Benford's Law and Continuous Dependent Random Variables
Becker, Thealexa; Miller, Steven J; Ronan, Ryan; Strauch, Frederick W
2011-01-01
Many systems exhibit a digit bias. For example, the first digit base 10 of the Fibonacci numbers, or of $2^n$, equals 1 not 10% or 11% of the time, as one would expect if all digits were equally likely, but about 30% of the time. This phenomenon, known as Benford's Law, has many applications, ranging from detecting tax fraud for the IRS to analyzing round-off errors in computer science. The central question is determining which data sets follow Benford's law. Inspired by natural processes such as particle decay, our work examines models for the decomposition of conserved quantities. We prove that in many instances the distribution of lengths of the resulting pieces converges to Benford behavior as the number of divisions grow. The main difficulty is that the resulting random variables are dependent, which we handle by a careful analysis of the dependencies and tools from Fourier analysis to obtain quantified convergence rates.
Simple dependent pairs of exponential and uniform random variables
A. J. Lawrance; Lewis, Peter Adrian Walter
1982-01-01
A random-coefficient linear function of two independent exponential variables yielding a third exponential variable is used in the construction of simple, dependent pairs of exponential variables. By employing antithetic exponential variables, the constructions are developed to encompass negative dependency. By employing negative exponentiation, the constructions yield simple multiplicative-based models for dependent uniform pairs. The ranges of dependency allowable in the models are assessed...
LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR SUMS OF NEGATIVELY DEPENDENT RANDOM VARIABLES
Liu Li; Wan Chenggao; Feng Yanqin
2011-01-01
In this article, we obtain the large deviations and moderate deviations for negatively dependent (ND) and non-identically distributed random variables defined on (-∞, +∞). The results show that for some non-identical random variables, precise large deviations and moderate deviations remain insensitive to negative dependence structure.
Yongfeng Wu
2014-01-01
Full Text Available The authors first present a Rosenthal inequality for sequence of extended negatively dependent (END random variables. By means of the Rosenthal inequality, the authors obtain some complete moment convergence and mean convergence results for arrays of rowwise END random variables. The results in this paper extend and improve the corresponding theorems by Hu and Taylor (1997.
无
2010-01-01
This paper studies the moderate deviations of real-valued extended negatively dependent(END) random variables with consistently varying tails.The moderate deviations of partial sums are first given.The results are then used to establish the necessary and sufficient conditions for the moderate deviations of random sums under certain circumstances.
Non-uniform approximations for sums of discrete m-dependent random variables
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.
Tail dependence of random variables from ARCH and heavy tailed bilinear models
PAN; Jiazhu(潘家柱)
2002-01-01
Discussed in this paper is the dependent structure in the tails of distributions of random variables from some heavy-tailed stationary nonlinear time series. One class of models discussed is the first-order autoregressive conditional heteroscedastic (ARCH) process introduced by Engle (1982). The other class is the simple first-order bilinear models driven by heavy-tailed innovations. We give some explicit formulas for the asymptotic values of conditional probabilities used for measuring the tail dependence between two random variables from these models. Our results have significant meanings in finance.
Central limit theorem for the Banach-valued weakly dependent random variables
The central limit theorem (CLT) for the Banach-valued weakly dependent random variables is proved. In proving CLT convergence of finite-measured (i.e. cylindrical) distributions is established. A weak compactness of the family of measures generated by a certain sequence is confirmed. The continuity of the limiting field is checked
An edgeworth expansion for a sum of M-Dependent random variables
Wan Soo Rhee
1985-01-01
Full Text Available Given a sequence X1,X2,…,Xn of m-dependent random variables with moments of order 3+α (0<α≦1, we give an Edgeworth expansion of the distribution of Sσ−1(S=X1+X2+…+Xn, σ2=ES2 under the assumption that E[exp(it Sσ1] is small away from the origin. The result is of the best possible order.
The Randomized Dependence Coefficient
Lopez-Paz, David; Hennig, Philipp; Schölkopf, Bernhard
2013-01-01
We introduce the Randomized Dependence Coefficient (RDC), a measure of non-linear dependence between random variables of arbitrary dimension based on the Hirschfeld-Gebelein-R\\'enyi Maximum Correlation Coefficient. RDC is defined in terms of correlation of random non-linear copula projections; it is invariant with respect to marginal distribution transformations, has low computational cost and is easy to implement: just five lines of R code, included at the end of the paper.
Matricially free random variables
Lenczewski, Romuald
2008-01-01
We show that the operatorial framework developed by Voiculescu for free random variables can be extended to arrays of random variables whose multiplication imitates matricial multiplication. The associated notion of independence, called matricial freeness, can be viewed as a generalization of both freeness and monotone independence. At the same time, the sums of matricially free random variables, called random pseudomatrices, are closely related to Gaussian random matrices. The main results presented in this paper concern the standard and tracial central limit theorems for random pseudomatrices and the corresponding limit distributions which can be viewed as matricial generalizations of semicirle laws.
Penzlin AI
2015-10-01
Full Text Available Ana Isabel Penzlin,1 Timo Siepmann,2 Ben Min-Woo Illigens,3 Kerstin Weidner,4 Martin Siepmann4 1Institute of Clinical Pharmacology, 2Department of Neurology, University Hospital Carl Gustav Carus, Technische Universität Dresden, Dresden, Saxony, Germany; 3Department of Neurology, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA, USA; 4Department of Psychotherapy and Psychosomatic Medicine, University Hospital Carl Gustav Carus, Technische Universität Dresden, Dresden, Saxony, Germany Background and objective: In patients with alcohol dependence, ethyl-toxic damage of vasomotor and cardiac autonomic nerve fibers leads to autonomic imbalance with neurovascular and cardiac dysfunction, the latter resulting in reduced heart rate variability (HRV. Autonomic imbalance is linked to increased craving and cardiovascular mortality. In this study, we sought to assess the effects of HRV biofeedback training on HRV, vasomotor function, craving, and anxiety. Methods: We conducted a randomized controlled study in 48 patients (14 females, ages 25–59 years undergoing inpatient rehabilitation treatment. In the treatment group, patients (n=24 attended six sessions of HRV biofeedback over 2 weeks in addition to standard rehabilitative care, whereas, in the control group, subjects received standard care only. Psychometric testing for craving (Obsessive Compulsive Drinking Scale, anxiety (Symptom Checklist-90-Revised, HRV assessment using coefficient of variation of R-R intervals (CVNN analysis, and vasomotor function assessment using laser Doppler flowmetry were performed at baseline, immediately after completion of treatment or control period, and 3 and 6 weeks afterward (follow-ups 1 and 2. Results: Psychometric testing showed decreased craving in the biofeedback group immediately postintervention (OCDS scores: 8.6±7.9 post-biofeedback versus 13.7±11.0 baseline [mean ± standard deviation], P<0.05, whereas craving was unchanged at
Ming He
2015-11-01
Full Text Available We propose a random effects panel data model with both spatially correlated error components and spatially lagged dependent variables. We focus on diagnostic testing procedures and derive Lagrange multiplier (LM test statistics for a variety of hypotheses within this model. We first construct the joint LM test for both the individual random effects and the two spatial effects (spatial error correlation and spatial lag dependence. We then provide LM tests for the individual random effects and for the two spatial effects separately. In addition, in order to guard against local model misspecification, we derive locally adjusted (robust LM tests based on the Bera and Yoon principle (Bera and Yoon, 1993. We conduct a small Monte Carlo simulation to show the good finite sample performances of these LM test statistics and revisit the cigarette demand example in Baltagi and Levin (1992 to illustrate our testing procedures.
Guillaume Marrelec
Full Text Available The use of mutual information as a similarity measure in agglomerative hierarchical clustering (AHC raises an important issue: some correction needs to be applied for the dimensionality of variables. In this work, we formulate the decision of merging dependent multivariate normal variables in an AHC procedure as a Bayesian model comparison. We found that the Bayesian formulation naturally shrinks the empirical covariance matrix towards a matrix set a priori (e.g., the identity, provides an automated stopping rule, and corrects for dimensionality using a term that scales up the measure as a function of the dimensionality of the variables. Also, the resulting log Bayes factor is asymptotically proportional to the plug-in estimate of mutual information, with an additive correction for dimensionality in agreement with the Bayesian information criterion. We investigated the behavior of these Bayesian alternatives (in exact and asymptotic forms to mutual information on simulated and real data. An encouraging result was first derived on simulations: the hierarchical clustering based on the log Bayes factor outperformed off-the-shelf clustering techniques as well as raw and normalized mutual information in terms of classification accuracy. On a toy example, we found that the Bayesian approaches led to results that were similar to those of mutual information clustering techniques, with the advantage of an automated thresholding. On real functional magnetic resonance imaging (fMRI datasets measuring brain activity, it identified clusters consistent with the established outcome of standard procedures. On this application, normalized mutual information had a highly atypical behavior, in the sense that it systematically favored very large clusters. These initial experiments suggest that the proposed Bayesian alternatives to mutual information are a useful new tool for hierarchical clustering.
Barcella, William; Iorio, Maria De; Baio, Gianluca; Malone-Lee, James
2016-04-15
Lower urinary tract symptoms can indicate the presence of urinary tract infection (UTI), a condition that if it becomes chronic requires expensive and time consuming care as well as leading to reduced quality of life. Detecting the presence and gravity of an infection from the earliest symptoms is then highly valuable. Typically, white blood cell (WBC) count measured in a sample of urine is used to assess UTI. We consider clinical data from 1341 patients in their first visit in which UTI (i.e. WBC ≥ 1) is diagnosed. In addition, for each patient, a clinical profile of 34 symptoms was recorded. In this paper, we propose a Bayesian nonparametric regression model based on the Dirichlet process prior aimed at providing the clinicians with a meaningful clustering of the patients based on both the WBC (response variable) and possible patterns within the symptoms profiles (covariates). This is achieved by assuming a probability model for the symptoms as well as for the response variable. To identify the symptoms most associated to UTI, we specify a spike and slab base measure for the regression coefficients: this induces dependence of symptoms selection on cluster assignment. Posterior inference is performed through Markov Chain Monte Carlo methods. PMID:26536840
Strong Decomposition of Random Variables
Hoffmann-Jørgensen, Jørgen; Kagan, Abram M.; Pitt, Loren D.;
2007-01-01
A random variable X is stongly decomposable if X=Y+Z where Y=Φ(X) and Z=X-Φ(X) are independent non-degenerated random variables (called the components). It is shown that at least one of the components is singular, and we derive a necessary and sufficient condition for strong decomposability of a...... discrete random variable....
WEAK UNCORRELATEDNESS OF RANDOM VARIABLES
Sofiya Ostrovska
2006-01-01
New measures of independence for n random variables, based on their moments, are studied. A scale of degrees of independence for random variables which starts with uncorrelatedness (for n = 2) and finishes at independence is constructed. The scale provides a countable linearly ordered set of measures of independence.
Students' Misconceptions about Random Variables
Kachapova, Farida; Kachapov, Ilias
2012-01-01
This article describes some misconceptions about random variables and related counter-examples, and makes suggestions about teaching initial topics on random variables in general form instead of doing it separately for discrete and continuous cases. The focus is on post-calculus probability courses. (Contains 2 figures.)
Symmetrization of binary random variables
Kagan, Abram; Mallows, Colin L.; Shepp, Larry A.; Vanderbei, Robert J.; Vardi, Yehuda
1999-01-01
A random variable [math] is called an independent symmetrizer of a given random variable [math] if (a) it is independent of [math] and (b) the distribution of [math] is symmetric about [math] . In cases where the distribution of [math] is symmetric about its mean, it is easy to see that the constant random variable [math] is a minimum-variance independent symmetrizer. Taking [math] to have the same distribution as [math] clearly produces a symmetric sum, but it may not be of minimum variance....
Complete Convergence for Weighted Sums of WOD Random Variables
ZHANG Ying; ZHANG Yu; SHEN Ai-ting
2016-01-01
In this article, we study the complete convergence for weighted sums of widely orthant dependent random variables. By using the exponential probability inequality, we establish a complete convergence result for weighted sums of widely orthant dependent ran-dom variables under mild conditions of weights and moments. The result obtained in the paper generalizes the corresponding ones for independent random variables and negatively dependent random variables.
On Sums of Conditionally Independent Subexponential Random Variables
Foss, Serguei; Richards, Andrew
2008-01-01
The asymptotic tail behaviour of sums of independent subexponential random variables is well understood, one of the main characteristics being the principle of the single big jump. We study the case of dependent subexponential random variables, for both deterministic and random sums, using a fresh approach, by considering conditional independence structures on the random variables. We seek sufficient conditions for the results of the theory with independent random variables still to hold. For...
Contextuality is about identity of random variables
Contextual situations are those in which seemingly ‘the same’ random variable changes its identity depending on the conditions under which it is recorded. Such a change of identity is observed whenever the assumption that the variable is one and the same under different conditions leads to contradictions when one considers its joint distribution with other random variables (this is the essence of all Bell-type theorems). In our Contextuality-by-Default approach, instead of asking why or how the conditions force ‘one and the same’ random variable to change ‘its’ identity, any two random variables recorded under different conditions are considered different ‘automatically.’ They are never the same, nor are they jointly distributed, but one can always impose on them a joint distribution (probabilistic coupling). The special situations when there is a coupling in which these random variables are equal with probability 1 are considered noncontextual. Contextuality means that such couplings do not exist. We argue that the determination of the identity of random variables by conditions under which they are recorded is not a causal relationship and cannot violate laws of physics. (paper)
Contextuality is about identity of random variables
Dzhafarov, Ehtibar N.; Kujala, Janne V.
2014-12-01
Contextual situations are those in which seemingly ‘the same’ random variable changes its identity depending on the conditions under which it is recorded. Such a change of identity is observed whenever the assumption that the variable is one and the same under different conditions leads to contradictions when one considers its joint distribution with other random variables (this is the essence of all Bell-type theorems). In our Contextuality-by-Default approach, instead of asking why or how the conditions force ‘one and the same’ random variable to change ‘its’ identity, any two random variables recorded under different conditions are considered different ‘automatically.’ They are never the same, nor are they jointly distributed, but one can always impose on them a joint distribution (probabilistic coupling). The special situations when there is a coupling in which these random variables are equal with probability 1 are considered noncontextual. Contextuality means that such couplings do not exist. We argue that the determination of the identity of random variables by conditions under which they are recorded is not a causal relationship and cannot violate laws of physics.
RANDOM VARIABLE WITH FUZZY PROBABILITY
吕恩琳; 钟佑明
2003-01-01
Mathematic description about the second kind fuzzy random variable namely the random variable with crisp event-fuzzy probability was studied. Based on the interval probability and using the fuzzy resolution theorem, the feasible condition about a probability fuzzy number set was given, go a step further the definition arid characters of random variable with fuzzy probability ( RVFP ) and the fuzzy distribution function and fuzzy probability distribution sequence of the RVFP were put forward. The fuzzy probability resolution theorem with the closing operation of fuzzy probability was given and proved. The definition and characters of mathematical expectation and variance of the RVFP were studied also. All mathematic description about the RVFP has the closing operation for fuzzy probability, as a result, the foundation of perfecting fuzzy probability operation method is laid.
A Measure of Monotonicity of two Random Variables
Ilias Kachapov; Farida Kachapova
2012-01-01
Problem statement: When analyzing random variables it was useful to measure the degree of their monotone dependence or compare pairs of random variables with respect to their monotonicity. Existing coefficients measure general or linear dependence of random variables. Developing a measure of monotonicity was useful for practical applications as well as for general theory, since monotonicity was an important type of dependence. Approach: Existing measures of dependence are briefly reviewed. Th...
De Mei YUAN; Jun AN
2012-01-01
Both residual Cesàro alpha-integrability (RCI(α)) and strongly residual Cesàro alphaintegrability (SRCI(α)) are two special kinds of extensions to uniform integrability,and both asymptotically almost negative association (AANA) and asymptotically quadrant sub-independence (AQSI)are two special kinds of dependence structures.By relating the RCI(α) property as well as the SRCI(α)property with dependence condition AANA or AQSI,we formulate some tail-integrability conditions under which for appropriate α the RCI(α) property yields L1-convergence results and the SRCI(α)property yields strong laws of large numbers,which is the continuation of the corresponding literature.
Randomness and Earth climate variability
Levinshtein, Michael E; Dmitriev, Alexander P; Shmakov, Pavel M
2015-01-01
Paleo-Sciences including palaeoclimatology and palaeoecology have accumulated numerous records related to climatic changes. The researchers have usually tried to identify periodic and quasi-periodic processes in these paleoscientific records. In this paper, we show that this analysis is incomplete. As follows from our results, random processes, namely processes with a single-time-constant (noise with a Lorentzian noise spectrum), play a very important and, perhaps, a decisive role in numerous natural phenomena. For several of very important natural phenomena the characteristic time constants are very similar and equal to (5-8)x10^3 years. However, this value is not universal. For example, the spectral density fluctuations of the atmospheric radiocarbon 14C are characterized by a Lorentzian with time constant 300 years. The frequency dependence of spectral density fluctuations for benthic 18O records contains two Lorentzians with time constans 8000 years and > 105 years.
The geometry of proper quaternion random variables
Bihan, Nicolas le
2015-01-01
Properness of a quaternion random variable is related to the symmetries of its probability density function in $4D$ space. Thus, properness should be defined with respect to the most general isometries in $4D$, i.e. rotations from $SO(4)$. Based on this, we propose a new definition of properness, namely the $(\\alpha,\\beta)$-properness, for quaternion random variables using invariance property under the action of the rotation group $SO(4)$. This new definition generalizes previously introduced...
Asymptotics for Associated Random Variables
Oliveira, Paulo Eduardo
2012-01-01
The book concerns the notion of association in probability and statistics. Association and some other positive dependence notions were introduced in 1966 and 1967 but received little attention from the probabilistic and statistics community. The interest in these dependence notions increased in the last 15 to 20 years, and many asymptotic results were proved and improved. Despite this increased interest, characterizations and results remained essentially scattered in the literature published in different journals. The goal of this book is to bring together the bulk of these results, presenting
Delocalization for Random Landau Hamiltonians with Unbounded Random Variables
Germinet, François; Mandy, Benoît
2009-01-01
In this note we prove the existence of a localization/delocalization transition for Landau Hamiltonians randomly perturbed by an electric potential with unbounded amplitude. In particular, with probability one, no Landau gaps survive as the random potential is turned on, the gaps close, filling up partly with localized states. A minimal rate of transport is exhibited in the region of delocalization. To do so, we exploit the a priori quantization of the Hall conductance and extend recent Wegner estimates to the case of unbounded random variables.
Probability Inequalities for Extended Negatively Dep endent Random Variables and Their Applications
TANG Xiao-feng
2014-01-01
Some probability inequalities are established for extended negatively dependent (END) random variables. The inequalities extend some corresponding ones for negatively associated random variables and negatively orthant dependent random variables. By using these probability inequalities, we further study the complete convergence for END random variables. We also obtain the convergence rate O(n−1/2 ln1/2 n) for the strong law of large numbers, which generalizes and improves the corresponding ones for some known results.
Polynomial chaos expansion with random and fuzzy variables
Jacquelin, E.; Friswell, M. I.; Adhikari, S.; Dessombz, O.; Sinou, J.-J.
2016-06-01
A dynamical uncertain system is studied in this paper. Two kinds of uncertainties are addressed, where the uncertain parameters are described through random variables and/or fuzzy variables. A general framework is proposed to deal with both kinds of uncertainty using a polynomial chaos expansion (PCE). It is shown that fuzzy variables may be expanded in terms of polynomial chaos when Legendre polynomials are used. The components of the PCE are a solution of an equation that does not depend on the nature of uncertainty. Once this equation is solved, the post-processing of the data gives the moments of the random response when the uncertainties are random or gives the response interval when the variables are fuzzy. With the PCE approach, it is also possible to deal with mixed uncertainty, when some parameters are random and others are fuzzy. The results provide a fuzzy description of the response statistical moments.
Product of n independent uniform random variables
Dettmann, Carl P.; Georgiou, Orestis
2009-01-01
Abstract We give an alternative proof of a useful formula for calculating the probability density function of the product of n uniform, independently and identically distributed random variables. Ishihara (2002, in Japanese) proves the result by induction; here we use Fourier analysis and contour integral methods which provide a more intuitive explanation of how the convolution theorem acts in this case. correspondance: Corresponding author. ...
The random-variable canonical distribution
An alternative interpretation to Gibbs' concept of the canonical distribution for an ensemble of systems in statistical equilibrium is proposed. Whereas Gibbs' theory is based upon a consideration of systems subject to dynamical law, the present analysis relies neither on the classical equations of motion nor makes use of any a priori probability of a complexion; rather, it makes avail of the basic algebra of random variables and, specifically, invokes the law of large numbers. Thereby, a canonical distribution is derived which describes a macrosystem in probabilistic, rather than deterministic, terms, and facilitates the understanding of energy fluctuations which occur in macrosystems at an overall constant ensemble temperature. A discussion is given of a modified form of the Gibbs canonical distribution which takes full account of the effects of random energy fluctuations. It is demonstrated that the results from this modified analysis are entirely consonant with those derived from the random-variable approach. (author)
LARGE DEVIATIONS AND MODERATE DEVIATIONS FOR m-NEGATIVELY ASSOCIATED RANDOM VARIABLES
Hu Yijun; Ming Ruixing; Yang Wenquan
2007-01-01
M-negatively associated random variables, which generalizes the classical one of negatively associated random variables and includes m-dependent sequences as its particular case, are introduced and studied. Large deviation principles and moderate deviation upper bounds for stationary m-negatively associated random variables are proved.Kolmogorov-type and Marcinkiewicz-type strong laws of large numbers as well as the three series theorem for m-negatively associated random variables are also given.
