the risk of emerging diseases and monitoring spatio-temporal dynamics. Thus methods for inferring [Formula: see text] and the degree of heterogeneity in transmission from stuttering chain data have important applications in disease surveillance and management. Previous researchers have used chain size distributions to infer [Formula: see text], but estimation of the degree of individual-level variation in infectiousness (as quantified by the dispersion parameter, [Formula: see text] has typically required contact tracing data. Utilizing branching process theory along with a negative binomial offspring distribution, we demonstrate how maximum likelihood estimation can be applied to chain size data to infer both [Formula: see text] and the dispersion parameter that characterizes heterogeneity. While the maximum likelihood value for [Formula: see text] is a simple function of the average chain size, the associated confidence intervals are dependent on the inferred degree of transmission heterogeneity. As demonstrated for monkeypox data from the Democratic Republic of Congo, this impacts when a statistically significant change in [Formula: see text] is detectable. In addition, by allowing for superspreading events, inference of [Formula: see text] shifts the threshold above which a transmission chain should be considered anomalously large for a given value of [Formula: see text] (thus reducing the probability of false alarms about pathogen adaptation. Our analysis of monkeypox also clarifies the various ways that imperfect observation can impact inference of transmission parameters, and highlights the need to quantitatively evaluate whether observation is likely to significantly bias results.

Modeling abundance using N-mixture models: the importance of considering ecological mechanisms.

Science.gov (United States)

Joseph, Liana N; Elkin, Ché; Martin, Tara G; Possinghami, Hugh P

2009-04-01

Predicting abundance across a species' distribution is useful for studies of ecology and biodiversity management. Modeling of survey data in relation to environmental variables can be a powerful method for extrapolating abundances across a species' distribution and, consequently, calculating total abundances and ultimately trends. Research in this area has demonstrated that models of abundance are often unstable and produce spurious estimates, and until recently our ability to remove detection error limited the development of accurate models. The N-mixture model accounts for detection and abundance simultaneously and has been a significant advance in abundance modeling. Case studies that have tested these new models have demonstrated success for some species, but doubt remains over the appropriateness of standard N-mixture models for many species. Here we develop the N-mixture model to accommodate zero-inflated data, a common occurrence in ecology, by employing zero-inflated count models. To our knowledge, this is the first application of this method to modeling count data. We use four variants of the N-mixture model (Poisson, zero-inflated Poisson, negative binomial, and zero-inflated negative binomial) to model abundance, occupancy (zero-inflated models only) and detection probability of six birds in South Australia. We assess models by their statistical fit and the ecological realism of the parameter estimates. Specifically, we assess the statistical fit with AIC and assess the ecological realism by comparing the parameter estimates with expected values derived from literature, ecological theory, and expert opinion. We demonstrate that, despite being frequently ranked the "best model" according to AIC, the negative binomial variants of the N-mixture often produce ecologically unrealistic parameter estimates. The zero-inflated Poisson variant is preferable to the negative binomial variants of the N-mixture, as it models an ecological mechanism rather than a

Distribution of physical activity facilities in Scotland by small area measures of deprivation and urbanicity

Directory of Open Access Journals (Sweden)

Ogilvie David

2010-10-01

Full Text Available Abstract Background The aim of this study was to examine the distribution of physical activity facilities by area-level deprivation in Scotland, adjusting for differences in urbanicity, and exploring differences between and within the four largest Scottish cities. Methods We obtained a list of all recreational physical activity facilities in Scotland. These were mapped and assigned to datazones. Poisson and negative binomial regression models were used to investigate associations between the number of physical activity facilities relative to population size and quintile of area-level deprivation. Results The results showed that prior to adjustment for urbanicity, the density of all facilities lessened with increasing deprivation from quintiles 2 to 5. After adjustment for urbanicity and local authority, the effect of deprivation remained significant but the pattern altered, with datazones in quintile 3 having the highest estimated mean density of facilities. Within-city associations were identified between the number of physical activity facilities and area-level deprivation in Aberdeen and Dundee, but not in Edinburgh or Glasgow. Conclusions In conclusion, area-level deprivation appears to have a significant association with the density of physical activity facilities and although overall no clear pattern was observed, affluent areas had fewer publicly owned facilities than more deprived areas but a greater number of privately owned facilities.