Inequalities for Walsh like random variables
D. Hajela
1990-01-01
Let (Xn)nÃ¢Â‰Â¥1 be a sequence of mean zero independent random variables. Let Wk={Ã¢ÂˆÂj=1kXij|1Ã¢Â‰Â¤i10 and let C(p,m)=16(52p2pÃ¢ÂˆÂ’1)mÃ¢ÂˆÂ’1plogp(KÃŽÂ´)m for 1
Lr Convergence for Arrays of Rowwise Negatively Sup eradditive Dep endent Random Variables
ZHU Hua-yan; SHEN Ai-ting; ZHANG Ying
2016-01-01
Let {Xnk, k≥1, n≥1} be an array of rowwise negatively superadditive depen-dent random variables and {an, n ≥ 1} be a sequence of positive real numbers such that an ↑ ∞. Under some suitable conditions, Lr convergence of a1n 1max≤j≤n ied. The results obtained in this paper generalize and improve some corresponding ones for negatively associated random variables and independent random variables. fl fl fl fl jP k=1 Xnk fl fl flfl is stud-ied. The results obtained in this paper generalize and improve some corresponding ones for negatively associated random variables and independent random variables.
Strong Laws of Large Numbers for Arrays of Rowwise NA and LNQD Random Variables
Jiangfeng Wang
2011-01-01
Full Text Available Some strong laws of large numbers and strong convergence properties for arrays of rowwise negatively associated and linearly negative quadrant dependent random variables are obtained. The results obtained not only generalize the result of Hu and Taylor to negatively associated and linearly negative quadrant dependent random variables, but also improve it.
Probabilistic norms and statistical convergence of random variables
Mohamad Rafi Segi Rahmat
2009-03-01
Full Text Available The paper extends certain stochastic convergence of sequences of Rk -valued random variables (namely, the convergence in probability, in Lp and almost surely to the context of E-valued random variables.
Summability of Double Independent Random Variables
Ekrem Savaş; Richard F. Patterson
2008-01-01
We will examine double sequence to double sequence transformation of independent identically distribution random variables with respect to four-dimensional summability matrix methods. The main goal of this paper is the presentation of the following theorem. If maxÃ¢ÂÂ¡k,l|am,n,k,l|=maxÃ¢ÂÂ¡k,l|am,kan,l|=O(mÃ¢ÂˆÂ’ÃŽÂ³1)O(nÃ¢ÂˆÂ’ÃŽÂ³2), ÃŽÂ³1,ÃŽÂ³2>0, then E|XÃ¢ÂŒÂ£|1+1/ÃŽÂ³1
Almost Sure Convergence Theorem and Strong Stability for Weighted Sums of NSD Random Variables
Yan SHEN; Xue Jun WANG; Wen Zhi YANG; Shu He HU
2013-01-01
In this paper,Kolmogorov-type inequality for negatively superadditive dependent (NSD)random variables is established.By using this inequality,we obtain the almost sure convergence for NSD sequences,which extends the corresponding results for independent sequences and negatively associated (NA) sequences.In addition,the strong stability for weighted sums of NSD random variables is studied.
Summability of Double Independent Random Variables
Ekrem Savaş
2008-09-01
Full Text Available We will examine double sequence to double sequence transformation of independent identically distribution random variables with respect to four-dimensional summability matrix methods. The main goal of this paper is the presentation of the following theorem. If maxÃ¢ÂÂ¡k,l|am,n,k,l|=maxÃ¢ÂÂ¡k,l|am,kan,l|=O(mÃ¢ÂˆÂ’ÃŽÂ³1O(nÃ¢ÂˆÂ’ÃŽÂ³2, ÃŽÂ³1,ÃŽÂ³2>0, then E|XÃ¢ÂŒÂ£|1+1/ÃŽÂ³1<Ã¢ÂˆÂž and E|XÃ¢ÂŒÂ£Ã¢ÂŒÂ£|1+1/ÃŽÂ³2<Ã¢ÂˆÂž imply that Ym,nÃ¢Â†Â’ÃŽÂ¼ almost sure P-convergence.
Probability, random variables, and random processes theory and signal processing applications
Shynk, John J
2012-01-01
Probability, Random Variables, and Random Processes is a comprehensive textbook on probability theory for engineers that provides a more rigorous mathematical framework than is usually encountered in undergraduate courses. It is intended for first-year graduate students who have some familiarity with probability and random variables, though not necessarily of random processes and systems that operate on random signals. It is also appropriate for advanced undergraduate students who have a strong mathematical background. The book has the following features: Several app
PROBABILITY INEQUALITIES FOR SUMS OF INDEPENDENT UNBOUNDED RANDOM VARIABLES
张涤新; 王志诚
2001-01-01
The tail probability inequalities for the sum of independent unbounded random variables on a probability space ( Ω , T, P) were studied and a new method was proposed to treat the sum of independent unbounded random variables by truncating the original probability space (Ω, T, P ). The probability exponential inequalities for sums of independent unbounded random variables were given. As applications of the results, some interesting examples were given. The examples show that the method proposed in the paper and the results of the paper are quite useful in the study of the large sample properties of the sums of independent unbounded random variables.
Environment-dependent continuous time random walk
Lin Fang; Bao Jing-Dong
2011-01-01
A generalized continuous time random walk model which is dependent on environmental damping is proposed in which the two key parameters of the usual random walk theory:the jumping distance and the waiting time, are replaced by two new ones:the pulse velocity and the flight time. The anomalous diffusion of a free particle which is characterized by the asymptotical mean square displacement ～tα is realized numerically and analysed theoretically, where the value of the power index a is in a region of 0<α<2. Particularly, the damping leads to a sub-diffusion when the impact velocities are drawn from a Gaussian density function and the super-diffusive effect is related to statistical extremes, which are called rare-though-dominant events.
Cardinality-dependent Variability in Orthogonal Variability Models
Mærsk-Møller, Hans Martin; Jørgensen, Bo Nørregaard
2012-01-01
During our work on developing and running a software product line for eco-sustainable greenhouse-production software tools, which currently have three products members we have identified a need for extending the notation of the Orthogonal Variability Model (OVM) to support what we refer to as...... cardinality range dependencies. The cardinality-range-dependency type enables expressing that the binding of a certain number of variants to a variation point can influence variability in other places in the model. In other words, we acknowledge that variability can be influenced, not necessarily by the...
Moment inequalities for the partial sums of random variables
杨善朝
2001-01-01
This paper discusses the conditions under which Rosenthal type inequality is obtained from M-Z-B type inequality. And M-Z-B type inequality is proved for a wide class of random variables. Hence Rosenthal type inequalities for some classes of random variables are obtained.
An Inequality for the Sum of Independent Bounded Random Variables
Dance, Christopher R.
2012-01-01
We give a simple inequality for the sum of independent bounded random variables. This inequality improves on the celebrated result of Hoeffding in a special case. It is optimal in the limit where the sum tends to a Poisson random variable.
On the product and ratio of Bessel random variables
Saralees Nadarajah
2005-01-01
Full Text Available The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product |XY| and the ratio |X/Y| are derived when X and Y are independent Bessel function random variables. An application of the results is provided by tabulating the associated percentage points.
Quantifying Redundant Information in Predicting a Target Random Variable
Virgil Griffith
2015-07-01
Full Text Available We consider the problem of defining a measure of redundant information that quantifies how much common information two or more random variables specify about a target random variable. We discussed desired properties of such a measure, and propose new measures with some desirable properties.
Communication Requirements for Generating Correlated Random Variables
Cuff, Paul
2008-01-01
Two familiar notions of correlation are rediscovered as extreme operating points for simulating a discrete memoryless channel, in which a channel output is generated based only on a description of the channel input. Wyner's "common information" coincides with the minimum description rate needed. However, when common randomness independent of the input is available, the necessary description rate reduces to Shannon's mutual information. This work characterizes the optimal tradeoff between the amount of common randomness used and the required rate of description.
On the minimum of independent geometrically distributed random variables
Ciardo, Gianfranco; Leemis, Lawrence M.; Nicol, David
1994-01-01
The expectations E(X(sub 1)), E(Z(sub 1)), and E(Y(sub 1)) of the minimum of n independent geometric, modifies geometric, or exponential random variables with matching expectations differ. We show how this is accounted for by stochastic variability and how E(X(sub 1))/E(Y(sub 1)) equals the expected number of ties at the minimum for the geometric random variables. We then introduce the 'shifted geometric distribution' and show that there is a unique value of the shift for which the individual shifted geometric and exponential random variables match expectations both individually and in the minimums.
Central limit theorem for a class of globally correlated random variables
Budini, Adrián A.
2016-06-01
The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in the presence of strong correlations between the added random contributions. Here, we study this problem for similar interchangeable globally correlated random variables. Under these conditions, a hierarchical set of equations is derived for the conditional transition probabilities. This result allows us to define different classes of memory mechanisms that depend on a symmetric way on all involved variables. Depending on the correlation mechanisms and statistics of the single variables, the corresponding sums are characterized by distinct probability densities. For a class of urn models it is also possible to characterize their domain of attraction, which, as in the standard case, is parametrized by the probability density of each random variable. Symmetric and asymmetric q -Gaussian attractors (q <1 ) arise in a particular two-state case of these urn models.
Randomly weighted sums of subexponential random variables with application to ruin theory
Q. Tang; G. Tsitsiashvili
2003-01-01
Let {X k , 1 k n} be n independent and real-valued random variables with common subexponential distribution function, and let {k, 1 k n} be other n random variables independent of {X k , 1 k n} and satisfying a k b for some 0 < a b < for all 1 k n. This paper proves that the asymptotic relations P (
刘艳; 胡亦钧
2003-01-01
We prove large deviation results on the partial and random sums Sn = ∑ni=1 Xi, n≥1; S(t) =∑N(t)i=1 Xi, t≥0, where {N(t);t≥0} are non-negative integer-valued random variables and {Xn;n≥1} areindependent non-negative random variables with distribution, Fn, of Xn, independent of {N(t); t≥0}. Specialattention is paid to the distribution of dominated variation.
Limiting Behavior of Weighted Sums of NOD Random Variables
De Hua QIU; Ping Yan CHEN
2011-01-01
The strong laws of large numbers and laws of the single logarithm for weighted sums of NOD random variables are established.The results presented generalize the corresponding results of Chen and Gan [5]in independent sequence case.
Designing neural networks that process mean values of random variables
We develop a class of neural networks derived from probabilistic models posed in the form of Bayesian networks. Making biologically and technically plausible assumptions about the nature of the probabilistic models to be represented in the networks, we derive neural networks exhibiting standard dynamics that require no training to determine the synaptic weights, that perform accurate calculation of the mean values of the relevant random variables, that can pool multiple sources of evidence, and that deal appropriately with ambivalent, inconsistent, or contradictory evidence. - Highlights: • High-level neural computations are specified by Bayesian belief networks of random variables. • Probability densities of random variables are encoded in activities of populations of neurons. • Top-down algorithm generates specific neural network implementation of given computation. • Resulting “neural belief networks” process mean values of random variables. • Such networks pool multiple sources of evidence and deal properly with inconsistent evidence
Random Forests for Ordinal Response Data: Prediction and Variable Selection
Janitza, Silke; Tutz, Gerhard; Boulesteix, Anne-Laure
2014-01-01
The random forest method is a commonly used tool for classification with high-dimensional data that is able to rank candidate predictors through its inbuilt variable importance measures (VIMs). It can be applied to various kinds of regression problems including nominal, metric and survival response variables. While classification and regression problems using random forest methodology have been extensively investigated in the past, there seems to be a lack of literature on handling ordinal re...
Some Limit Theorems for Negatively Associated Random Variables
Yu Miao; Wenfei Xu; Shanshan Chen; Andre Adler
2014-08-01
Let $\\{X_n,n≥ 1\\}$ be a sequence of negatively associated random variables. The aim of this paper is to establish some limit theorems of negatively associated sequence, which include the $L^p$-convergence theorem and Marcinkiewicz–Zygmund strong law of large numbers. Furthermore, we consider the strong law of sums of order statistics, which are sampled from negatively associated random variables.
Exponential Inequalities for Positively Associated Random Variables and Applications
Yang Shanchao
2008-01-01
Full Text Available Abstract We establish some exponential inequalities for positively associated random variables without the boundedness assumption. These inequalities improve the corresponding results obtained by Oliveira (2005. By one of the inequalities, we obtain the convergence rate for the case of geometrically decreasing covariances, which closes to the optimal achievable convergence rate for independent random variables under the Hartman-Wintner law of the iterated logarithm and improves the convergence rate derived by Oliveira (2005 for the above case.
Problems Identifying Independent and Dependent Variables
Leatham, Keith R.
2012-01-01
This paper discusses one step from the scientific method--that of identifying independent and dependent variables--from both scientific and mathematical perspectives. It begins by analyzing an episode from a middle school mathematics classroom that illustrates the need for students and teachers alike to develop a robust understanding of…
PaCAL: A Python Package for Arithmetic Computations with Random Variables
Marcin Korze?
2014-05-01
Full Text Available In this paper we present PaCAL, a Python package for arithmetical computations on random variables. The package is capable of performing the four arithmetic operations: addition, subtraction, multiplication and division, as well as computing many standard functions of random variables. Summary statistics, random number generation, plots, and histograms of the resulting distributions can easily be obtained and distribution parameter ?tting is also available. The operations are performed numerically and their results interpolated allowing for arbitrary arithmetic operations on random variables following practically any probability distribution encountered in practice. The package is easy to use, as operations on random variables are performed just as they are on standard Python variables. Independence of random variables is, by default, assumed on each step but some computations on dependent random variables are also possible. We demonstrate on several examples that the results are very accurate, often close to machine precision. Practical applications include statistics, physical measurements or estimation of error distributions in scienti?c computations.
New Results On the Sum of Two Generalized Gaussian Random Variables
Soury, Hamza
2015-01-01
We propose in this paper a new method to compute the characteristic function (CF) of generalized Gaussian (GG) random variable in terms of the Fox H function. The CF of the sum of two independent GG random variables is then deduced. Based on this results, the probability density function (PDF) and the cumulative distribution function (CDF) of the sum distribution are obtained. These functions are expressed in terms of the bivariate Fox H function. Next, the statistics of the distribution of the sum, such as the moments, the cumulant, and the kurtosis, are analyzed and computed. Due to the complexity of bivariate Fox H function, a solution to reduce such complexity is to approximate the sum of two independent GG random variables by one GG random variable with suitable shape factor. The approximation method depends on the utility of the system so three methods of estimate the shape factor are studied and presented.
Applying Free Random Variables to Random Matrix Analysis of Financial Data
Burda, Z; Jurkiewicz, J; Nowak, M A; Papp, G; Zahed, I
2006-01-01
We apply the concept of free random variables to correlated Wishart random matrix models. We give a comprehensive rederivation of various spectral densities for a number of financial covariance matrices involving stocks returns without and with exponentially weighted moving averages. We show through simple models how to identify the pertinent underlying correlations. We extend our results to Levy-Wishart random matrix models whereby the risk factors are heavy tailed.
A Random Variable Related to the Inversion Vector of a Partial Random Permutation
Laghate, Kavita; Deshpande, M. N.
2005-01-01
In this article, we define the inversion vector of a permutation of the integers 1, 2,..., n. We set up a particular kind of permutation, called a partial random permutation. The sum of the elements of the inversion vector of such a permutation is a random variable of interest.
Random Time Dependent Resistance Analysis on Reinforced Concrete Structures
GUAN Chang-sheng; WU Ling
2002-01-01
The analysis method on random time dependence of reinforced concrete material is introduced,the effect mechanism on reinforced concrete are discussed, and the random time dependence resistance of reinforced concrete is studied. Furthermore, the corrosion of steel bar in reinforced concrete structures is analyzed. A practical statistical method of evaluating the random time dependent resistance, which includes material, structural size and calculation influence, is also established. In addition, an example of predicting random time dependent resistance of reinforced concrete structural element is given.
Age-dependent branching processes in random environments
2008-01-01
We consider an age-dependent branching process in random environments. The environments are represented by a stationary and ergodic sequence ξ = (ξ0,ξ1,...) of random variables. Given an environment ξ, the process is a non-homogenous Galton-Watson process, whose particles in n-th generation have a life length distribution G(ξn) on R+, and reproduce independently new particles according to a probability law p(ξn) on N. Let Z(t) be the number of particles alive at time t. We first find a characterization of the conditional probability generating function of Z(t) (given the environment ξ) via a functional equation, and obtain a criterion for almost certain extinction of the process by comparing it with an embedded Galton-Watson process. We then get expressions of the conditional mean EξZ(t) and the global mean EZ(t), and show their exponential growth rates by studying a renewal equation in random environments.
Discrete Random Contention System with Variable Packet Length
Yingying Guo
2013-07-01
Full Text Available The paper researches the random contention system in-depth using the average cycle method, then gets the formulas of the systemic throughput, free rate and collision rate with variable packet length. The simulation results verify the correctness of the theory, meanwhile, gets some conclusions that the different arrival rate G is how to affect the main source of the throughput with variable packet length. It has some researching significance.
Repeated Sprints: An Independent Not Dependent Variable.
Taylor, Jonathan M; Macpherson, Tom W; Spears, Iain R; Weston, Matthew
2016-07-01
The ability to repeatedly perform sprints has traditionally been viewed as a key performance measure in team sports, and the relationship between repeated-sprint ability (RSA) and performance has been explored extensively. However, when reviewing the repeated-sprint profile of team-sports match play it appears that the occurrence of repeated-sprint bouts is sparse, indicating that RSA is not as important to performance as commonly believed. Repeated sprints are, however, a potent and time-efficient training strategy, effective in developing acceleration, speed, explosive leg power, aerobic power, and high-intensity-running performance--all of which are crucial to team-sport performance. As such, we propose that repeated-sprint exercise in team sports should be viewed as an independent variable (eg, a means of developing fitness) as opposed to a dependent variable (eg, a means of assessing fitness/performance). PMID:27197118
Reduction of the Random Variables of the Turbulent Wind Field
Sichani, Mahdi Teimouri; Nielsen, Søren R.K.
Applicability of the Probability Density Evolution Method (PDEM) for realizing evolution of the probability density for the wind turbines has rather strict bounds on the basic number of the random variables involved in the model. The efficiency of most of the Advanced Monte Carlo (AMC) methods, i...
ADORAVA - A computer code to sum random variables
The ADORAVA computer code was carried out aiming to determine the moments of random variable sum distribution when moments are known. The ADORAVA computer code was developed to be applied in probabilistic safety analysis, more specifically for uncertainty propagation in fault trees. The description of ADORAVA algorithm, input, examples and the output of compiled code are presented. (M.C.K.)
Some Limit Theorems for Weighted Sums of Random Variable Fields
无
2006-01-01
Let{X-n,-n∈Nd} be a field of Banach space valued random variables, 0 ＜r＜p≤2 and{a-n,-k,(-n,-k)∈Nd×Nd,-k≤-n} a triangular array of real numbers, where Nd is the d-dimensional lattice(d≥1). Under the minimal condition that {‖X-n‖r,-n∈Nd} is {|a-n,-k|r,(-n,-k)} ∈Nd×Nd,-k≤-n}-uniformly integrable, we show that ∑(-k≤-n)(a-n,-kX-k)Lr(or a.s.)→0 as |-n|→∞. In the above, if 0＜r＜1, the random variables are not needed to be independent. If 1≤r＜p≤2, and Banach space valued random variables are independent with mean zero we assume the Banach space is of type p. If 1≤r＜p≤2 and Banach space valued random variables are not independent we assume the Banach space is p-smoothable.
Gamma distributed random variables and their semi-quantum operators
We first introduce the joint semi-quantum operators of a finite family of random variables having finite moments of all orders. We then use the semi-quantum operators to characterize the one-dimensional Gamma and Gaussian distributions in terms of their commutators
Generation of correlated finite alphabet waveforms using gaussian random variables
Ahmed, Sajid
2016-01-13
Various examples of methods and systems are provided for generation of correlated finite alphabet waveforms using Gaussian random variables in, e.g., radar and communication applications. In one example, a method includes mapping an input signal comprising Gaussian random variables (RVs) onto finite-alphabet non-constant-envelope (FANCE) symbols using a predetermined mapping function, and transmitting FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The FANCE waveforms can be based upon the mapping of the Gaussian RVs onto the FANCE symbols. In another example, a system includes a memory unit that can store a plurality of digital bit streams corresponding to FANCE symbols and a front end unit that can transmit FANCE waveforms through a uniform linear array of antenna elements to obtain a corresponding beampattern. The system can include a processing unit that can encode the input signal and/or determine the mapping function.
Random variability explains apparent global clustering of large earthquakes
Michael, A.J.
2011-01-01
The occurrence of 5 Mw ≥ 8.5 earthquakes since 2004 has created a debate over whether or not we are in a global cluster of large earthquakes, temporarily raising risks above long-term levels. I use three classes of statistical tests to determine if the record of M ≥ 7 earthquakes since 1900 can reject a null hypothesis of independent random events with a constant rate plus localized aftershock sequences. The data cannot reject this null hypothesis. Thus, the temporal distribution of large global earthquakes is well-described by a random process, plus localized aftershocks, and apparent clustering is due to random variability. Therefore the risk of future events has not increased, except within ongoing aftershock sequences, and should be estimated from the longest possible record of events.
Problems of variance reduction in the simulation of random variables
The definition of the uniform linear generator is given and some of the mostly used tests to evaluate the uniformity and the independence of the obtained determinations are listed. The problem of calculating, through simulation, some moment W of a random variable function is taken into account. The Monte Carlo method enables the moment W to be estimated and the estimator variance to be obtained. Some techniques for the construction of other estimators of W with a reduced variance are introduced
Entropy power inequality for a family of discrete random variables
Sharma, Naresh; Muthukrishnan, Siddharth
2010-01-01
It is known that the Entropy Power Inequality (EPI) always holds if the random variables have density. Not much work has been done to identify discrete distributions for which the inequality holds with the differential entropy replaced by the discrete entropy. Harremo\\"{e}s and Vignat showed that it holds for the pair (B(m,p), B(n,p)), m,n \\in \\mathbb{N}, (where B(n,p) is a Binomial distribution with n trials each with success probability p) for p = 0.5. In this paper, we considerably expand the set of Binomial distributions for which the inequality holds and, in particular, identify n_0(p) such that for all m,n \\geq n_0(p), the EPI holds for (B(m,p), B(n,p)). We further show that the EPI holds for the discrete random variables that can be expressed as the sum of n independent identical distributed (IID) discrete random variables for large n.
A Stepwise Approach of Finding Dependent Variables via Coefficient of Intrinsic Dependence.
Hsiao, Ya-Chun; Liu, Li-Yu Daisy
2016-01-01
The coefficient of intrinsic dependence (CID) is capable of determining associations among variables without making distributional or functional assumptions regarding random variables. In this study, we developed the partial coefficient of intrinsic dependence (pCID) to facilitate the step-by-step selection of variables that are relevant to a target variable. The strategy of selecting relevant variables using the CID along with the pCID can eliminate interference from other relevant variables. From simulation results, we observed that the proposed method is more sensitive to curvilinearity and more specific to linearity than the combination of Pearsons correlation coefficient and the partial correlation coefficient (PCC/pPCC). This property may provide the opportunity to index different levels of curvilinearity according to CID/pCID outcomes. In practice trials conducted using publicly available microarray data, the CID/pCID procedure successfully identified cold-responsive genes related to three C-repeat binding factors, and was especially effective at identifying some sample-specific gene-gene interactions. Therefore, the proposed strategy may be beneficial in meta-analysis to distinguish general forms of relationships from the noise. PMID:26645623
On the behavior of the product of independent random variables
无
2006-01-01
For two independent non-negative random variables X and Y, we treat X as the initial variable of major importance and Y as a modifier (such as the interest rate of a portfolio).Stability in the tail behaviors of the product compared with that of the original variable X is of practical interests. In this paper, we study the tail behaviors of the product XY when the distribution of X belongs to the classes L and S, respectively. Under appropriate conditions, we show that the distribution of the product XY is in the same class as X when X belongs to class L or S, in other words, classes L and S are stable under some mild conditions on the distribution of Y. We also show that if the distribution of X is in class L(γ) (γ＞ 0) and continuous, then the product XY is in L if and only if Y is unbounded.
Partial summations of stationary sequences of non-Gaussian random variables
Mohr, Gunnar; Ditlevsen, Ove Dalager
1996-01-01
The distribution of the sum of a finite number of identically distributed random variables is in many cases easily determined given that the variables are independent. The moments of any order of the sum can always be expressed by the moments of the single term without computational problems...... lognormal variables or polynomials of standard Gaussian variables. The dependency structure is induced by specifying the autocorrelation structure of the sequence of standard Gaussian variables. Particularly useful polynomials are the Winterstein approximations that distributionally fit with non......-Gaussian variables up to the moments of the fourth order [Winterstein, S. R. Nonlinear vibration models for extremes and fatigue. J. Engng Mech. ASCE 114 (1988) 1772-1790](1). A method to obtain the Winterstein approximation to a partial sum of a sequence of Winterstein approximations is explained and results are...
Moderate Deviations for Random Sums of Heavy-Tailed Random Variables
Fu Qing GAO
2007-01-01
Let{Xn ;n ≥ 1}be a sequence of independent non-negative random variables with commondistribution function F having extended regularly varying tail and finite mean μ = E(X1) and let{N(t);t≥0}be a random process taking non-negative integer values with finite mean λ(t) = E(N(t))x) uniformly for x ∈[γb(t),∞) are obtained,where γ 0 and b(t) can be taken to be a positive functionwith lim t→∞ b(t)/λ(t) = 0.
Casabán, M.-C.; Cortés, J.-C.; Romero, J.-V.; Roselló, M.-D.
2015-07-01
This paper presents a full probabilistic description of the solution of random SI-type epidemiological models which are based on nonlinear differential equations. This description consists of determining: the first probability density function of the solution in terms of the density functions of the diffusion coefficient and the initial condition, which are assumed to be independent random variables; the expectation and variance functions of the solution as well as confidence intervals and, finally, the distribution of time until a given proportion of susceptibles remains in the population. The obtained formulas are general since they are valid regardless the probability distributions assigned to the random inputs. We also present a pair of illustrative examples including in one of them the application of the theoretical results to model the diffusion of a technology using real data.
Moment Estimation Inequalities Based on gλ Random Variable on Sugeno Measure Space
Jingfeng Tian; Zhiming Zhang; Dazeng Tian
2010-01-01
The definitions and properties of moment of gλ random variable are provided on Sugeno measure space. Then some important moment estimation inequalities based on gλ random variable are presented and proven.
Generation of correlated finite alphabet waveforms using gaussian random variables
Jardak, Seifallah
2014-09-01
Correlated waveforms have a number of applications in different fields, such as radar and communication. It is very easy to generate correlated waveforms using infinite alphabets, but for some of the applications, it is very challenging to use them in practice. Moreover, to generate infinite alphabet constant envelope correlated waveforms, the available research uses iterative algorithms, which are computationally very expensive. In this work, we propose simple novel methods to generate correlated waveforms using finite alphabet constant and non-constant-envelope symbols. To generate finite alphabet waveforms, the proposed method map the Gaussian random variables onto the phase-shift-keying, pulse-amplitude, and quadrature-amplitude modulation schemes. For such mapping, the probability-density-function of Gaussian random variables is divided into M regions, where M is the number of alphabets in the corresponding modulation scheme. By exploiting the mapping function, the relationship between the cross-correlation of Gaussian and finite alphabet symbols is derived. To generate equiprobable symbols, the area of each region is kept same. If the requirement is to have each symbol with its own unique probability, the proposed scheme allows us that as well. Although, the proposed scheme is general, the main focus of this paper is to generate finite alphabet waveforms for multiple-input multiple-output radar, where correlated waveforms are used to achieve desired beampatterns. © 2014 IEEE.
Analysis of Secret Key Randomness Exploiting the Radio Channel Variability
Taghrid Mazloum
2015-01-01
Full Text Available A few years ago, physical layer based techniques have started to be considered as a way to improve security in wireless communications. A well known problem is the management of ciphering keys, both regarding the generation and distribution of these keys. A way to alleviate such difficulties is to use a common source of randomness for the legitimate terminals, not accessible to an eavesdropper. This is the case of the fading propagation channel, when exact or approximate reciprocity applies. Although this principle has been known for long, not so many works have evaluated the effect of radio channel properties in practical environments on the degree of randomness of the generated keys. To this end, we here investigate indoor radio channel measurements in different environments and settings at either 2.4625 GHz or 5.4 GHz band, of particular interest for WIFI related standards. Key bits are extracted by quantizing the complex channel coefficients and their randomness is evaluated using the NIST test suite. We then look at the impact of the carrier frequency, the channel variability in the space, time, and frequency degrees of freedom used to construct a long secret key, in relation to the nature of the radio environment such as the LOS/NLOS character.
Strong Law of Large Numb ers for Array of Rowwise AANA Random Variables
CHEN Zhi-yong; LIU Ting-ting; WANG Xue-jun; LI Xiao-qin
2014-01-01
In this article, the strong laws of large numbers for array of rowwise asymptot-ically almost negatively associated(AANA) random variables are studied. Some suﬃcient conditions for strong laws of large numbers for array of rowwise AANA random variables are presented without assumption of identical distribution. Our results extend the corresponding ones for independent random variables to case of AANA random variables.
Frequency dependent polarization variability of AGN
Bao, G.; Wiita, P. J.; Hadrava, Petr
San Francisco : Astronomical Society of the Pacific, 1996 - (Miller, H.; Webb, J.; Noble, J.), s. 150-155 - (ASP Conference series.. 110). [Blazar Continuum Variability . Miami (US), 04.02.1996-07.02.1996
Separation of Variable Treatment for Solving Time—Dependent Potentials
QIANShang－Wu; GUZhi－Yu; 等
2001-01-01
We use the separation of variable treatment to treat some time-dependent systems,and point out that the condition of separability is the same as the condition of existence of invariant,and the separation of variable treatment is interrelated with the quantum-invariant method and the propagator method.We directly use the separation of variable treatment to obtain the wavefunctions of the time-dependent Coulomb potential and the time-dependent Hulthen potential.
Automatic Probabilistic Program Verification through Random Variable Abstraction
Barsotti, Damián; 10.4204/EPTCS.28.3
2010-01-01
The weakest pre-expectation calculus has been proved to be a mature theory to analyze quantitative properties of probabilistic and nondeterministic programs. We present an automatic method for proving quantitative linear properties on any denumerable state space using iterative backwards fixed point calculation in the general framework of abstract interpretation. In order to accomplish this task we present the technique of random variable abstraction (RVA) and we also postulate a sufficient condition to achieve exact fixed point computation in the abstract domain. The feasibility of our approach is shown with two examples, one obtaining the expected running time of a probabilistic program, and the other the expected gain of a gambling strategy. Our method works on general guarded probabilistic and nondeterministic transition systems instead of plain pGCL programs, allowing us to easily model a wide range of systems including distributed ones and unstructured programs. We present the operational and weakest pr...
Generating Correlated QPSK Waveforms By Exploiting Real Gaussian Random Variables
Jardak, Seifallah
2012-11-01
The design of waveforms with specified auto- and cross-correlation properties has a number of applications in multiple-input multiple-output (MIMO) radar, one of them is the desired transmit beampattern design. In this work, an algorithm is proposed to generate quadrature phase shift- keying (QPSK) waveforms with required cross-correlation properties using real Gaussian random-variables (RV’s). This work can be considered as the extension of what was presented in [1] to generate BPSK waveforms. This work will be extended for the generation of correlated higher-order phase shift-keying (PSK) and quadrature amplitude modulation (QAM) schemes that can better approximate the desired beampattern.
Nimon, Kim; Henson, Robin K.
2015-01-01
The authors empirically examined whether the validity of a residualized dependent variable after covariance adjustment is comparable to that of the original variable of interest. When variance of a dependent variable is removed as a result of one or more covariates, the residual variance may not reflect the same meaning. Using the pretest-posttest…
刘华汉; 蒋玮; 杨光辉; 吕海霆
2015-01-01
The single mode reliability of the mechanical component is studied with dependent random variables which do not obey the normal distribution.The non-normal distribution random variables are transformed into the normal distribution random variables by using the Rosenblatt transformation (RT),R-F transformation and Edgeworth method.The correlation standard normal random variables are changed into the independent variables on the basis of the linear algebra theory.Then,the single mode reliability index and reliability of mechanical components are obtained by using the first-order second-moment (FOSM)method and advanced first-order second-moment (AFOSM)method.On the basis of the non-normal distribution random variables and the correlation of the variables,computer realization of the reliability calculation algorithm of the mechanical component with single failure mode is proposed.A pair of spur gear in 1 .6 MW wind turbine gearbox is taken as an example with considering one failure mode — tooth surface contact fatigue failure,the effect of the variables' correlation coefficient on the component reliability is analyzed.The high efficiency and applicability of the algorithm are also verified by the example.%研究含有非正态随机变量且随机变量具有相关性的机械零件单模可靠度统一模型，运用 Rosenblatt变换(RT变换)、R-F变换、Edgeworth级数法将非正态分布随机变量变换为正态随机变量，利用线性代数理论将相关标准正态随机变量转换为线性无关的正态随机变量，然后利用一次二阶矩(FOSM)法、改进的一次二阶矩(AFOSM)法求得机械零件单模可靠度指数及可靠度.基于所建机械零件单模可靠度统一模型，提出了含有非正态随机变量且随机变量间具有相关性的零件单模可靠度计算机求解的实现算法.以某1.6 MW风电齿轮箱中一对标准直齿轮啮合传动为例，通过探讨齿面接触疲劳这一单模失效下的可靠度
Warech, E. J.
1967-01-01
Computer program finds values of independent variables which minimize the dependent variable. This optimization program has been used on the F-1 and J-2 engine programs to establish minimum film coolant requirements.
A preliminary, randomized trial of aerobic exercise for alcohol dependence
Brown, Richard A.; Abrantes, Ana M.; Minami, Haruka; Read, Jennifer P.; Marcus, Bess H.; Jakicic, John M.; Strong, David R.; Dubreuil, Mary Ella; Gordon, Alan A.; Ramsey, Susan E.; Kahler, Christopher W.; Stuart, Gregory L.
2014-01-01
Interventions targeting physical activity may be valuable as an adjunct to alcohol treatment, but have been relative untested. In the current study, alcohol dependent, physically sedentary patients were randomized to: a 12-week moderate-intensity, group aerobic exercise intervention (AE; n = 25) or a brief advice to exercise intervention (BA-E; n=23). Results showed that individuals in AE reported significantly fewer drinking and heavy drinking days, relative to BA-E during treatment. Further...
Generalized linear models for categorical and continuous limited dependent variables
Smithson, Michael
2013-01-01
Introduction and OverviewThe Nature of Limited Dependent VariablesOverview of GLMsEstimation Methods and Model EvaluationOrganization of This BookDiscrete VariablesBinary VariablesLogistic RegressionThe Binomial GLMEstimation Methods and IssuesAnalyses in R and StataExercisesNominal Polytomous VariablesMultinomial Logit ModelConditional Logit and Choice ModelsMultinomial Processing Tree ModelsEstimation Methods and Model EvaluationAnalyses in R and StataExercisesOrdinal Categorical VariablesModeling Ordinal Variables: Common Practice versus Best PracticeOrdinal Model AlternativesCumulative Mod
Instrumental variables and Mendelian randomization with invalid instruments
Kang, Hyunseung
Instrumental variables (IV) methods have been widely used to determine the causal effect of a treatment, exposure, policy, or an intervention on an outcome of interest. The IV method relies on having a valid instrument, a variable that is (A1) associated with the exposure, (A2) has no direct effect on the outcome, and (A3) is unrelated to the unmeasured confounders associated with the exposure and the outcome. However, in practice, finding a valid instrument, especially those that satisfy (A2) and (A3), can be challenging. For example, in Mendelian randomization studies where genetic markers are used as instruments, complete knowledge about instruments' validity is equivalent to complete knowledge about the involved genes' functions. The dissertation explores the theory, methods, and application of IV methods when invalid instruments are present. First, when we have multiple candidate instruments, we establish a theoretical bound whereby causal effects are only identified as long as less than 50% of instruments are invalid, without knowing which of the instruments are invalid. We also propose a fast penalized method, called sisVIVE, to estimate the causal effect. We find that sisVIVE outperforms traditional IV methods when invalid instruments are present both in simulation studies as well as in real data analysis. Second, we propose a robust confidence interval under the multiple invalid IV setting. This work is an extension of our work on sisVIVE. However, unlike sisVIVE which is robust to violations of (A2) and (A3), our confidence interval procedure provides honest coverage even if all three assumptions, (A1)-(A3), are violated. Third, we study the single IV setting where the one IV we have may actually be invalid. We propose a nonparametric IV estimation method based on full matching, a technique popular in causal inference for observational data, that leverages observed covariates to make the instrument more valid. We propose an estimator along with
Random recurrence equations and ruin in a Markov-dependent stochastic economic environment
Collamore, Jeffrey F.
2009-01-01
We develop sharp large deviation asymptotics for the probability of ruin in a Markov-dependent stochastic economic environment and study the extremes for some related Markovian processes which arise in financial and insurance mathematics, related to perpetuities and the ARCH(1) and GARCH(1,1) time...... series models. Our results build upon work of Goldie, who has developed tail asymptotics applicable for independent sequences of random variables subject to a random recurrence equation. In contrast, we adopt a general approach based on the theory of Harris recurrent Markov chains and the associated...
Automatic Probabilistic Program Verification through Random Variable Abstraction
Damián Barsotti
2010-06-01
Full Text Available The weakest pre-expectation calculus has been proved to be a mature theory to analyze quantitative properties of probabilistic and nondeterministic programs. We present an automatic method for proving quantitative linear properties on any denumerable state space using iterative backwards fixed point calculation in the general framework of abstract interpretation. In order to accomplish this task we present the technique of random variable abstraction (RVA and we also postulate a sufficient condition to achieve exact fixed point computation in the abstract domain. The feasibility of our approach is shown with two examples, one obtaining the expected running time of a probabilistic program, and the other the expected gain of a gambling strategy. Our method works on general guarded probabilistic and nondeterministic transition systems instead of plain pGCL programs, allowing us to easily model a wide range of systems including distributed ones and unstructured programs. We present the operational and weakest precondition semantics for this programs and prove its equivalence.
Almost Sure Convergence of the General Jamison Weighted Sum of B-Valued Random Variables
Chun SU; Tie Jun TONG
2004-01-01
In this paper, two new functions are introduced to depict the Jamison weighted sum of random variables instead using the common methods, their properties and relationships are systematically discussed. We also analysed the implication of the conditions in previous papers. Then we apply these consequences to B-valued random variables, and greatly improve the original results of the strong convergence of the general Jamison weighted sum. Furthermore, our discussions are useful to the corresponding questions of real-valued random variables.
Separation of Variable Treatment for Solving Time-Dependent Potentials
QIAN Shang-Wu; GU Zhi-Yu; XIE Guo-Qiang
2001-01-01
We use the separation of variable treatment to treat some time-dependent systems, and point out that the condition of separability is the same as the condition of existence of invariant, and the separation of variable treatment is interrelated with the quantum-invariant method and the propagator method. We directly use the separation of potential.
Gologit2: Generalized Logistic Regression Models for Ordinal Dependent Variables
Richard Williams
2005-01-01
-gologit2- is a user-written program that estimates generalized logistic regression models for ordinal dependent variables. The actual values taken on by the dependent variable are irrelevant except that larger values are assumed to correspond to "higher" outcomes. A major strength of -gologit2- is that it can also estimate two special cases of the generalized model: the proportional odds model and the partial proportional odds model. Hence, -gologit2- can estimate models that are less restri...
Yevdomakha, H. V.; Yu. M. Ivchenko; Skalozub, V. V.; Zhelieznov, K. H.; Litvinov, V. A.; O. P. Ivanov
2004-01-01
The authors propose models and calculation methods for optimal modes of running emu trains, taking into account the random character of catenary voltages and the conditions of dependence of electric power price upon the time of day. The paper suggests criteria for efficient use of variable tariffs and provides examples of calculating the optimal modes of running suburban emu trains.
The dependence of quasar variability on black hole mass
Wold, M; Shang, Z
2006-01-01
In order to investigate the dependence of quasar variability on fundamental physical parameters like black hole mass, we have matched quasars from the QUEST1 Variability Survey with broad-lined objects from the Sloan Digital Sky Survey. The matched sample contains approximately 100 quasars, and the Sloan spectra are used to estimate black hole masses and bolometric luminosities. Variability amplitudes are measured from the QUEST1 light curves. We find that black hole mass correlates with several measures of the variability amplitude at the 99% significance level or better. The correlation does not appear to be caused by obvious selection effects inherent to flux-limited quasar samples, host galaxy contamination or other well-known correlations between quasar variability and luminosity/redshift. We evaluate variability as a function of rest-frame time lag using structure functions, and find further support for the variability--black hole mass correlation. The correlation is strongest for time lags of the order...
Bias in random forest variable importance measures: Illustrations, sources and a solution
Hothorn Torsten; Zeileis Achim; Boulesteix Anne-Laure; Strobl Carolin
2007-01-01
Abstract Background Variable importance measures for random forests have been receiving increased attention as a means of variable selection in many classification tasks in bioinformatics and related scientific fields, for instance to select a subset of genetic markers relevant for the prediction of a certain disease. We show that random forest variable importance measures are a sensible means for variable selection in many applications, but are not reliable in situations where potential pred...
History dependent quantum random walks as quantum lattice gas automata
Quantum Random Walks (QRW) were first defined as one-particle sectors of Quantum Lattice Gas Automata (QLGA). Recently, they have been generalized to include history dependence, either on previous coin (internal, i.e., spin or velocity) states or on previous position states. These models have the goal of studying the transition to classicality, or more generally, changes in the performance of quantum walks in algorithmic applications. We show that several history dependent QRW can be identified as one-particle sectors of QLGA. This provides a unifying conceptual framework for these models in which the extra degrees of freedom required to store the history information arise naturally as geometrical degrees of freedom on the lattice
Explaining the Dark Energy, Baryon and Dark Matter Coincidence via Domain-Dependent Random Densities
McDonald, John
2013-01-01
The dark energy, dark matter and baryon densities in the Universe are observed to be similar, with a factor of no more than 20 between the largest and smallest densities. We show that this coincidence can be understood via superhorizon domains of randomly varying densities when the baryon density at initial collapse of galaxy-forming perturbations is determined by anthropic selection. The baryon and dark matter densities are assumed to be dependent on random variables \\theta_{d} and \\theta_{b} according to \\rho_{dm} ~ \\theta_{d}^{\\alpha} and \\rho_{b} ~ \\theta_{b}^{\\beta}, while the effectively constant dark energy density is dependent upon a random variable \\phi_{Q} according to \\rho_{Q} ~ \\phi_{Q}^{n}. The ratio of the baryon density to the dark energy density at initial collapse, r_{Q}, and the baryon-to-dark matter ratio, r, are then determined purely statistically, with no dependence on the anthropically-preferred baryon density. We compute the probability distribution for r_{Q} and r and show that the ob...
Stable limits for sums of dependent infinite variance random variables
Bartkiewicz, Katarzyna; Jakubowski, Adam; Mikosch, Thomas;
2011-01-01
The aim of this paper is to provide conditions which ensure that the affinely transformed partial sums of a strictly stationary process converge in distribution to an infinite variance stable distribution. Conditions for this convergence to hold are known in the literature. However, most of these...
Fuzzy random variables — II. Algorithms and examples for the discrete case
Kwakernaak, Huibert
1979-01-01
The results obtained in part I of the paper are specialized to the case of discrete fuzzy random variables. A more intuitive interpretation is given of the notion of fuzzy random variables. Algorithms are derived for determining expectations, fuzzy probabilities, fuzzy conditional expectations and f
Guo Ming-le; Xu Chun-yu; Zhu Dong-jin
2014-01-01
In this paper, we discuss the complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables. By applying moment inequality and truncation methods, the sufficient conditions of complete convergence of weighted sums for arrays of rowwise m-negatively associated random variables are established. These results generalize and complement some known conclusions.
Bogdan Gheorghe Munteanu
2013-01-01
Full Text Available Using the stochastic approximations, in this paper it was studiedthe convergence in distribution of the fractional parts of the sum of random variables to the truncated exponential distribution with parameter lambda. This fact is feasible by means of the Fourier-Stieltjes sequence (FSS of the random variable.
An almost Sure Central Limit Theorem for the Weight Function Sequences of NA Random Variables
Qunying Wu
2011-08-01
Consider the weight function sequences of NA random variables. This paper proves that the almost sure central limit theorem holds for the weight function sequences of NA random variables. Our results generalize and improve those on the almost sure central limit theorem previously obtained from the i.i.d. case to NA sequences.
How fast increasing powers of a continuous random variable converge to Benford's law
Wójcik, Michał Ryszard
2013-01-01
It is known that increasing powers of a continuous random variable converge in distribution to Benford's law as the exponent approaches infinity. The rate of convergence has been estimated using Fourier analysis, but we present an elementary method, which is easier to apply and provides a better estimation in the widely studied case of a uniformly distributed random variable.
Strong Approximation Theorems for Sums of Random Variables When Extreme Terms are Excluded
ZHANG Li Xin
2002-01-01
Let {Xn; n ≥1} be a sequence of i.i.d. random variables and let Xn(r) = Xj if |Xj| is the and necessary conditions for (r)Sn approximating to sums of independent normal random variables are obtained. Via approximation results, the convergence rates of the strong law of large numbers for (r)Sn are studied.
LARGE DEVIATION FOR THE EMPIRICAL CORRELATION COEFFICIENT OF TWO GAUSSIAN RANDOM VARIABLES
Shen Si
2007-01-01
In this article, the author obtains the large deviation principles for the empirical correlation coefficient of two Gaussian random variables X and Y. Especially, when considering two independent Gaussian random variables X, Y with the means EX, EY(both known), wherein the author gives two kinds of different proofs and gets the same results.
Ji-hua Xu; Jing-hui Zhao
2000-01-01
After giving the representation of moment gqnerating function for the S-λ type random variable by solving a differential equation, we prove that this type random variable is of regular n-r order moment. Furthermore we establish the higher order asymptotic formula for generalized Feller operators by making use of the generalized Taylor formula.
Complete Convergence for Arrays of Rowwise ϕ-mixing Random Variables
LI Jing
2013-01-01
In the paper, the complete convergence for arrays of rowwise ϕ-mixing random variables is studied. Some sufficient conditions for complete convergence for an array of row-wiseϕ-mixing random variables without assumptions of identical distribution and stochastic domination are presented.
Stochastic Optimal Estimation with Fuzzy Random Variables and Fuzzy Kalman Filtering
FENG Yu-hu
2005-01-01
By constructing a mean-square performance index in the case of fuzzy random variable, the optimal estimation theorem for unknown fuzzy state using the fuzzy observation data are given. The state and output of linear discrete-time dynamic fuzzy system with Gaussian noise are Gaussian fuzzy random variable sequences. An approach to fuzzy Kalman filtering is discussed. Fuzzy Kalman filtering contains two parts: a real-valued non-random recurrence equation and the standard Kalman filtering.
Bias in random forest variable importance measures: Illustrations, sources and a solution
Hothorn Torsten
2007-01-01
Full Text Available Abstract Background Variable importance measures for random forests have been receiving increased attention as a means of variable selection in many classification tasks in bioinformatics and related scientific fields, for instance to select a subset of genetic markers relevant for the prediction of a certain disease. We show that random forest variable importance measures are a sensible means for variable selection in many applications, but are not reliable in situations where potential predictor variables vary in their scale of measurement or their number of categories. This is particularly important in genomics and computational biology, where predictors often include variables of different types, for example when predictors include both sequence data and continuous variables such as folding energy, or when amino acid sequence data show different numbers of categories. Results Simulation studies are presented illustrating that, when random forest variable importance measures are used with data of varying types, the results are misleading because suboptimal predictor variables may be artificially preferred in variable selection. The two mechanisms underlying this deficiency are biased variable selection in the individual classification trees used to build the random forest on one hand, and effects induced by bootstrap sampling with replacement on the other hand. Conclusion We propose to employ an alternative implementation of random forests, that provides unbiased variable selection in the individual classification trees. When this method is applied using subsampling without replacement, the resulting variable importance measures can be used reliably for variable selection even in situations where the potential predictor variables vary in their scale of measurement or their number of categories. The usage of both random forest algorithms and their variable importance measures in the R system for statistical computing is illustrated and
'Sequence' dependent elasticity and local stiffness of a random heteropolymer
We study the 'sequence' distribution of thermally averaged global and local elastic properties of a random heteropolymer of fixed length N, within the framework of a disordered Kratky–Porod (KP) model. We arrive at a number of qualitative results on the form of the distribution function of the thermally averaged end-to-end distance (R2), and its moments. For long N→∞ chains, this distribution is a Gaussian; for shorter chains, there is a crossover to an exponential distribution, with the most probable end-to-end distance deviating significantly from the mean. Further, the distributions of local quantities related to the thermally averaged tangent–tangent correlator are typically broad, even in the thermodynamic limit, i.e., they do not self-average. This is consistent with the general consensus that DNA–protein binding/unbinding strengths and rates are sensitive to local elastic distortion which is 'sequence' dependent
Generating Variable and Random Schedules of Reinforcement Using Microsoft Excel Macros
Bancroft, Stacie L; Bourret, Jason C
2008-01-01
Variable reinforcement schedules are used to arrange the availability of reinforcement following varying response ratios or intervals of time. Random reinforcement schedules are subtypes of variable reinforcement schedules that can be used to arrange the availability of reinforcement at a constant probability across number of responses or time. Generating schedule values for variable and random reinforcement schedules can be difficult. The present article describes the steps necessary to writ...
Concentrated Hitting Times of Randomized Search Heuristics with Variable Drift
Lehre, Per Kristian; Witt, Carsten
2014-01-01
Drift analysis is one of the state-of-the-art techniques for the runtime analysis of randomized search heuristics (RSHs) such as evolutionary algorithms (EAs), simulated annealing etc. The vast majority of existing drift theorems yield bounds on the expected value of the hitting time for a target...... precise sharp-concentration results on the running time of a simple EA on standard benchmark problems, including the class of general linear functions. The usefulness of the theorem outside the theory of RSHs is demonstrated by deriving tail bounds on the number of cycles in random permutations. All...
Local search methods based on variable focusing for random K-satisfiability.
Lemoy, Rémi; Alava, Mikko; Aurell, Erik
2015-01-01
We introduce variable focused local search algorithms for satisfiabiliity problems. Usual approaches focus uniformly on unsatisfied clauses. The methods described here work by focusing on random variables in unsatisfied clauses. Variants are considered where variables are selected uniformly and randomly or by introducing a bias towards picking variables participating in several unsatistified clauses. These are studied in the case of the random 3-SAT problem, together with an alternative energy definition, the number of variables in unsatisfied constraints. The variable-based focused Metropolis search (V-FMS) is found to be quite close in performance to the standard clause-based FMS at optimal noise. At infinite noise, instead, the threshold for the linearity of solution times with instance size is improved by picking preferably variables in several UNSAT clauses. Consequences for algorithmic design are discussed. PMID:25679737
THE STRUCTURE AND PRECISE MODERATE DEVIATIONS OF RANDOM VARIABLES WITH DOMINATEDLY VARYING TAILS
WANG Yuebao; YANG Yang
2005-01-01
This paper shows the structure of the random variables with dominatedly varying tails and that of the associated random variables,and obtains some results on these r.v.s' precise moderate deviations with random centralizing constants,which extend the boundary γλ(t) of large deviations to γ(λ(t))1/s,where γ＞0,1＜s＜2,λ(t) is the expectation of the random index N(t),t＞O.
2009-01-01
In this paper, we establish some Rosenthal type inequalities for maximum partial sums of asymptotically almost negatively associated random variables, which extend the corresponding results for negatively associated random variables. As applications of these inequalities, by employing the notions of residual Cesàro α-integrability and strong residual Cesàro α-integrability, we derive some results on Lp convergence where 1 < p < 2 and complete convergence. In addition, we estimate the rate of convergence in Marcinkiewicz-Zygmund strong law for partial sums of identically distributed random variables.
YUAN DeMei; AN Jun
2009-01-01
In this paper, we establish some Rosenthal type inequalities for maximum partial sums of asymptotically almost negatively associated random variables, which extend the corresponding results for negatively associated random variables. As applications of these inequalities, by employing the notions of residual Cesaro α-integrability and strong residual Cesaro α-integrability, we derive some results on Lp convergence where 1
random variables.
On the Strong Law of Large Numbers for Non-Independent B-Valued Random Variables
Gan Shi-xin
2004-01-01
This paper investigates some conditions which imply the strong laws of large numbers for Banach space valued random variable sequences. Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-Jφrgensen and Pisier theorem are obtained.
Zero Distribution of System with Unknown Random Variables Case Study: Avoiding Collision Path
Parman Setyamartana
2014-07-01
Full Text Available This paper presents the stochastic analysis of finding the feasible trajectories of robotics arm motion at obstacle surrounding. Unknown variables are coefficients of polynomials joint angle so that the collision-free motion is achieved. ãk is matrix consisting of these unknown feasible polynomial coefficients. The pattern of feasible polynomial in the obstacle environment shows as random. This paper proposes to model the pattern of this randomness values using random polynomial with unknown variables as coefficients. The behavior of the system will be obtained from zero distribution as the characteristic of such random polynomial. Results show that the pattern of random polynomial of avoiding collision can be constructed from zero distribution. Zero distribution is like building block of the system with obstacles as uncertainty factor. By scale factor k, which has range, the random coefficient pattern can be predicted.
Bujok, K.; Hambly, B. M.; Reisinger, C.
2012-01-01
We consider $N$ Bernoulli random variables, which are independent conditional on a common random factor determining their probability distribution. We show that certain expected functionals of the proportion $L_N$ of variables in a given state converge at rate 1/N as $N\\rightarrow \\infty$. Based on these results, we propose a multi-level simulation algorithm using a family of sequences with increasing length, to obtain estimators for these expected functionals with a mean-square error of $\\ep...
Random variables as pathwise integrals with respect to fractional Brownian motion
Mishura, Yuliya; Valkeila, Esko
2011-01-01
We show that a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand $g$ can have any prescribed distribution, moreover, we give both necessary and sufficient conditions when random variables can be represented in this form. We also prove that any random variable is a value of such integral in some improper sense. We discuss some applications of these results, in particular, to fractional Black--Scholes model of financial market.
Sample estimation of distribution parameters if upper and lower bounds of random variable are known
The point and interval distribution parameter estimators are obtained by direct numerical approximation of the definition integral with the use of upper and lower bounds of distributed random variable. Like in Bayesian estimation, the distribution parameters are treated as random variables, and their uncertainty is described as a distribution. The Monte Carlo procedure is involved to get the posteriori parameter distributions and the correspondent confidence interval limits.
A Robbins-Monro procedure for the estimation of parametric deformations on random variables
Fraysse, Philippe; Lescornel, Hélène; Loubès, Jean-Michel
2013-01-01
The paper is devoted to the study of a parametric deformation model of independent and identically random variables. Firstly, we construct an efficient and very easy to compute recursive estimate of the parameter. Our stochastic estimator is similar to the Robbins-Monro procedure where the contrast function is the Wasserstein distance. Secondly, we propose a recursive estimator similar to that of Parzen-Rosenblatt kernel density estimator in order to estimate the density of the random variabl...
The discovery of timescale-dependent color variability of quasars
Quasars are variable on timescales from days to years in UV/optical and generally appear bluer while they brighten. The physics behind the variations in fluxes and colors remains unclear. Using Sloan Digital Sky Survey g- and r-band photometric monitoring data for quasars in Stripe 82, we find that although the flux variation amplitude increases with timescale, the color variability exhibits the opposite behavior. The color variability of quasars is prominent at timescales as short as ∼10 days, but gradually reduces toward timescales up to years. In other words, the variable emission at shorter timescales is bluer than that at longer timescales. This timescale dependence is clearly and consistently detected at all redshifts from z = 0 to 3.5; thus, it cannot be due to contamination to broadband photometry from emission lines that do not respond to fast continuum variations. The discovery directly rules out the possibility that simply attributes the color variability to contamination from a non-variable redder component such as the host galaxy. It cannot be interpreted as changes in global accretion rate either. The thermal accretion disk fluctuation model is favored in the sense that fluctuations in the inner, hotter region of the disk are responsible for short-term variations, while longer-term and stronger variations are expected from the larger and cooler disk region. An interesting implication is that one can use quasar variations at different timescales to probe disk emission at different radii.
Small, Dylan S.
2011-01-01
In randomized trials, researchers are often interested in mediation analysis to understand how a treatment works, in particular how much of a treatment's effect is mediated by an intermediated variable and how much the treatment directly affects the outcome not through the mediator. The standard regression approach to mediation analysis assumes sequential ignorability of the mediator, that is that the mediator is effectively randomly assigned given baseline covariates and the randomized treat...
Stability of Random Variables and Iterated Logarithm Laws for Martingales and Quadratic Forms
Fernholz, Luisa Turrin; Teicher, Henry
1980-01-01
Strong laws of large numbers, obtained for positive, independent random variables, are utilized to prove iterated logarithm laws (with a nonrandom normalizing sequence) for a class of martingales. A law of the iterated logarithm is also established for certain random quadratic forms.
On the Strong Laws for Weighted Sums of m-negatively Asso ciated Random Variables
WU Yong-feng
2014-01-01
In this article, the author establishes the strong laws for linear statistics that are weighted sums of a m-negatively associated(m-NA) random sample. The obtained results extend and improve the result of Qiu and Yang in [1] to m-NA random variables.
高海峰; 白广忱; 高阳; 鲍天未
2015-01-01
The fatigue life of aeroengine turbine disc presents great dispersion due to the randomness of the basic variables, such as applied load, working temperature, geometrical dimensions and material properties. In order to ameliorate reliability analysis efficiency without loss of reliability, the distributed collaborative response surface method (DCRSM) was proposed, and its basic theories were established in this work. Considering the failure dependency among the failure modes, the distributed response surface was constructed to establish the relationship between the failure mode and the relevant random variables. Then, the failure modes were considered as the random variables of system response to obtain the distributed collaborative response surface model based on structure failure criterion. Finally, the given turbine disc structure was employed to illustrate the feasibility and validity of the presented method. Through the comparison of DCRSM, Monte Carlo method (MCM) and the traditional response surface method (RSM), the results show that the computational precision for DCRSM is more consistent with MCM than RSM, while DCRSM needs far less computing time than MCM and RSM under the same simulation conditions. Thus, DCRSM is demonstrated to be a feasible and valid approach for improving the computational efficiency of reliability analysis for aeroengine turbine disc fatigue life with multiple random variables, and has great potential value for the complicated mechanical structure with multi-component and multi-failure mode.
Couso, Inés; Sánchez, Luciano
2014-01-01
This short book provides a unified view of the history and theory of random sets and fuzzy random variables, with special emphasis on its use for representing higher-order non-statistical uncertainty about statistical experiments. The authors lay bare the existence of two streams of works using the same mathematical ground, but differing form their use of sets, according to whether they represent objects of interest naturally taking the form of sets, or imprecise knowledge about such objects. Random (fuzzy) sets can be used in many fields ranging from mathematical morphology, economics, artificial intelligence, information processing and statistics per se, especially in areas where the outcomes of random experiments cannot be observed with full precision. This book also emphasizes the link between random sets and fuzzy sets with some techniques related to the theory of imprecise probabilities. This small book is intended for graduate and doctoral students in mathematics or engineering, but also provides an i...
Shoulder pain and time dependent structure in wheelchair propulsion variability.
Jayaraman, Chandrasekaran; Moon, Yaejin; Sosnoff, Jacob J
2016-07-01
Manual wheelchair propulsion places considerable repetitive mechanical strain on the upper limbs leading to shoulder injury and pain. While recent research indicates that the amount of variability in wheelchair propulsion and shoulder pain may be related. There has been minimal inquiry into the fluctuation over time (i.e. time-dependent structure) in wheelchair propulsion variability. Consequently the purpose of this investigation was to examine if the time-dependent structure in the wheelchair propulsion parameters are related to shoulder pain. 27 experienced wheelchair users manually propelled their own wheelchair fitted with a SMARTWheel on a roller at 1.1m/s for 3min. Time-dependent structure of cycle-to-cycle fluctuations in contact angle and inter push time interval was quantified using sample entropy (SampEn) and compared between the groups with/without shoulder pain using non-parametric statistics. Overall findings were, (1) variability observed in contact angle fluctuations during manual wheelchair propulsion is structured (Z=3.15;pshoulder pain exhibited higher SampEn magnitude for contact angle during wheelchair propulsion than those without pain (χ(2)(1)=6.12;pshoulder pain (rs (WUSPI) =0.41;rs (VAS)=0.56;pshoulder pain. PMID:27134151
LARGE DEVIATIONS FOR SUMS OF INDEPENDENT RANDOM VARIABLES WITH DOMINATEDLY VARYING TAILS
Kong Fanchao; Zhang Ying
2007-01-01
In this paper the large deviation results for partial and random sums Sn-ESn=n∑i=1Xi-n∑i=1EXi,n≥1;S(t)-ES(t)=N(t)∑i=1Xi-E(N(t)∑i=1Xi),t≥0are proved, where {N(t); t≥ 0} is a counting process of non-negative integer-valued random variables, and {Xn; n ≥ 1} are a sequence of independent non-negative random variables independent of {N(t); t ≥ 0}. These results extend and improve some known conclusions.
Dasgupta, Sakyasingha; Nishikawa, Isao; Aihara, Kazuyuki; Toyoizumi, Taro
Source of cortical variability and its influence on signal processing remain an open question. We address the latter, by studying two types of balanced randomly connected networks of quadratic I-F neurons, with irregular spontaneous activity: (a) a deterministic network with strong connections generating noise by chaotic dynamics (b) a stochastic network with weak connections receiving noisy input. They are analytically tractable in the limit of large network-size and channel time-constant. Despite different sources of noise, spontaneous activity of these networks are identical unless majority of neurons are simultaneously recorded. However, the two networks show remarkably different sensitivity to external stimuli. In the former, input reverberates internally and can be read out over long time, but in the latter, inputs rapidly decay. This is further enhanced with activity-dependent plasticity at input synapses producing marked difference in decoding inputs from neural activity. We show, this leads to distinct performance of the two networks to integrate temporally separate signals from multiple sources, with the deterministic chaotic network activity serving as reservoir for Monte Carlo sampling to perform near optimal Bayesian integration, unlike its stochastic counterpart.
Generating Variable and Random Schedules of Reinforcement Using Microsoft Excel Macros
Bancroft, Stacie L.; Bourret, Jason C.
2008-01-01
Variable reinforcement schedules are used to arrange the availability of reinforcement following varying response ratios or intervals of time. Random reinforcement schedules are subtypes of variable reinforcement schedules that can be used to arrange the availability of reinforcement at a constant probability across number of responses or time.…
The Central Limit Theorem for Exchangeable Random Variables Without Moments
Klass, Michael; Teicher, Henry
1987-01-01
If $\\{X_n, n \\geq 1\\}$ is an exchangeable sequence with $(1/b_n(\\sum^n_1X_i - a_n)) \\rightarrow N(0, 1)$ for some constants $a_n$ and $0 < b_n \\rightarrow \\infty$ then $b_n/n^\\alpha$ is slowly varying with $\\alpha = 1$ or $\\frac{1}{2}$ and necessary conditions (depending on $\\alpha$) which are also sufficient, are obtained. Three such examples are given, one with infinite mean, one with no positive moments, and the third with almost all conditional distributions belonging to no domain of attr...
Krøigård, Thomas; Gaist, David; Otto, Marit;
2014-01-01
SUMMARY: The reproducibility of variables commonly included in studies of peripheral nerve conduction in healthy individuals has not previously been analyzed using a random effects regression model. We examined the temporal changes and variability of standard nerve conduction measures in the leg...... conduction studies have a high reproducibility, and variables are mainly unaltered during 6 months. This study provides a solid basis for the planning of future clinical trials assessing changes in nerve conduction....
Variable Selection for Varying-Coefficient Models with Missing Response at Random
Pei Xin ZHAO; Liu Gen XUE
2011-01-01
In this paper, we present a variable selection procedure by combining basis function approximations with penalized estimating equations for varying-coefficient models with missing response at random. With appropriate selection of the tuning parameters, we establish the consistency of the variable selection procedure and the optimal convergence rate of the regularized estimators. A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.
Correction to: "On the Chambers-Mallows-Stuck Method for Simulating Skewed Stable Random Variables"
Weron, Rafal
1996-01-01
In the paper Weron (1996, Statist. Probab. Lett. 28, 165-171), I gave a proof to the equality in law of a skewed stable variable and a nonlinear transformation of two independent uniform and exponential variables. The Chambers et al. (1976, J. Amer. Statist. Assoc. 71, 340–344) method of computer generation of a skewed stable random variable is based on this equality. Unfortunately an error crept into my calculations for alpha=1. This note corrects the error.
Vardeman, Stephen B.; Wendelberger, Joanne R.
2004-01-01
There is a little-known but very simple generalization of the standard result that for uncorrelated variables with a common mean and variance, the expected sample variance is the marginal variance. The generalization justifies the use of the usual standard error of the sample mean in possibly heteroscedastic situations and motivates some simple estimators for unbalanced linear random effects models. The latter is illustrated for the simple one-way context.
Scalable statistics of correlated random variables and extremes applied to deep borehole porosities
Guadagnini, A.; Neuman, S. P.; Nan, T.; Riva, M.; Winter, C. L.
2015-02-01
We analyze scale-dependent statistics of correlated random hydrogeological variables and their extremes using neutron porosity data from six deep boreholes, in three diverse depositional environments, as example. We show that key statistics of porosity increments behave and scale in manners typical of many earth and environmental (as well as other) variables. These scaling behaviors include a tendency of increments to have symmetric, non-Gaussian frequency distributions characterized by heavy tails that decay with separation distance or lag; power-law scaling of sample structure functions (statistical moments of absolute increments) in midranges of lags; linear relationships between log structure functions of successive orders at all lags, known as extended self-similarity or ESS; and nonlinear scaling of structure function power-law exponents with function order, a phenomenon commonly attributed in the literature to multifractals. Elsewhere we proposed, explored and demonstrated a new method of geostatistical inference that captures all of these phenomena within a unified theoretical framework. The framework views data as samples from random fields constituting scale mixtures of truncated (monofractal) fractional Brownian motion (tfBm) or fractional Gaussian noise (tfGn). Important questions not addressed in previous studies concern the distribution and statistical scaling of extreme incremental values. Of special interest in hydrology (and many other areas) are statistics of absolute increments exceeding given thresholds, known as peaks over threshold or POTs. In this paper we explore the statistical scaling of data and, for the first time, corresponding POTs associated with samples from scale mixtures of tfBm or tfGn. We demonstrate that porosity data we analyze possess properties of such samples and thus follow the theory we proposed. The porosity data are of additional value in revealing a remarkable cross-over from one scaling regime to another at certain
Modelling the statistical dependence of rainfall event variables by a trivariate copula function
M. Balistrocchi
2011-01-01
Full Text Available In many hydrological models, such as those derived by analytical probabilistic methods, the precipitation stochastic process is represented by means of individual storm random variables which are supposed to be independent of each other. However, several proposals were advanced to develop joint probability distributions able to account for the observed statistical dependence. The traditional technique of the multivariate statistics is nevertheless affected by several drawbacks, whose most evident issue is the unavoidable subordination of the dependence structure assessment to the marginal distribution fitting. Conversely, the copula approach can overcome this limitation, by splitting the problem in two distinct items. Furthermore, goodness-of-fit tests were recently made available and a significant improvement in the function selection reliability has been achieved. Herein a trivariate probability distribution of the rainfall event volume, the wet weather duration and the interevent time is proposed and verified by test statistics with regard to three long time series recorded in different Italian climates. The function was developed by applying a mixing technique to bivariate copulas, which were formerly obtained by analyzing the random variables in pairs. A unique probabilistic model seems to be suitable for representing the dependence structure, despite the sensitivity shown by the dependence parameters towards the threshold utilized in the procedure for extracting the independent events. The joint probability function was finally developed by adopting a Weibull model for the marginal distributions.
On the use of fractional calculus for the probabilistic characterization of random variables
Cottone, Giulio; 10.1016/j.probengmech.2008.08.002
2013-01-01
In this paper, the classical problem of the probabilistic characterization of a random variable is re-examined. A random variable is usually described by the probability density function (PDF) or by its Fourier transform, namely the characteristic function (CF). The CF can be further expressed by a Taylor series involving the moments of the random variable. However, in some circumstances, the moments do not exist and the Taylor expansion of the CF is useless. This happens for example in the case of $\\alpha$--stable random variables. Here, the problem of representing the CF or the PDF of random variables (r.vs) is examined by introducing fractional calculus. Two very remarkable results are obtained. Firstly, it is shown that the fractional derivatives of the CF in zero coincide with fractional moments. This is true also in case of CF not derivable in zero (like the CF of $\\alpha$--stable r.vs). Moreover, it is shown that the CF may be represented by a generalized Taylor expansion involving fractional moments. ...
CONVERGENCE RATES IN THE STRONG LAWS FOR A CLASS OF DEPENDENT RANDOM FIFLDS
CaiGuanghui
2003-01-01
By using a Rosenthal type inequality established in this paper,the complete convergence rates in the strong laws for a class of dependent random fields are discussed.And the result obtained extends those for ρ--mixing random fields,ρ*-mixing random fields and negatively associated fields.
Epoch-dependent absorption line profile variability in lambda Cep
Uuh-Sonda, J M; Eenens, P; Mahy, L; Palate, M; Gosset, E; Flores, C A
2014-01-01
We present the analysis of a multi-epoch spectroscopic monitoring campaign of the O6Ief star lambda Cep. Previous observations reported the existence of two modes of non-radial pulsations in this star. Our data reveal a much more complex situation. The frequency content of the power spectrum considerably changes from one epoch to the other. We find no stable frequency that can unambiguously be attributed to pulsations. The epoch-dependence of the frequencies and variability patterns are similar to what is seen in the wind emission lines of this and other Oef stars, suggesting that both phenomena likely have the same, currently still unknown, origin.
A Particle Swarm Optimization Algorithm with Variable Random Functions and Mutation
ZHOU Xiao-Jun; YANG Chun-Hua; GUI Wei-Hua; DONG Tian-Xue
2014-01-01
The convergence analysis of the standard particle swarm optimization (PSO) has shown that the changing of random functions, personal best and group best has the potential to improve the performance of the PSO. In this paper, a novel strategy with variable random functions and polynomial mutation is introduced into the PSO, which is called particle swarm optimization algorithm with variable random functions and mutation (PSO-RM). Random functions are adjusted with the density of the population so as to manipulate the weight of cognition part and social part. Mutation is executed on both personal best particle and group best particle to explore new areas. Experiment results have demonstrated the effectiveness of the strategy.
Autoclassification of the Variable 3XMM Sources Using the Random Forest Machine Learning Algorithm
Farrell, Sean A; Lo, Kitty K
2015-01-01
In the current era of large surveys and massive data sets, autoclassification of astrophysical sources using intelligent algorithms is becoming increasingly important. In this paper we present the catalog of variable sources in the Third XMM-Newton Serendipitous Source catalog (3XMM) autoclassified using the Random Forest machine learning algorithm. We used a sample of manually classified variable sources from the second data release of the XMM-Newton catalogs (2XMMi-DR2) to train the classifier, obtaining an accuracy of ~92%. We also evaluated the effectiveness of identifying spurious detections using a sample of spurious sources, achieving an accuracy of ~95%. Manual investigation of a random sample of classified sources confirmed these accuracy levels and showed that the Random Forest machine learning algorithm is highly effective at automatically classifying 3XMM sources. Here we present the catalog of classified 3XMM variable sources. We also present three previously unidentified unusual sources that wer...
Pei Xin ZHAO; Liu Gen XUE
2011-01-01
In this paper,we present a variable selection procedure by combining basis function approximations with penalized estimating equations for semiparametric varying-coefficient partially linear models with missing response at random.The proposed procedure simultaneously selects significant variables in parametric components and nonparametric components.With appropriate selection of the tuning parameters,we establish the consistency of the variable selection procedure and the convergence rate of the regularized estimators.A simulation study is undertaken to assess the finite sample performance of the proposed variable selection procedure.
The generation of dependent input variables to a performance assessment simulation code
Mathematical models are being developed in many countries to aid in the assessment of risks associated with the deep geologic disposal of high-level nuclear wastes. The models are designed to simulate one or more steps in the following scenario: waste containment is lost, and the radionuclides are released from the repository, are transported to the biosphere, and become accessible to man. The models typically involve a large number of variables that may be highly dependent. When the models are implemented in computer simulation codes, it becomes necessary to generate input values for these variables. Widely used methods for generating input values, such as simple random sampling (SRS) and Latin hypercube sampling (LHS), do not necessarily produce samples that are consistent with the known dependence structure of the input variables. Moreover, it is procedurally impracticable to generate realizations of correlated input variables from many multivariate probability distributions of interest. Two important cases in which it is feasible to generate multivariate realizations are those in which all input variables are either normally distributed or mutually independent. Neither case is adequate for large-scale performance assessment codes with many input variables. Iman and Conover (1982) have developed a practical method for generating nonzero pairwise rank correlations among the components of an input vector that overcomes some of these difficulties. The method requires samples of specified size from the marginal (univariate) distributions of the input variables. The method further requires a target matrix of desired pairwise correlations among the input variables. The Cholesky decomposition of the target matrix is used to transform the rank matrix of the input sample
Effect of spatial variability on the slope stability using Random Field Numerical Limit Analyses
Kasama, Kiyonobu; Whittle, Andrew
2015-01-01
This paper presents a probabilistic approach to evaluating the geotechnical stability problem by incorporating the stochastic spatial variability of soil property within the numerical limit analyses (NLAs). The undrained shear strength and unit weight of soil are treated as a random field which is characterized by a log-normal distribution and a spatial correlation length. The current calculations use a Cholesky Decomposition technique to incorporate these random properties in NLAs. The Rando...
Zwan, van der, G.; Vente, de, W.; Huizink, A.C.; Bögels, S.M.; Bruin, de, B.
2015-01-01
In contemporary western societies stress is highly prevalent, therefore the need for stress-reducing methods is great. This randomized controlled trial compared the efficacy of self-help physical activity (PA), mindfulness meditation (MM), and heart rate variability biofeedback (HRV-BF) in reducing stress and its related symptoms. We randomly allocated 126 participants to PA, MM, or HRV-BF upon enrollment, of whom 76 agreed to participate. The interventions consisted of psycho-education and a...
Scheduling of Dependent Tasks Application using Random Search Technique
vegda, Deepak. c.; Prajapati, Harshad B.
2013-01-01
Since beginning of Grid computing, scheduling of dependent tasks application has attracted attention of researchers due to NP-Complete nature of the problem. In Grid environment, scheduling is deciding about assignment of tasks to available resources. Scheduling in Grid is challenging when the tasks have dependencies and resources are heterogeneous. The main objective in scheduling of dependent tasks is minimizing make-span. Due to NP-complete nature of scheduling problem, exact solutions can...
The Law of the Iterated Logarithm for Independent Random Variables with Multidimensional Indices
Li, Deli; Rao, M. Bhaskara; Wang, Xiangchen
1992-01-01
Let $X_{\\bar n}, \\bar{n} \\in \\mathbb{N}^d$, be a field of independent real random variables, where $\\mathbb{N}^d$ is the $d$-dimensional lattice. In this paper, the law of the iterated logarithm is established for such a field of random variables. Theorem 1 brings into focus a connection between a certain strong law of large numbers and the law of the iterated logarithm. A general technique is developed by which one can derive the strong law of large numbers and the law of the iterated logari...
Exponential inequalities for associated random variables and strong laws of large numbers
Shan-chao YANG; Min CHEN
2007-01-01
Some exponential inequalities for partial sums of associated random variables are established. These inequalities improve the corresponding results obtained by Ioannides and Roussas (1999), and Oliveira (2005). As application, some strong laws of large numbers are given. For the case of geometrically decreasing covariances, we obtain the rate of convergence n-1/2(log log n)1/2(log n) which is close to the optimal achievable convergence rate for independent random variables under an iterated logarithm, while Ioannides and Roussas (1999), and Oliveira (2005) only got n-1/3 (log n)2/3 and n-1/3 (log n)5/3, separately.
Exponential inequalities for associated random variables and strong laws of large numbers
2007-01-01
Some exponential inequalities for partial sums of associated random variables are established. These inequalities improve the corresponding results obtained by Ioannides and Roussas (1999), and Oliveira (2005). As application, some strong laws of large numbers are given. For the case of geometrically decreasing covariances, we obtain the rate of convergence n-1/2(log log n)1/2(logn) which is close to the optimal achievable convergence rate for independent random variables under an iterated logarithm, while Ioannides and Roussas (1999), and Oliveira (2005) only got n-1/3(logn)2/3 and n-1/3(logn)5/3, separately.
Convergence in distribution norms in the CLT for non identical distributed random variables
Bally, Vlad; Caramellino, Lucia; Poly, Guillaume
2016-01-01
We study the convergence in distribution norms in the Central Limit Theorem for non identical distributed random variables that is $$ \\varepsilon _{n}(f):=\\mathbb{E}\\Big(f\\Big(\\sum_{i=1}^{n}Z_{i}\\Big)\\Big)-\\mathbb{E}\\big(f(G)\\big)\\rightarrow 0 $$ where $S_{n}=\\sum_{i=1}^{n}Z_{i}$ with $Z_{i}$ centred independent random variables (with a suitable re-normalization for $S_{n}$) and $G$ is standard normal. We also consider local developments (Edgeworth expansion). This kind of results is well und...
A note on strong law of large numbers of random variables
LIN Zheng-yan; SHEN Xin-mei
2006-01-01
In this paper, the Chung's strong law of large numbers is generalized to the random variables which do not need the condition of independence, while the sequence of Borel functions verifies some conditions weaker than that in Chung's theorem.Some convergence theorems for martingale difference sequence such as Lp martingale difference sequence are the particular cases of results achieved in this paper. Finally, the convergence theorem for A-summability of sequence of random variables is proved,where A is a suitable real infinite matrix.
ON THE LIMITING BEHAVIOR OF THE MAXIMUM PARTIAL SUMS FOR ARRAYS OF ROWWISE NA RANDOM VARIABLES
无
2007-01-01
Let {Xni, 1 ≤ n,i ＜∞} be an array of rowwise NA random variables and {an, n ≥ 1} a sequence of constants with 0 ＜ an ↑∞. The limiting behavior of maximum partial sums 1/an max 1≤k≤n| kΣi=1 Xni| is investigated and some new results are obtained. The results extend and improve the corresponding theorems of rowwise independent random variable arrays by Hu and Taylor [1] and Hu and Chang [2].
Randomly Weighted Sums for Negatively Associated Random Variables with Heavy Tails%重尾情形下NA随机变量的随机加权和
宗高峰; 孔繁超
2009-01-01
In 2003, Tang Qihe et al. obtained a simple asymptotic formula for independent identically distributed (i.i.d.) random variables with heavy tails. In this paper, under certain moment conditions, we establish a formula as the same as Tang's, when random variables are negatively associated (NA).
A Simple Linear Ranking Algorithm Using Query Dependent Intercept Variables
Ailon, Nir
2008-01-01
The LETOR website contains three information retrieval datasets used as a benchmark for testing machine learning ideas for ranking. Algorithms participating in the challenge are required to assign score values to search results for a collection of queries, and are measured using standard IR ranking measures (NDCG, precision, MAP) that depend only the relative score-induced order of the results. Similarly to many of the ideas proposed in the participating algorithms, we train a linear classifier. In contrast with other participating algorithms, we define an additional free variable (intercept, or benchmark) for each query. This allows expressing the fact that results for different queries are incomparable for the purpose of determining relevance. The cost of this idea is the addition of relatively few nuisance parameters. Our approach is simple, and we used a standard logistic regression library to test it. The results beat the reported participating algorithms. Hence, it seems promising to combine our approac...
Discovery of Fourier-dependent time lags in cataclysmic variables
Scaringi, S; Groot, P J; Uttley, P; Marsh, T; Knigge, C; Maccarone, T; Dhillon, V S
2013-01-01
We report the first study of Fourier-frequency-dependent coherence and phase/time lags at optical wavelengths of cataclysmic variables (MV Lyr and LU Cam) displaying typical flickering variability in white light. Observations were performed on the William Herschel Telescope using ULTRACAM. Lightcurves for both systems have been obtained with the SDSS filters $u'$, $g'$ and $r'$ simultaneously with cadences between $\\approx0.5-2$ seconds, and allow us to probe temporal frequencies between ~10^{-3} Hz and ~1 Hz. We find high levels of coherence between the u', g' and r' lightcurves up to at least ~10^{-2} Hz. Furthermore we detect red/negative lags where the redder bands lag the bluer ones at the lowest observed frequencies. For MV Lyr time lags up to ~3 seconds are observed, whilst LU Cam displays larger time lags of ~10 seconds. Mechanisms which seek to explain red/negative lags observed in X-ray binaries and Active Galactic Nuclei involve reflection of photons generated close to the compact object onto the s...
A NONCLASSICAL LAW OF ITERATED LOGARITHM FOR NEGATIVELY ASSOCIATED RANDOM VARIABLES
JiangYe
2003-01-01
A nonclassical law of iterated logarithm that holds for a stationary negatively associated sequence of random variables with finite variance is proved in this paper.The proof is based on a Rosenthal type maximal inequality and the subsequence method.This result extends the work of Klesov,Rosalsky(2001)and Shao.Su(1999).
Laws of Large Numbers of Negatively Correlated Random Variables for Capacities
Wen-juan LI; Zeng-jing CHEN
2011-01-01
Our aim is to present some limit theorems for capacities.We consider a sequence of pairwise negatively correlated random variables.We obtain laws of large numbers for upper probabilities and 2-aiternating capacities,using some results in the classical probability theory and a non-additive version of Chebyshev's inequality and Borai-Contelli lemma for capacities.
On Complete Convergence for Arrays of Rowwise Strong Mixing Random Variables
ZHOU XING-CAI; LIN JIN-GUAN; WANG XUE-JUN; HU SHU-HE
2011-01-01
In this paper,we present a general method to prove the complete convergence for arrays of rowwise strong mixing random variables,and give some results on complete convergence under some suitable conditions.Some Marcinkiewicz-Zygmund type strong laws of large numbers are also obtained.
2008-01-01
In this paper,we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables.As an interesting application,we obtain the law of the iterated logarithm for the empirical covariance of Hilbertian autoregressive processes.
LIU WeiDong; FU KeAng; ZHANG LiXin
2008-01-01
In this paper, we prove a general law of the iterated logarithm (LIL) for independent non-identically distributed B-valued random variables. As an interesting application, we obtain the law of the iterated logarithm for the empirical covariance of Hilbertian autoregressive processes.
Moments of the maximum of normed partial sums of ρ--mixing random variables
LIU Xiang-dong; LIU Jin-xia
2009-01-01
Let {Xn, n ≥ 1} be a sequence of identically distributed ρ--mixing random variables and set Sn= ∑ni=1>Xi,n ≥ 1, the sufficient and necessary conditions for the existence of moments of sup n≥1> |Sn/n1/r|p(00) are given, which are the same as that in the independent case.
Random forest (RF) is popular in ecological and environmental modeling, in part, because of its insensitivity to correlated predictors and resistance to overfitting. Although variable selection has been proposed to improve both performance and interpretation of RF models, it is u...
Zwan, van der J.E.; Vente, de W.; Huizink, A.C.; Bögels, S.M.; Bruin, de E.I.
2015-01-01
In contemporary western societies stress is highly prevalent, therefore the need for stress-reducing methods is great. This randomized controlled trial compared the efficacy of self-help physical activity (PA), mindfulness meditation (MM), and heart rate variability biofeedback (HRV-BF) in reducing
Oracle Efficient Variable Selection in Random and Fixed Effects Panel Data Models
Kock, Anders Bredahl
This paper generalizes the results for the Bridge estimator of Huang et al. (2008) to linear random and fixed effects panel data models which are allowed to grow in both dimensions. In particular we show that the Bridge estimator is oracle efficient. It can correctly distinguish between relevant...... and irrelevant variables and the asymptotic distribution of the estimators of the coefficients of the relevant variables is the same as if only these had been included in the model, i.e. as if an oracle had revealed the true model prior to estimation. In the case of more explanatory variables than...
Multilevel Cell Storage and Resistance Variability in Resistive Random Access Memory
Pantelis, D. I.; Karakizis, P. N.; Dragatogiannis, D. A.; Charitidis, C. A.
2016-06-01
Multilevel per cell (MLC) storage in resistive random access memory (ReRAM) is attractive in achieving high-density and low-cost memory and will be required in future. In this chapter, MLC storage and resistance variability and reliability of multilevel in ReRAM are discussed. Different MLC operation schemes with their physical mechanisms and a comprehensive analysis of resistance variability have been provided. Various factors that can induce variability and their effect on the resistance margin between the multiple resistance levels are assessed. The reliability characteristics and the impact on MLC storage have also been assessed.
Cluster-size dependent randomization traffic flow model
Gao, Kun; Wang, Bing-Hong; Fu, Chuan-Ji; Lu, Yu-Feng
2007-11-01
In order to exhibit the meta-stable states, several slow-to-start rules have been investigated as modification to Nagel-Schreckenberg (NS) model. These models can reproduce some realistic phenomena which are absent in the original NS model. But in these models, the size of cluster is still not considered as a useful parameter. In real traffic, the slow-to-start motion of a standing vehicle often depends on the degree of congestion which can be measured by the clusters' size. According to this idea, we propose a cluster-size dependent slow-to-start model based on the speed-dependent slow-to-start rule (VDR) model. It gives expected results through simulations. Comparing with the VDR model, our new model has a better traffic efficiency and shows richer complex characters.
Random Forests for Metric Learning with Implicit Pairwise Position Dependence
Xiong, Caiming; Xu, Ran; Corso, Jason J
2012-01-01
Metric learning makes it plausible to learn distances for complex distributions of data from labeled data. However, to date, most metric learning methods are based on a single Mahalanobis metric, which cannot handle heterogeneous data well. Those that learn multiple metrics throughout the space have demonstrated superior accuracy, but at the cost of computational efficiency. Here, we take a new angle to the metric learning problem and learn a single metric that is able to implicitly adapt its distance function throughout the feature space. This metric adaptation is accomplished by using a random forest-based classifier to underpin the distance function and incorporate both absolute pairwise position and standard relative position into the representation. We have implemented and tested our method against state of the art global and multi-metric methods on a variety of data sets. Overall, the proposed method outperforms both types of methods in terms of accuracy (consistently ranked first) and is an order of ma...
Structural Fatigue Reliability Based on Extension of Random Loads into Interval Variables
Qiangfeng Wang
2013-01-01
Full Text Available According to the problem that for a structure under random loads, the structural fatigue life cant be directly calculated out by S-N curves and linear Miner cumulative damage rule. Owing to the uncertainty of loads, and the problem of the inaccuracy of calculated structural reliability index for the existence of deviation between measured data in projects and real data, the research method for structural fatigue reliability based on extension of random loads into interval variables is proposed. The innovation is that we can accurately calculate out the interval of the structural fatigue life and reliability index of a structure according to the probability density function of stress level of random loads and the coefficient of variation of measured loads. By practical calculation example, it is proved that this method is more suitable to practical engineering comparing to traditional methods. It will provide a perfect research approach for reliability analysis of the structure under random loads.
Cluster-size dependent randomization traffic flow model
Gao Kun; Wang Bing-Hong; Fu Chuan-Ji; Lu Yu-Feng
2007-01-01
In order to exhibit the meta-stable states, several slow-to-start rules have been investigated as modification to Nagel-Schreckenberg (NS) model. These models can reproduce some realistic phenomena which are absent in the original NS model. But in these models, the size of cluster is still not considered as a useful parameter. In real traffic,the slow-to-start motion of a standing vehicle often depends on the degree of congestion which can be measured by the clusters'size. According to this idea, we propose a cluster-size dependent slow-to-start model based on the speeddependent slow-to-start rule (VDR) model. It gives expected results through simulations. Comparing with the VDR model, our new model has a better traffic efficiency and shows richer complex characters.
El-Wakil, S. A.; Sallah, M.; El-Hanbaly, A. M.
2015-10-01
The stochastic radiative transfer problem is studied in a participating planar finite continuously fluctuating medium. The problem is considered for specular- and diffusly-reflecting boundaries with linear anisotropic scattering. Random variable transformation (RVT) technique is used to get the complete average for the solution functions, that are represented by the probability-density function (PDF) of the solution process. In the RVT algorithm, a simple integral transformation to the input stochastic process (the extinction function of the medium) is applied. This linear transformation enables us to rewrite the stochastic transport equations in terms of the optical random variable (x) and the optical random thickness (L). Then the transport equation is solved deterministically to get a closed form for the solution as a function of x and L. So, the solution is used to obtain the PDF of the solution functions applying the RVT technique among the input random variable (L) and the output process (the solution functions). The obtained averages of the solution functions are used to get the complete analytical averages for some interesting physical quantities, namely, reflectivity and transmissivity at the medium boundaries. In terms of the average reflectivity and transmissivity, the average of the partial heat fluxes for the generalized problem with internal source of radiation are obtained and represented graphically.
Hashimoto, H.; Nemani, R. R.
2015-12-01
Regional scale ecosystem modeling requires high-resolution data of surface climate variables. Spatial variability in temperature and precipitation has been well studied over the past two decades resulting in several sophisticated algorithms. However, compared to temperature and precipitation, other surface climate variables, such as humidity, solar radiation and wind speed, are not available to use, even though those data are equally important for ecosystem modeling. The main reason for this is the lack of governing physical equations for interpolating observations and the lack of comparable satellite observations. Therefore, scientists have been using reanalysis data or simply interpolated data for ecosystem modeling, though they are too coarse for regional scale ecosystem analysis. In this study, we developed a method to spatially map daily climate variables, including humidity, solar radiation, wind, precipitation, and temperature. We applied the method to the conterminous USA from 1980 to 2015. Previously, we successfully developed a precipitation interpolation method using random forest algorithm, and now we extended it to the other variables. Because this method does not require any assumptions about physical equations, this method can potentially be applicable to any climate variable if measured data are available. The method requires point data along with a host of spatial data sets . Satellite data, reanalysis data, and radar data were used and the importance of each dataset was analyzed using random forest algorithm. The only parameter we need to adjust is the radius from the target point, in which statistically meaningful relationships between observed and spatial co-variate data is calculated. The radius was optimized using mean absolute error and bias. We also analyzed temporal consistency and spatial patterns of the results. Because it is relatively easy to customize the setup depending on user's request, the resulting datasets may be useful for
Zhu, Xiang-Wei; Xin, Yan-Jun; Ge, Hui-Lin
2015-04-27
Variable selection is of crucial significance in QSAR modeling since it increases the model predictive ability and reduces noise. The selection of the right variables is far more complicated than the development of predictive models. In this study, eight continuous and categorical data sets were employed to explore the applicability of two distinct variable selection methods random forests (RF) and least absolute shrinkage and selection operator (LASSO). Variable selection was performed: (1) by using recursive random forests to rule out a quarter of the least important descriptors at each iteration and (2) by using LASSO modeling with 10-fold inner cross-validation to tune its penalty λ for each data set. Along with regular statistical parameters of model performance, we proposed the highest pairwise correlation rate, average pairwise Pearson's correlation coefficient, and Tanimoto coefficient to evaluate the optimal by RF and LASSO in an extensive way. Results showed that variable selection could allow a tremendous reduction of noisy descriptors (at most 96% with RF method in this study) and apparently enhance model's predictive performance as well. Furthermore, random forests showed property of gathering important predictors without restricting their pairwise correlation, which is contrary to LASSO. The mutual exclusion of highly correlated variables in LASSO modeling tends to skip important variables that are highly related to response endpoints and thus undermine the model's predictive performance. The optimal variables selected by RF share low similarity with those by LASSO (e.g., the Tanimoto coefficients were smaller than 0.20 in seven out of eight data sets). We found that the differences between RF and LASSO predictive performances mainly resulted from the variables selected by different strategies rather than the learning algorithms. Our study showed that the right selection of variables is more important than the learning algorithm for modeling. We hope
Are the Variability Properties of the Kepler AGN Light Curves Consistent with a Damped Random Walk?
Kasliwal, Vishal P.; Vogeley, Michael S.; Richards, Gordon T.
2015-01-01
We test the consistency of active galactic nuclei (AGN) optical flux variability with the $\\textit{damped random walk}$ (DRW) model. Our sample consists of 20 multi-quarter $\\textit{Kepler}$ AGN light curves including both Type 1 and 2 Seyferts, radio-loud and -quiet AGN, quasars, and blazars. $\\textit{Kepler}$ observations of AGN light curves offer a unique insight into the variability properties of AGN light curves because of the very rapid ($11.6-28.6$ min) and highly uniform rest-frame sa...
The probability distribution function for the sum of squares of independent random variables
Fateev, Yury; Dmitriev, Dmitry; Tyapkin, Valery; Kremez, Nikolai; Shaidurov, Vladimir
2016-08-01
In the present paper, the probability distribution function is derived for the sum of squares of random variables for nonzero expectations. This distribution function enables one to develop an efficient one-step algorithm for phase ambiguity resolution when determining the spatial orientation from signals of satellite radio-navigation systems. Threshold values for rejecting false solutions and statistical properties of the algorithm are obtained.
Seok Yoon Hwang; Dug Hun Hong
1999-01-01
LetÃ‚Â {Xij} be a double sequence of pairwise independent random variables.Ã‚Â IfÃ‚Â P{|Xmn|Ã¢Â‰Â¥t}Ã¢Â‰Â¤P{|X|Ã¢Â‰Â¥t} for all nonnegative real numbersÃ‚Â t and E|X|p(log+|X|)3
General Limit Distributions for Sums of Random Variables with a Matrix Product Representation
Angeletti, Florian; Bertin, Eric; Abry, Patrice
2014-12-01
The general limit distributions of the sum of random variables described by a finite matrix product ansatz are characterized. Using a mapping to a Hidden Markov Chain formalism, non-standard limit distributions are obtained, and related to a form of ergodicity breaking in the underlying non-homogeneous Hidden Markov Chain. The link between ergodicity and limit distributions is detailed and used to provide a full algorithmic characterization of the general limit distributions.
Central limit theorems for directional and linear random variables with applications
García-Portugués, Eduardo; Crujeiras, Rosa M.; González-Manteiga, Wenceslao
2014-01-01
A central limit theorem for the integrated squared error of the directional-linear kernel density estimator is established. The result enables the construction and analysis of two testing procedures based on squared loss: a nonparametric independence test for directional and linear random variables and a goodness-of-fit test for parametric families of directional-linear densities. Limit distributions for both test statistics, and a consistent bootstrap strategy for the goodness-of-fit test, a...
1999-01-01
Suppose X1,X2 are independent random variables satisfying a second-order regular variation condition on the tail-sum and a balance condition on the tails. In this paper we give a description of the asymptotic behaviour as t → ∞ for P(X1 + X2 > t). The result is applied to the problem of risk diversification in portfolio analysis and to the estimation of the parameter in a MA(1) model.
On Stein's method for products of normal random variables and zero bias couplings
Gaunt, Robert E.
2013-01-01
In this paper we extend Stein's method to the distribution of the product of $n$ independent mean zero normal random variables. A Stein equation is obtained for this class of distributions, which reduces to the classical normal Stein equation in the case $n=1$. This Stein equation motivates a generalisation of the zero bias transformation. We establish properties of this new transformation, and illustrate how they may be used together with the Stein equation to assess distributional distances...
Autoclassification of the Variable 3XMM Sources Using the Random Forest Machine Learning Algorithm
Farrell, Sean A.; Murphy, Tara; Lo, Kitty K.
2015-11-01
In the current era of large surveys and massive data sets, autoclassification of astrophysical sources using intelligent algorithms is becoming increasingly important. In this paper we present the catalog of variable sources in the Third XMM-Newton Serendipitous Source catalog (3XMM) autoclassified using the Random Forest machine learning algorithm. We used a sample of manually classified variable sources from the second data release of the XMM-Newton catalogs (2XMMi-DR2) to train the classifier, obtaining an accuracy of ∼92%. We also evaluated the effectiveness of identifying spurious detections using a sample of spurious sources, achieving an accuracy of ∼95%. Manual investigation of a random sample of classified sources confirmed these accuracy levels and showed that the Random Forest machine learning algorithm is highly effective at automatically classifying 3XMM sources. Here we present the catalog of classified 3XMM variable sources. We also present three previously unidentified unusual sources that were flagged as outlier sources by the algorithm: a new candidate supergiant fast X-ray transient, a 400 s X-ray pulsar, and an eclipsing 5 hr binary system coincident with a known Cepheid.
Extended q -Gaussian and q -exponential distributions from gamma random variables
Budini, Adrián A.
2015-05-01
The family of q -Gaussian and q -exponential probability densities fit the statistical behavior of diverse complex self-similar nonequilibrium systems. These distributions, independently of the underlying dynamics, can rigorously be obtained by maximizing Tsallis "nonextensive" entropy under appropriate constraints, as well as from superstatistical models. In this paper we provide an alternative and complementary scheme for deriving these objects. We show that q -Gaussian and q -exponential random variables can always be expressed as a function of two statistically independent gamma random variables with the same scale parameter. Their shape index determines the complexity q parameter. This result also allows us to define an extended family of asymmetric q -Gaussian and modified q -exponential densities, which reduce to the standard ones when the shape parameters are the same. Furthermore, we demonstrate that a simple change of variables always allows relating any of these distributions with a beta stochastic variable. The extended distributions are applied in the statistical description of different complex dynamics such as log-return signals in financial markets and motion of point defects in a fluid flow.
Measures of between-cluster variability in cluster randomized trials with binary outcomes.
Thomson, Andrew; Hayes, Richard; Cousens, Simon
2009-05-30
Cluster randomized trials (CRTs) are increasingly used to evaluate the effectiveness of health-care interventions. A key feature of CRTs is that the observations on individuals within clusters are correlated as a result of between-cluster variability. Sample size formulae exist which account for such correlations, but they make different assumptions regarding the between-cluster variability in the intervention arm of a trial, resulting in different sample size estimates. We explore the relationship for binary outcome data between two common measures of between-cluster variability: k, the coefficient of variation and rho, the intracluster correlation coefficient. We then assess how the assumptions of constant k or rho across treatment arms correspond to different assumptions about intervention effects. We assess implications for sample size estimation and present a simple solution to the problems outlined. PMID:19378266
St. Martin, Clara M.; Lundquist, Julie K.; Handschy, Mark A.
2015-04-01
The variability in wind-generated electricity complicates the integration of this electricity into the electrical grid. This challenge steepens as the percentage of renewably-generated electricity on the grid grows, but variability can be reduced by exploiting geographic diversity: correlations between wind farms decrease as the separation between wind farms increases. But how far is far enough to reduce variability? Grid management requires balancing production on various timescales, and so consideration of correlations reflective of those timescales can guide the appropriate spatial scales of geographic diversity grid integration. To answer ‘how far is far enough,’ we investigate the universal behavior of geographic diversity by exploring wind-speed correlations using three extensive datasets spanning continents, durations and time resolution. First, one year of five-minute wind power generation data from 29 wind farms span 1270 km across Southeastern Australia (Australian Energy Market Operator). Second, 45 years of hourly 10 m wind-speeds from 117 stations span 5000 km across Canada (National Climate Data Archive of Environment Canada). Finally, four years of five-minute wind-speeds from 14 meteorological towers span 350 km of the Northwestern US (Bonneville Power Administration). After removing diurnal cycles and seasonal trends from all datasets, we investigate dependence of correlation length on time scale by digitally high-pass filtering the data on 0.25-2000 h timescales and calculating correlations between sites for each high-pass filter cut-off. Correlations fall to zero with increasing station separation distance, but the characteristic correlation length varies with the high-pass filter applied: the higher the cut-off frequency, the smaller the station separation required to achieve de-correlation. Remarkable similarities between these three datasets reveal behavior that, if universal, could be particularly useful for grid management. For high
Correchel Vladia
2005-01-01
Full Text Available The precision of the 137Cs fallout redistribution technique for the evaluation of soil erosion rates is strongly dependent on the quality of an average inventory taken at a representative reference site. The knowledge of the sources and of the degree of variation of the 137Cs fallout spatial distribution plays an important role on its use. Four reference sites were selected in the South-Central region of Brazil which were characterized in terms of soil chemical, physical and mineralogical aspects as well as the spatial variability of 137Cs inventories. Some important differences in the patterns of 137Cs depth distribution in the soil profiles of the different sites were found. They are probably associated to chemical, physical, mineralogical and biological differences of the soils but many questions still remain open for future investigation, mainly those regarding the adsorption and dynamics of the 137Cs ions in soil profiles under tropical conditions. The random spatial variability (inside each reference site was higher than the systematic spatial variability (between reference sites but their causes were not clearly identified as possible consequences of chemical, physical, mineralogical variability, and/or precipitation.
无
2010-01-01
To analyze the effect of basic variable on failure probability in reliability analysis,a moment-independent importance measure of the basic random variable is proposed,and its properties are analyzed and verified.Based on this work,the importance measure of the basic variable on the failure probability is compared with that on the distribution density of the response.By use of the probability density evolution method,a solution is established to solve two importance measures,which can efficiently avoid the difficulty in solving the importance measures.Some numerical examples and engineering examples are used to demonstrate the proposed importance measure on the failure probability and that on the distribution density of the response.The results show that the proposed importance measure can effectively describe the effect of the basic variable on the failure probability from the distribution density of the basic variable.Additionally,the results show that the established solution on the probability density evolution is efficient for the importance measures.
Blind estimation of statistical properties of non-stationary random variables
Mansour, Ali; Mesleh, Raed; Aggoune, el-Hadi M.
2014-12-01
To identify or equalize wireless transmission channels, or alternatively to evaluate the performance of many wireless communication algorithms, coefficients or statistical properties of the used transmission channels are often assumed to be known or can be estimated at the receiver end. For most of the proposed algorithms, the knowledge of transmission channel statistical properties is essential to detect signals and retrieve data. To the best of our knowledge, most proposed approaches assume that transmission channels are static and can be modeled by stationary random variables (uniform, Gaussian, exponential, Weilbul, Rayleigh, etc.). In the majority of sensor networks or cellular systems applications, transmitters and/or receivers are in motion. Therefore, the validity of static transmission channels and the underlying assumptions may not be valid. In this case, coefficients and statistical properties change and therefore the stationary model falls short of making an accurate representation. In order to estimate the statistical properties (represented by the high-order statistics and probability density function, PDF) of dynamic channels, we firstly assume that the dynamic channels can be modeled by short-term stationary but long-term non-stationary random variable (RV), i.e., the RVs are stationary within unknown successive periods but they may suddenly change their statistical properties between two successive periods. Therefore, this manuscript proposes an algorithm to detect the transition phases of non-stationary random variables and introduces an indicator based on high-order statistics for non-stationary transmission which can be used to alter channel properties and initiate the estimation process. Additionally, PDF estimators based on kernel functions are also developed. The first part of the manuscript provides a brief introduction for unbiased estimators of the second and fourth-order cumulants. Then, the non-stationary indicators are formulated
Records and sequences of records from random variables with a linear trend
Franke, Jasper; Wergen, Gregor; Krug, Joachim
2010-01-01
We consider records and sequences of records drawn from discrete time series of the form $X_{n}=Y_{n}+cn$, where the $Y_{n}$ are independent and identically distributed random variables and $c$ is a constant drift. For very small and very large drift velocities, we investigate the asymptotic behavior of the probability $p_n(c)$ of a record occurring in the $n$th step and the probability $P_N(c)$ that all $N$ entries are records, i.e. that $X_1 < X_2 < ... < X_N$. Our work is motivated by the ...
Genuer, Robin; Toussile, Wilson
2011-01-01
Malaria control strategies aiming at reducing disease transmission intensity may impact both oocyst intensity and infection prevalence in the mosquito vector. Thus far, mathematical models failed to identify a clear relationship between Plasmodium falciparum gametocytes and their infectiousness to mosquitoes. Natural isolates of gametocytes are genetically diverse and biologically complex. Infectiousness to mosquitoes relies on multiple parameters such as density, sex-ratio, maturity, parasite genotypes and host immune factors. In this article, we investigated how density and genetic diversity of gametocytes impact on the success of transmission in the mosquito vector. We analyzed data for which the number of covariates plus attendant interactions is at least of order of the sample size, precluding usage of classical models such as general linear models. We then considered the variable importance from random forests to address the problem of selecting the most influent variables. The selected covariates were ...
Latitudinal dependence of the variability of the micrometeor altitude distribution
Sparks, J. J.; Janches, D.
2009-06-01
We present a study of the diurnal behavior of the observed meteor altitude distribution at different seasons and latitudes. The meteor altitude distribution provides an indication of where the meteoric mass deposition occurs in the mesosphere and lower thermosphere (MLT). This can be utilized to model the input of metallic constituents into the MLT and accurately understand the chemistry of this region. We show that the observed altitude distributions have distinct variability at each location: at high latitudes there is a weak diurnal and strong seasonal variability while at tropical latitudes the opposite behavior is observed. We explain these results by correlating them with the astronomical and physical properties of the meteoric flux. Finally, we discussed the potential influences that these results have on the metal chemistry and aeronomy of this atmospheric region.
The Energy Dependence of GRB Minimum Variability Timescales
Golkhou, V. Zach; Butler, Nathaniel R.; Littlejohns, Owen M.
2015-10-01
We constrain the minimum variability timescales for 938 gamma-ray bursts (GRBs) observed by the Fermi/Gamma-ray Burst Monitor instrument prior to 2012 July 11. The tightest constraints on progenitor radii derived from these timescales are obtained from light curves in the hardest energy channel. In the softer bands—or from measurements of the same GRBs in the hard X-rays from Swift—we show that variability timescales tend to be a factor of two to three longer. Applying a survival analysis to account for detections and upper limits, we find median minimum timescale in the rest frame for long-duration and short-duration GRBs of 45 and 10 ms, respectively. Less than 10% of GRBs show evidence for variability on timescales below 2 ms. These shortest timescales require Lorentz factors ≳ 400 and imply typical emission radii R≈ 1× {10}14 cm for long-duration GRBs and R≈ 3× {10}13 cm for short-duration GRBs. We discuss implications for the GRB fireball model and investigate whether or not GRB minimum timescales evolve with cosmic time.
The Energy-Dependence of GRB Minimum Variability Timescales
Golkhou, V Zach; Littlejohns, Owen M
2015-01-01
We constrain the minimum variability timescales for 938 GRBs observed by the Fermi/GBM instrument prior to July 11, 2012. The tightest constraints on progenitor radii derived from these timescales are obtained from light curves in the hardest energy channel. In the softer bands -- or from measurements of the same GRBs in the hard X-rays from Swift -- we show that variability timescales tend to be a factor 2--3 longer. Applying a survival analysis to account for detections and upper limits, we find median minimum timescale in the rest frame for long-duration and short-duration GRBs of 45 ms and 10 ms, respectively. Fewer than 10% of GRBs show evidence for variability on timescales below 2 ms. These shortest timescales require Lorentz factors $\\gtrsim 400$ and imply typical emission radii $R \\approx 1 {\\times} 10^{14}$ cm for long-duration GRBs and $R \\approx 3 {\\times} 10^{13}$ cm for short-duration GRBs. We discuss implications for the GRB fireball model and investigate whether GRB minimum timescales evolve w...
Nutrition education intervention for dependent patients: protocol of a randomized controlled trial
Arija Victoria; Martín Núria; Canela Teresa; Anguera Carme; Castelao Ana I; García-Barco Montserrat; García-Campo Antoni; González-Bravo Ana I; Lucena Carme; Martínez Teresa; Fernández-Barrés Silvia; Pedret Roser; Badia Waleska; Basora Josep
2012-01-01
Abstract Background Malnutrition in dependent patients has a high prevalence and can influence the prognosis associated with diverse pathologic processes, decrease quality of life, and increase morbidity-mortality and hospital admissions. The aim of the study is to assess the effect of an educational intervention for caregivers on the nutritional status of dependent patients at risk of malnutrition. Methods/Design Intervention study with control group, randomly allocated, of 200 patients of t...
van der Zwan, Judith Esi; de Vente, Wieke; Huizink, Anja C; Bögels, Susan M; de Bruin, Esther I
2015-12-01
In contemporary western societies stress is highly prevalent, therefore the need for stress-reducing methods is great. This randomized controlled trial compared the efficacy of self-help physical activity (PA), mindfulness meditation (MM), and heart rate variability biofeedback (HRV-BF) in reducing stress and its related symptoms. We randomly allocated 126 participants to PA, MM, or HRV-BF upon enrollment, of whom 76 agreed to participate. The interventions consisted of psycho-education and an introduction to the specific intervention techniques and 5 weeks of daily exercises at home. The PA exercises consisted of a vigorous-intensity activity of free choice. The MM exercises consisted of guided mindfulness meditation. The HRV-BF exercises consisted of slow breathing with a heart rate variability biofeedback device. Participants received daily reminders for their exercises and were contacted weekly to monitor their progress. They completed questionnaires prior to, directly after, and 6 weeks after the intervention. Results indicated an overall beneficial effect consisting of reduced stress, anxiety and depressive symptoms, and improved psychological well-being and sleep quality. No significant between-intervention effect was found, suggesting that PA, MM, and HRV-BF are equally effective in reducing stress and its related symptoms. These self-help interventions provide easily accessible help for people with stress complaints. PMID:26111942
Brief Treatments for Cannabis Dependence: Findings From a Randomized Multisite Trial
Babor, Thomas F.
2004-01-01
This study evaluated the efficacy of 2 brief interventions for cannabis-dependent adults. A multisite randomized controlled trial compared cannabis use outcomes across 3 study conditions: (a) 2 sessions of motivational enhancement therapy (MET); (b) 9 sessions of multicomponent therapy that included MET, cognitive-behavioral therapy, and case…
Measures of dependence between random vectors and tests of independence. Literature review
Josse, Julie; Holmes, Susan
2013-01-01
Simple correlation coefficients between two variables have been generalized to measure association between two matrices in many ways. Coefficients such as the RV coefficient, the distance covariance (dCov) coefficient and kernel based coefficients have been adopted by different research communities. Scientists use these coefficients to test whether two random vectors are linked. If they are, it is important to uncover what patterns exist in these associations. We discuss the topic of measures...
Lloret Cabot, M.; Hicks, M. A.; van den Eijnden, A. P.
2012-01-01
Spatial variability of soil properties is inherent in soil deposits, whether as a result of natural geological processes or engineering construction. It is therefore important to account for soil variability in geotechnical design in order to represent more realistically a soil’s in situ state. This variability may be modelled as a random field, with a given probability density function and scale of fluctuation. A more convenient way to deal with the uncertainty of a soil property due to spat...
Energy decay of a variable-coefficient wave equation with nonlinear time-dependent localized damping
Jieqiong Wu
2015-09-01
Full Text Available We study the energy decay for the Cauchy problem of the wave equation with nonlinear time-dependent and space-dependent damping. The damping is localized in a bounded domain and near infinity, and the principal part of the wave equation has a variable-coefficient. We apply the multiplier method for variable-coefficient equations, and obtain an energy decay that depends on the property of the coefficient of the damping term.
Age-dependence and intersubject variability of tracheobronchial particle clearance
Robert Sturm
2011-01-01
Full Text Available SUMMARY.Background: The detailed study of tracheobronchial clearanceof inhaled particles represents one of the basic research questionsin lung medicine. The clearance efficiency varies in different agegroups and between males and females.The differences can bepartly clarified by the application of a well validated theoreticalapproach. This study applied a relevant model to children (1 year,5 years, 10 years, juveniles (15 years, and adults of different ages(18, 21, 25, 34, 50, and 60 years and to both sexes. Methods: Themathematical model used for clearance simulation is based on theconcept of a stochastic lung structure and considers both early fastmucociliary clearance and a later, slow clearance fraction, fs, effectedby particular uptake by tracheobronchial cells, e.g., macrophagesand epithelial cells. According to this model, the calculated mucusvelocities for each airway generation of the tracheobronchial compartmentare normalized to a respective tracheal mucus velocitythat is estimated for each of the age groups studied from an allometricfunction. Results: In general, tracheobronchial clearanceefficiency undergoes a significant increase from childhood to youngadulthood, reaching a maximum at 25-30 years and decreasingagain from about 30 years to 60 years. Conversely to the improvementof clearance, the continuous change of airway morphometrywith increasing age causes a decrease of the filtering effect in thetrachea and main bronchi, which is of marked importance in infants.The modelling results demonstrate differences in tracheobronchialclearance between males and females, generally in the range from0 to 5%, which are exclusively determined by the individual lunggeometry. Conclusions: Based on theoretical computations itcan be concluded that tracheobronchial clearance is a phenomenonthat depends on both age and sex. Biological studies are necessaryto determine the cellular and molecular mechanisms underlyingthe age-dependent development of
A Random Variable Substitution Lemma With Applications to Multiple Description Coding
Wang, Jia; Zhao, Lei; Cuff, Paul; Permuter, Haim
2009-01-01
We establish a random variable substitution lemma and use it to investigate the role of refinement layer in multiple description coding, which clarifies the relationship among several existing achievable multiple description rate-distortion regions. Specifically, it is shown that the El Gamal-Cover (EGC) region is equivalent to the EGC* region (an antecedent version of the EGC region) while the Venkataramani-Kramer-Goyal (VKG) region (when specialized to the 2-description case) is equivalent to the Zhang-Berger (ZB) region. Moreover, we prove that for multiple description coding with individual and hierarchical distortion constraints, the number of layers in the VKG scheme can be significantly reduced when only certain weighted sum rates are concerned. The role of refinement layer in scalable coding (a special case of multiple description coding) is also studied.
Tyson H Holmes
2011-07-01
Full Text Available The HIV risk-taking behavior scale (HRBS is an 11-item instrument designed to assess the risks of HIV infection due self-reported injection drug use and sexual behavior. A retrospective analysis was performed on HRBS data collected from approximately 1,000 participants pooled across seven clinical trials of pharmacotherapies for either the treatment of cocaine-dependence or methamphetamine-dependence. Analysis faced three important challenges. The sample contained a high proportion of missing assessments after randomization. Also, the HRBS scale consists of two distinct behavioral components which may or may not coincide in response patterns. In addition, distributions of responses on the subscales were highly concentrated at just a few values (e.g., 0, 6. To address these challenges, a single probit regression model was fit to three outcomes variables simultaneously—the two subscale totals plus an indicator variable for assessments not obtained (non-response. This joint-outcome regression model was able to identify that those who left assessment early had higher self-reported risk of injection-drug use and lower self-reported risky sexual behavior because the model was able to draw on information on associations among the three outcomes collectively. These findings were not identified in analyses performed on each outcome separately. No evidence for an effect of pharmacotherapies was observed, except to reduce missing assessments. Univariate-outcome modeling is not recommended for the HRBS.
无
2002-01-01
Objective To design and develop a novel, sensitive and versatile method for in vivo foot printing and studies of DNA damage, such as DNA adducts and strand breaks. Methods Starting with mammalian genomic DNA, single-stranded products were made by repeated primer extension, these products were ligated to a double-stranded linker having a randomized 3′ overhang, and used for PCR.DNA breaks in p53 gene produced by restriction endonuclease AfaI were detected by using this new method followed by Southern hybridization with DIG-labeled probe. Results This randomized terminal linker-dependent PCR (RDPCR) method could generate band signals many-fold stronger than conventional ligation-mediated PCR (LMPCR), and it was more rapid, convenient and accurate than the terminal transferase-dependent PCR (TDPCR). Conclusion DNA strand breakage can be detected sensitively in the gene level by RDPCR. Any lesion that blocks primer extension should be detectable.
Are the Variability Properties of the Kepler AGN Light Curves Consistent with a Damped Random Walk?
Kasliwal, Vishal P; Richards, Gordon T
2015-01-01
We test the consistency of active galactic nuclei (AGN) optical flux variability with the \\textit{damped random walk} (DRW) model. Our sample consists of 20 multi-quarter \\textit{Kepler} AGN light curves including both Type 1 and 2 Seyferts, radio-loud and -quiet AGN, quasars, and blazars. \\textit{Kepler} observations of AGN light curves offer a unique insight into the variability properties of AGN light curves because of the very rapid ($11.6-28.6$ min) and highly uniform rest-frame sampling combined with a photometric precision of $1$ part in $10^{5}$ over a period of 3.5 yr. We categorize the light curves of all 20 objects based on visual similarities and find that the light curves fall into 5 broad categories. We measure the first order structure function of these light curves and model the observed light curve with a general broken power-law PSD characterized by a short-timescale power-law index $\\gamma$ and turnover timescale $\\tau$. We find that less than half the objects are consistent with a DRW and ...
LIU Hai; LIU JinSong; L(U) JianTao; WANG KeJia
2009-01-01
Polarization-dependent difference of the power spectra from a set of two-dimensional (2D) passive random media is investigated by simultaneously solving Maxwell's equations for both transverse magnetic (TM) and transverse electric (TE) fields. The random media have the same random constitution but different shapes. Results show that both two polarized states are morphology dependent,and the variety of the shapes has more influence on the selection of TM polarized modes than that of TE polarized modes. Such polarization-dependent difference of morphology property presents a new modeselecting technique for random lasers.
Neto, Elias Chaibub; Bot, Brian M.; Kellen, Mike; Friend, Stephen H; Trister, Andrew D.
2016-01-01
Mobile health studies can leverage longitudinal sensor data from smartphones to guide the application of personalized medical interventions. These studies are particularly appealing due to their ability to attract a large number of participants. In this paper, we argue that the adoption of an instrumental variable approach for randomized trials with imperfect compliance provides a natural framework for personalized causal inference of medication response in mobile health studies. Randomized t...
Kaspar, H.; Newsbaum, J. B.
1967-01-01
Relationships between independent and dependent variables are determined by multiple correlation computer program. This is applied to research and experimental design and development of complex hardware and components that require test programs.
Dhingra, R. R.; Jacono, F. J.; Fishman, M; Loparo, K. A.; Rybak, I. A.; Dick, T E
2011-01-01
Physiological rhythms, including respiration, exhibit endogenous variability associated with health, and deviations from this are associated with disease. Specific changes in the linear and nonlinear sources of breathing variability have not been investigated. In this study, we used information theory-based techniques, combined with surrogate data testing, to quantify and characterize the vagal-dependent nonlinear pattern variability in urethane-anesthetized, spontaneously breathing adult rat...
Diffusion in time-dependent random environments: mass fluctuations and scaling properties
A mass-ejection model in a time-dependent random environment with both temporal and spatial correlations is introduced. When the environment has a finite correlation length, individual particle trajectories are found to diffuse at large times with a displacement distribution that approaches a Gaussian. The collective dynamics of diffusing particles reaches a statistically stationary state, which is characterized in terms of a fluctuating mass density field. The probability distribution of density is studied numerically for both smooth and non-smooth scale-invariant random environments. Competition between trapping in the regions where the ejection rate of the environment vanishes and mixing due to its temporal dependence leads to large fluctuations of mass. These mechanisms are found to result in the presence of intermediate power-law tails in the probability distribution of the mass density. For spatially differentiable environments, the exponent of the right tail is shown to be universal and equal to -3/2. However, at small values, it is found to depend on the environment. Finally, spatial scaling properties of the mass distribution are investigated. The distribution of the coarse-grained density is shown to possess some rescaling properties that depend on the scale, the amplitude of the ejection rate and the Hölder exponent of the environment. (paper)
Vardeman, Stephen B.; Wendelberger, Joanne R.
2003-01-01
There is a little-known but very simple generalization of the standard result that for uncorrelated variables with a common mean and variance, the expected sample variance is the marginal variance. The generalization justifies the use of the usual standard error of the sample mean in possibly heteroscedastic situations and motivates some simple estimators for unbalanced linear random effects models. The latter is illustrated for the simple one-way context.
Anita Sharma
2011-01-01
Full Text Available Blinking statistics of quantum dot has attracted much attraction in recent years. Various experiments were conducted and various theories have been given to explain this phenomenon. However, the problem is not yet resolved. The weak temperature dependence of the power law parameters have complicated the phenomena. We have simulated the blinking statistics of quantum dot based on the random walk model. We have shown that three-dimensional biased Levy random walk of electrons, the bias being the Columbic interaction between electrons and ionized atoms can explain the observed experimental results. We have simulated the blinking properties of quantum dots in a broad temperature range (10-300 K. The distributions exhibit power law behavior for a wide range of temperature, but the power law parameter increases marginally with temperature. The trend of change is independent of the size of the quantum dots as confirmed from the simulation.
Bell-Boole Inequality: Nonlocality or Probabilistic Incompatibility of Random Variables?
Andrei Khrennikov
2008-03-01
Full Text Available The main aim of this report is to inform the quantum information community about investigations on the problem of probabilistic compatibility of a family of random variables: a possibility to realize such a family on the basis of a single probability measure (to construct a single Kolmogorov probability space. These investigations were started hundred of years ago by J. Boole (who invented Boolean algebras. The complete solution of the problem was obtained by Soviet mathematician Vorobjev in 60th. Surprisingly probabilists and statisticians obtained inequalities for probabilities and correlations among which one can find the famous BellÃ¢Â€Â™s inequality and its generalizations. Such inequalities appeared simply as constraints for probabilistic compatibility. In this framework one can not see a priori any link to such problems as nonlocality and Ã¢Â€Âœdeath of realityÃ¢Â€Â which are typically linked to BellÃ¢Â€Â™s type inequalities in physical literature. We analyze the difference between positions of mathematicians and quantum physicists. In particular, we found that one of the most reasonable explanations of probabilistic incompatibility is mixing in BellÃ¢Â€Â™s type inequalities statistical data from a number of experiments performed under different experimental contexts.
K.Manikandan
2011-02-01
Full Text Available The Wide-expansion of mobile telecommunication technology mobile banking emerged as a new type of financial services and can provide efficient and effective financial services for clients. Mobile banking is a way for the customer to perform banking actions on his or her cell phone or other mobile device. It is a quite popular method of banking that fits in well with a busy, technologically oriented lifestyle. Framework conditions for mobile banking services differ from country to country but one thing is certain: the future of mobile banking depends on getting the security right. In this paper, we present a new way of securing mobile banking. We introduce a system which makes use of Elliptic curve cryptography and RGB Intensity Based Randomized pixels with variable Bits image Steganography [5]. Elliptic Curve Cryptography suites well for resources constraint devices like mobile phones and PDA, because of its less computation time, short key’s length, fast digital signature, flexibility and less resource consumption
Cryptography based on chaotic random maps with position dependent weighting probabilities
Chaotic cryptology has been widely investigated recently. A common feature in the most recent developments of chaotic cryptosystems is the use of a single dynamical rule in the encoding-decoding process. The main objective of this paper is to provide a set of chaotic systems instead of a single one for cryptography. In this paper, we introduce a chaotic cryptosystem based on the symbolic dynamics of random maps with position dependent weighting probabilities. The random maps model is a deterministic dynamical system in a finite phase space with n points. The maps that establish the dynamics of the system are chosen randomly for every point. The essential idea of this paper is that, given two dynamical systems that behave in a certain way, it is possible to combine them (by composing) into a new dynamical system. This dynamically composed system behaves in a completely different way compared to the constituent systems. The proposed scheme exploits the symbolic dynamics of a set of chaotic maps in order to encode the binary information. The performance of the new cryptosystem based on chaotic dynamical systems properties is examined. Both theoretical and experimental results demonstrate that the proposed algorithm using symbolic dynamics achieves the optimal security criteria.
A new reliability measure is proposed and equations are derived which determine the probability of existence of a specified set of minimum gaps between random variables following a homogeneous Poisson process in a finite interval. Using the derived equations, a method is proposed for specifying the upper bound of the random variables' number density which guarantees that the probability of clustering of two or more random variables in a finite interval remains below a maximum acceptable level. It is demonstrated that even for moderate number densities the probability of clustering is substantial and should not be neglected in reliability calculations. In the important special case where the random variables are failure times, models have been proposed for determining the upper bound of the hazard rate which guarantees a set of minimum failure-free operating intervals before the random failures, with a specified probability. A model has also been proposed for determining the upper bound of the hazard rate which guarantees a minimum availability target. Using the models proposed, a new strategy, models and reliability tools have been developed for setting quantitative reliability requirements which consist of determining the intersection of the hazard rate envelopes (hazard rate upper bounds) which deliver a minimum failure-free operating period before random failures, a risk of premature failure below a maximum acceptable level and a minimum required availability. It is demonstrated that setting reliability requirements solely based on an availability target does not necessarily mean a low risk of premature failure. Even at a high availability level, the probability of premature failure can be substantial. For industries characterised by a high cost of failure, the reliability requirements should involve a hazard rate envelope limiting the risk of failure below a maximum acceptable level
Quantum treatment of the time-dependent coupled oscillators under the action of a random force
In this communication we introduce the problem of time-dependent frequency converter under the action of external random force. We have assumed that the coupling parameter and the phase pump are explicitly time dependent. Using the equations of motion in the Heisenberg picture the dynamical operators are obtained, however, under a certain integrability condition. When the system is initially prepared in the even coherent states the squeezing phenomenon is discussed. The correlation function is also considered and it has been shown that the nonclassical properties are apparent and sensitive to any variation in the integrability parameter. Furthermore, the wave function in Schroedinger picture is calculated and used it to derive the wave function in the coherent states. The accurate definition of the creation and annihilation operators are also introduced and employed to diagonalize the Hamiltonian system
Large Deviations for Sums of Heavy-tailed Random Variables%重尾随机变量和的大偏差
郭晓燕; 孔繁超
2007-01-01
This paper is a further investigation of large deviations for sums of random variables Sn =n∑i=1 Xi and S(t)=N(t)∑i=1 Xi,(t≥0), where {Xn,n≥1} are independent identically distribution and non-negative random variables, and {N(t),t≥0} is a counting process of non-negative integer-valued random variables, independent of {Xn,n≥1}. In this paper, under the suppose F ∈G, which is a bigger heavy-tailed class than C, proved large deviation results for sums of random variables.
Seok Yoon Hwang
1999-03-01
Full Text Available LetÃ‚Â {Xij} be a double sequence of pairwise independent random variables.Ã‚Â IfÃ‚Â P{|Xmn|Ã¢Â‰Â¥t}Ã¢Â‰Â¤P{|X|Ã¢Â‰Â¥t} for all nonnegative real numbersÃ‚Â t and E|X|p(log+|X|3<Ã¢ÂˆÂž, for 1
random variables under the conditions E|X|p(log+|X|r+1<Ã¢ÂˆÂž,E|X|p(log+|X|rÃ¢ÂˆÂ’1<Ã¢ÂˆÂž, respectively, thus, extending Choi and Sung's result [1] of the one-dimensional case.
Homogenization for rigid suspensions with random velocity-dependent interfacial forces
Gorb, Yuliya
2014-12-01
We study suspensions of solid particles in a viscous incompressible fluid in the presence of random velocity-dependent interfacial forces. The flow at a small Reynolds number is modeled by the Stokes equations, coupled with the motion of rigid particles arranged in a periodic array. The objective is to perform homogenization for the given suspension and obtain an equivalent description of a homogeneous (effective) medium, the macroscopic effect of the interfacial forces and the effective viscosity are determined using the analysis on a periodicity cell. In particular, the solutions uωε to a family of problems corresponding to the size of microstructure ε and describing suspensions of rigid particles with random surface forces imposed on the interface, converge H1-weakly as ε→0 a.s. to a solution of a Stokes homogenized problem, with velocity dependent body forces. A corrector to a homogenized solution that yields a strong H1-convergence is also determined. The main technical construction is built upon the Γ-convergence theory. © 2014 Elsevier Inc.
DIYAH MARTANTI
2008-10-01
Full Text Available Amorphophallus muelleri Blume (Araceae is valued for its glucomanan content for use in food industry (healthy diet food, paper industry, pharmacy and cosmetics. The species is triploid (2n=3x=39 and the seed is developed apomictically. The present research is aimed to identify genetic variability of six population of A. muelleri from Java (consisted of 50 accessions using random amplified polymorphic DNA (RAPD. The six populations of the species are: East Java: (1 Silo-Jember, (2 Saradan-Madiun, (3 IPB (cultivated, from Saradan-Madiun, (4 Panti-Jember, (5 Probolinggo; and Central Java: (6 Cilacap. The results showed that five RAPD primers generated 42 scorable bands of which 29 (69.05% were polymorphic. Size of the bands varied from 300bp to 1.5kbp. The 50 accessions of A. muelleri were divided into two main clusters, some of them were grouped based on their populations, and some others were not. The range of individual genetic dissimilarity was from 0.02 to 0.36. The results showed that among six populations investigated, Saradan population showed the highest levels of genetic variation with mean values of na = 1.500+ 0.5061, ne = 1.3174 + 0.3841, PLP = 50% and He = 0, 0.1832+0.2054, whereas Silo-Jember population showed the lowest levels of genetic variation with mean values na = 1.2619+ 0.4450, ne = 1.1890 + 0.3507, PLP = 26.19% and He = 0.1048+0.1887. Efforts to conserve, domesticate, cultivate and improve genetically should be based on the genetic properties of each population and individual within population, especially Saradan population which has the highest levels of genetic variation, need more attention for its conservation.
A WntD-Dependent Integral Feedback Loop Attenuates Variability in Drosophila Toll Signaling.
Rahimi, Neta; Averbukh, Inna; Haskel-Ittah, Michal; Degani, Neta; Schejter, Eyal D; Barkai, Naama; Shilo, Ben-Zion
2016-02-22
Patterning by morphogen gradients relies on the capacity to generate reproducible distribution profiles. Morphogen spread depends on kinetic parameters, including diffusion and degradation rates, which vary between embryos, raising the question of how variability is controlled. We examined this in the context of Toll-dependent dorsoventral (DV) patterning of the Drosophila embryo. We find that low embryo-to-embryo variability in DV patterning relies on wntD, a Toll-target gene expressed initially at the posterior pole. WntD protein is secreted and disperses in the extracellular milieu, associates with its receptor Frizzled4, and inhibits the Toll pathway by blocking the Toll extracellular domain. Mathematical modeling predicts that WntD accumulates until the Toll gradient narrows to its desired spread, and we support this feedback experimentally. This circuit exemplifies a broadly applicable induction-contraction mechanism, which reduces patterning variability through a restricted morphogen-dependent expression of a secreted diffusible inhibitor. PMID:26906736
Nutrition education intervention for dependent patients: protocol of a randomized controlled trial
Arija Victoria
2012-05-01
Full Text Available Abstract Background Malnutrition in dependent patients has a high prevalence and can influence the prognosis associated with diverse pathologic processes, decrease quality of life, and increase morbidity-mortality and hospital admissions. The aim of the study is to assess the effect of an educational intervention for caregivers on the nutritional status of dependent patients at risk of malnutrition. Methods/Design Intervention study with control group, randomly allocated, of 200 patients of the Home Care Program carried out in 8 Primary Care Centers (Spain. These patients are dependent and at risk of malnutrition, older than 65, and have caregivers. The socioeconomic and educational characteristics of the patient and the caregiver are recorded. On a schedule of 0–6–12 months, patients are evaluated as follows: Mini Nutritional Assessment (MNA, food intake, dentures, degree of dependency (Barthel test, cognitive state (Pfeiffer test, mood status (Yesavage test, and anthropometric and serum parameters of nutritional status: albumin, prealbumin, transferrin, haemoglobin, lymphocyte count, iron, and ferritin. Prior to the intervention, the educational procedure and the design of educational material are standardized among nurses. The nurses conduct an initial session for caregivers and then monitor the education impact at home every month (4 visits up to 6 months. The North American Nursing Diagnosis Association (NANDA methodology will be used. The investigators will study the effect of the intervention with caregivers on the patient’s nutritional status using the MNA test, diet, anthropometry, and biochemical parameters. Bivariate normal test statistics and multivariate models will be created to adjust the effect of the intervention. The SPSS/PC program will be used for statistical analysis. Discussion The nutritional status of dependent patients has been little studied. This study allows us to know nutritional risk from different points of
On the dependence of QCD splitting functions on the choice of the evolution variable
Jadach, S; Placzek, W; Skrzypek, M
2016-01-01
We show that already at the NLO level the DGLAP evolution kernel Pqq starts to depend on the choice of the evolution variable. We give an explicit example of such a variable, namely the maximum of transverse momenta of emitted partons and we identify a class of evolution variables that leave the NLO Pqq kernel unchanged with respect to the known standard MS-bar results. The kernels are calculated using a modified Curci-Furmanski-Petronzio method which is based on a direct Feynman-graphs calculation.
Janssen Patricia A
2012-12-01
Full Text Available Abstract Background The prevalence of maternal drug use during pregnancy in North America has been estimated to be as high as 6-10%. The consequences for the newborn include increased risk for perinatal mortality and ongoing physical, neurobehavioral, and psychosocial problems. Methadone is frequently used to wean women off street drugs but is implicated as a cause of adverse fetal/neonatal outcomes itself. The purpose of our study was to test the ability of maternal acupuncture treatment among mothers who use illicit drugs to reduce the frequency and severity of withdrawal symptoms among their newborns. Methods We randomly assigned chemically dependent pregnant women at BC Women’s Hospital in Vancouver, British Columbia to daily acupuncture treatments versus usual care. By necessity, neither our participants nor acupuncturists were blinded as to treatment allocation. Our primary outcome was days of neonatal morphine treatment for symptoms of neonatal withdrawal. Secondary neonatal outcomes included admission to a neonatal ICU and transfer to foster care. Results We randomized 50 women to acupuncture and 39 to standard care. When analyzed by randomized groups, we did not find benefit of acupuncture; the average length of treatment with morphine for newborns in the acupuncture group was 2.7 (6.3 compared to 2.8 (7.0 in the control group. Among newborns of women who were compliant with the acupuncture regime, we observed a reduction of 2.1 and 1.5 days in length of treatment for neonatal abstinence syndrome compared to the non-compliant and control groups, respectively. These differences were not statistically significant. Conclusions Acupuncture may be a safe and feasible treatment to assist mothers to reduce their dosage of methadone. Our results should encourage ongoing studies to test the ability of acupuncture to mitigate the severity of neonatal abstinence syndrome among their newborns. Clinical Trial Registration http
Time-dependent Relativistic Mean-field Theory and Random Phase Approximation
P.Ring; D.Vretenar; A.Wandelt; NguyenVanGiai; MAZhong-yu; CAOLi-gang
2001-01-01
The relativistic random phase approximation (RRPA) is derived from the time-dependent relativistic mean field (TD RMF) theory in the limit of small amplitude oscillations. In the no-sea approximation of the RMF theory, the RRPA configuration space includes not only the usual particle-hole ph-states, but also ah configurations, i.e. pairs formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The contribution of the negative energy states to the RRPA matrices is examined in a schematic model, and the large effect of Dirac sea states on isoscalar strength distributions is illustrated for the giant monopole resonance in 116Sn. It is shown that
A modified NaSch model with density-dependent randomization for traffic flow
Zhu, H. B.; Ge, H. X.; Dong, L. Y.; Dai, S. Q.
2007-05-01
Based on the Nagel-Schreckenberg (NaSch) model of traffic flow, a modified cellular automaton (CA) traffic model with the density-dependent randomization (abbreviated as the DDR model) is proposed to simulate traffic flow. The fundamental diagram obtained by simulation shows the ability of this modified NaSch model to capture the essential features of traffic flow, e.g., synchronized flow, metastable state, hysteresis and phase separation at higher densities. Comparisons are made between this DDR model and the NaSch model, also between this DDR model and the VDR model. And the underlying mechanism is analyzed. All these results indicate that the presented model is reasonable and more realistic.
Hernández, Damián G.; Zanette, Damián H.; Samengo, Inés
2015-08-01
We develop the information-theoretical concepts required to study the statistical dependencies among three variables. Some of such dependencies are pure triple interactions, in the sense that they cannot be explained in terms of a combination of pairwise correlations. We derive bounds for triple dependencies, and characterize the shape of the joint probability distribution of three binary variables with high triple interaction. The analysis also allows us to quantify the amount of redundancy in the mutual information between pairs of variables, and to assess whether the information between two variables is or is not mediated by a third variable. These concepts are applied to the analysis of written texts. We find that the probability that a given word is found in a particular location within the text is not only modulated by the presence or absence of other nearby words, but also, on the presence or absence of nearby pairs of words. We identify the words enclosing the key semantic concepts of the text, the triplets of words with high pairwise and triple interactions, and the words that mediate the pairwise interactions between other words.
Hernández, Damián G; Samengo, Inés
2015-01-01
We develop the information-theoretical concepts required to study the statistical dependencies among three variables. Some of such dependencies are pure triple interactions, in the sense that they cannot be explained in terms of a combination of pairwise correlations. We derive bounds for triple dependencies, and characterize the shape of the joint probability distribution of three binary variables with high triple interaction. The analysis also allows us to quantify the amount of redundancy in the mutual information between pairs of variables, and to assess whether the information between two variables is or is not mediated by a third variable. These concepts are applied to the analysis of written texts. We find that the probability that a given word is found in a particular location within the text is not only modulated by the presence or absence of other nearby words, but also, on the presence or absence of nearby pairs of words. We identify the words enclosing the key semantic concepts of the text, the tr...
Senol Emir
2016-04-01
Full Text Available The purpose of this study is to explore the importance and ranking of technical analysis variables in Turkish banking sector. Random Forest method is used for determining importance scores of inputs for eight banks in Borsa Istanbul. Then two predictive models utilizing Random Forest (RF and Artificial Neural Networks (ANN are built for predicting BIST-100 index and bank closing prices. Results of the models are compared by three metrics namely Mean Absolute Error (MAE, Mean Square Error (MSE, Median Absolute Error (MedAE. Findings show that moving average (MAV-100 is the most important variable for both BIST -100 index and bank closing prices. Therefore, investors should follow this technical indicator with respect to Turkish banks. In addition ANN shows better performance for all metrics.
Theodorou, C. G.; Ioannidis, E. G.; Haendler, S.; Josse, E.; Dimitriadis, C. A.; Ghibaudo, G.
2016-03-01
In this paper, a parametric statistical analysis of the low-frequency noise (LFN) in very small area (W·L ≈ 10-3 μm2) 14 nm fully depleted silicon-on-insulator (FD-SOI) n-MOS devices is presented. It has been demonstrated that the LFN origin is due to carrier trapping/detrapping into gate dielectric traps near the interface and the mean noise level in such small area MOSFETs is well approached by the carrier number fluctuations model in all measurement conditions. The impact of gate voltage bias and temperature on the LFN variability, as well as the standard deviation dependence on frequency have been studied for the first time, focusing on their relation to the Random Telegraph Noise (RTN) effect and its characteristics.
Major, Péter
1999-01-01
Let $\\xi_1,\\xi_2\\ldots$ be a sequence of i.i.d.random variables, and consider the elementary symmetric polynomial $S ^(k)(n)$ of order $k =k(n)$ of the first $n$ elements $\\xi_1\\ldots,\\xi_n$ of this sequence. We are interested in the limit behavior of $S^(k) (n)$ with an appropriate transformation if $k(n)/n\\rightarrow\\alpha, 0
Kim, Junhan; Chan, Chi-kwan; Medeiros, Lia; Ozel, Feryal; Psaltis, Dimitrios
2016-01-01
The Event Horizon Telescope (EHT) is a millimeter-wavelength, very-long baseline interferometer (VLBI) that is capable of observing black holes with horizon-scale resolution. Early observations have revealed variable horizon-scale emission in the Galactic Center black hole, Sagittarius A* (Sgr A*). Comparing such observations to time-dependent general relativistic magnetohydrodynamic (GRMHD) simulations requires statistical tools that explicitly consider the variability in both the data and the models. We develop here a Bayesian method to compare time-resolved simulation images to variable VLBI data, in order to infer model parameters and perform model comparisons. We use mock EHT data based on GRMHD simulations to explore the robustness of this Bayesian method and contrast it to approaches that do not consider the effects of variability. We find that time-independent models lead to offset values of the inferred parameters with artificially reduced uncertainties. We also apply our method to the early EHT data...
Based on simple random sampling (SRS), we propose a Monte Carlo method for the faster computation of the smoothed part of the density of nuclear states. To test the applicability of the SRS approach we study in this framework the excitation energy (E), angular momentum (J) and parity dependence of nuclear level densities for an independent particle system. As an illustrative example, we consider a pf-shell nucleus, 48Cr. It is found that the values of a few lower order moments for the state density I(E) calculated using SRS and combinatorial (or direct counting) methods are almost the same and a locally smoothed part of the state density can be constructed using these moments in a univariate Edgeworth expansion. We calculate the energy dependent spin-cutoff factor and parity asymmetry and find that for both cases the SRS approach works quite well. We use the SRS moments to construct different forms of the bivariate distribution for I(E,M) (M is the z-component of J) namely (a) a bivariate Edgeworth expansion, (b) a product of the univariate Edgeworth expansion (I(E)) and a Gaussian form for conditional M distribution I(M vertical stroke E) and (c) a product of the univariate Edgeworth expansions for both I(E) and I(M vertical stroke E) and compare the resulting fixed-J level density Il(E,J) with the corresponding combinatorial results. (orig.)
Nagar, Lokesh; Dutta, Pankaj; Jain, Karuna
2014-05-01
In the present day business scenario, instant changes in market demand, different source of materials and manufacturing technologies force many companies to change their supply chain planning in order to tackle the real-world uncertainty. The purpose of this paper is to develop a multi-objective two-stage stochastic programming supply chain model that incorporates imprecise production rate and supplier capacity under scenario dependent fuzzy random demand associated with new product supply chains. The objectives are to maximise the supply chain profit, achieve desired service level and minimise financial risk. The proposed model allows simultaneous determination of optimum supply chain design, procurement and production quantities across the different plants, and trade-offs between inventory and transportation modes for both inbound and outbound logistics. Analogous to chance constraints, we have used the possibility measure to quantify the demand uncertainties and the model is solved using fuzzy linear programming approach. An illustration is presented to demonstrate the effectiveness of the proposed model. Sensitivity analysis is performed for maximisation of the supply chain profit with respect to different confidence level of service, risk and possibility measure. It is found that when one considers the service level and risk as robustness measure the variability in profit reduces.
Ahmadi-Abhari Seyed Ali; Radgoodarzi Reza; Assadi Seyed Mohammad
2003-01-01
Abstract Background Results of preclinical studies suggest that the GABAB receptor agonist baclofen may be useful in treatment of opioid dependence. This study was aimed at assessing the possible efficacy of baclofen for maintenance treatment of opioid dependence. Methods A total of 40 opioid-dependent patients were detoxified and randomly assigned to receive baclofen (60 mg/day) or placebo in a 12-week, double blind, parallel-group trial. Primary outcome measure was retention in treatment. S...
On clustering financial time series: a need for distances between dependent random variables
Marti, Gautier; Nielsen, Frank; Donnat, Philippe; Andler, Sébastien
2016-01-01
The following working document summarizes our work on the clustering of financial time series. It was written for a workshop on information geometry and its application for image and signal processing. This workshop brought several experts in pure and applied mathematics together with applied researchers from medical imaging, radar signal processing and finance. The authors belong to the latter group. This document was written as a long introduction to further development of geometric tools i...
FUNCTIONAL DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY AND RANDOM EFFECTS
AMEL BENAISSA
2015-07-01
Full Text Available In this work we study the existence of mild solutions of a functional differential equation with delay and random effects. We use a random fixed point theorem with stochastic domain to show the existence of mild random solutions.
Scales of variability of black carbon plumes and their dependence on resolution of ECHAM6-HAM
Weigum, Natalie; Stier, Philip; Schutgens, Nick; Kipling, Zak
2015-04-01
Prediction of the aerosol effect on climate depends on the ability of three-dimensional numerical models to accurately estimate aerosol properties. However, a limitation of traditional grid-based models is their inability to resolve variability on scales smaller than a grid box. Past research has shown that significant aerosol variability exists on scales smaller than these grid-boxes, which can lead to discrepancies between observations and aerosol models. The aim of this study is to understand how a global climate model's (GCM) inability to resolve sub-grid scale variability affects simulations of important aerosol features. This problem is addressed by comparing observed black carbon (BC) plume scales from the HIPPO aircraft campaign to those simulated by ECHAM-HAM GCM, and testing how model resolution affects these scales. This study additionally investigates how model resolution affects BC variability in remote and near-source regions. These issues are examined using three different approaches: comparison of observed and simulated along-flight-track plume scales, two-dimensional autocorrelation analysis, and 3-dimensional plume analysis. We find that the degree to which GCMs resolve variability can have a significant impact on the scales of BC plumes, and it is important for models to capture the scales of aerosol plume structures, which account for a large degree of aerosol variability. In this presentation, we will provide further results from the three analysis techniques along with a summary of the implication of these results on future aerosol model development.
无
2007-01-01
In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process Xn =-μ+∞∑j=-∞ψn-jεj, where {ε, εn; -∞＜ n ＜ +∞}is a sequence of independent, identically distributed random variables with zero mean, μ＞0 is a constant and the coefficients {ψi;-∞＜ i ＜∞} satisfy 0 ＜∞∑j=-∞|jψj| ＜∞. Under the conditions that the distribution function of |ε| has dominated variation and ε satisfies certain tail balance conditions, the asymptotic behavior of P{supn≥0(-nμ+∞∑j=-∞εjβnj) ＞ x}is discussed. Then the result is applied to ultimate ruin probability.
Improved Estimators of Population Mean Using Two Auxiliary Variables in Stratified random Sampling
Rajesh Singh
2012-01-01
Full Text Available An exponential family of estimators, which use the information of two auxiliary variables in the stratified sampling, is proposed to estimate the population mean of the variable under study. The mean-squared error of the suggested family of estimators are derived under large sample approximation. The family of estimators in its optimum case is carried out to show the properties of the proposed estimators.