Download or read book Characterizations of Some Discrete Probability Distributions written by Kumar, Ashish and published by 1976.. This book was released on 1976 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Characterizations of Some Discrete Distributions written by Masood Anwar and published by LAP Lambert Academic Publishing. This book was released on 2010-08 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The characterization of distribution is useful for selection of adequate distribution to describe the observed values obtained in an experiment and is one of the methods of finding the distribution. Chapter 3 and 4 are concerned with the characterization developed by Kemp and Kemp (2004) and Ahmad and Roohi (2004). In Chapter 5, the recurrence relations between ordinary moments are established. A general characterization theorem, based on recurrence relation of ordinary moments is derived for a general class of discrete distributions. Chapter 6 deals with the recursive relations of factorial moments obtained by successive differentiation of factorial moment generating functions. In Chapters 7, 8, and 9 the theorems are then applied to numerous discrete probability distributions to provide specific characterizations for each one of them. Since information concerning moments is more often available than the knowledge of probability distribution as a whole, we expect these properties to be useful in dealing with the practical problems.
Download or read book Characterizations of Probability Distributions written by Janos Galambos and published by Springer. This book was released on 2006-11-15 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Characterization of Discrete Probability Distributions by Partial Independence written by University of Pittsburgh. Center for Multivariate Analysis and published by . This book was released on 1985 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: If X and Y are random variables such that P (X> Y) = 1 and the conditional distribution of Y given X is binomial, then Moran (1952) showed that Y and (X-Y) are independent if X is Poisson. This document extends Moran's result to a more general type of conditional distribution of Y given X, using only partial independence of Y and X-Y. This provides a generalization of a recent results of Janardhan and Rao (1982) on the characterization of generalized Polya-Eggenberger distribution. A variant of Moran's theorem is proved which generalizes the results of Patil and Seshadri (1964) on the characterization of the distribution of a random variable x based on some conditions on the conditional distribution of Y given X and the independence of Y and X-Y.
Download or read book Characterizations of Univariate Continuous Distributions written by Mohammad Ahsanullah and published by Springer. This book was released on 2017-04-18 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides in an organized manner characterizations of univariate probability distributions with many new results published in this area since the 1978 work of Golambos & Kotz "Characterizations of Probability Distributions" (Springer), together with applications of the theory in model fitting and predictions.
Download or read book Stability Characterizations of Some Probability Distributions written by Romanas Yanushkevichius and published by LAP Lambert Academic Publishing. This book was released on 2014-03 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Characterization theorems in probability theory and mathematical statistics are such theorems that establish a connection between the type of the distribution of random variables or random vectors and certain general properties of functions in them. For example, the assumption that two linear (or non-linear) statistics are identically distributed (or independent, or have a constancy regression and so on) can be used to characterize various populations. Verification of conditions of this or that characterization theorem in practice is possible only with some error, i.e., only to a certain degree of accuracy. Such a situation is observed, for instance, in the cases where a sample of finite size is considered. That is why there arises the following natural question. Suppose that the conditions of the characterization theorem are fulfilled not exactly but only approximately. May we assert that the conclusion of the theorem is also fulfilled approximately? Questions of this kind give rise to a following problem: determine the degree of realizability of the conclusions of mathematical statements in the case of approximate validity of conditions.
Download or read book Some Generalized Probability Distributions with Special Reference to the Mineral Industries written by Robert M. Becker and published by . This book was released on 1964 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Characterizations of Some Multivariate Discrete Distributions by Partial Independence written by T. Sapatinas and published by . This book was released on 1991 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recent Results on Characterization of Probability Distributions a Unified Approach Through Extensions of Deny s Theorem written by University of Pittsburgh. Center for Multivariate Analysis and published by . This book was released on 1984 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of identifying solutions of general convolution equations relative to a group has been studied in two classical papers by Choquet and Deny. Recently, Lau and Rao have considered the analogous problem relative to a certain semigroup of the real line, which extends the results of Marsaglia and Tubilla and a lemma of Shanbhag. The extended versions of Deny's theorem contained in the papers by Lau and Rao, and Shanbhag (which referred to as LRS theorems) yield as special cases improved versions of several characterizations of exponential, Weibull, stable, Pareto, geometric, Poisson and negative binomial distributions obtained by various authors during the last few years. This paper reviews some of the recent contributions to characterization of probability distributions (whose authors do not seem to be aware of LRS theorems or special cases existing earlier) and show how improved versions of these results follow as immediate corollaries to LRS theorems. It also gives a short proof of Lau-Rao theorem based on Deny's theorem and thus establish a direct link between the results of Deny and those of Lau and Rao. A variant of Lau-Rao theorem is proved and applied to some characterization problems.
Download or read book Arithmetic of Probability Distributions and Characterization Problems on Abelian Groups written by Gennadij M. Fel'dman and published by American Mathematical Soc.. This book was released on with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the problem of the decomposition of a given random variable introduction a sum of independent random variables (components). The central feature of the book is Feldman's use of powerful analytical techniques.
Download or read book Characterization of Discrete Distributions Based on Conditionality and Damage Models written by John Panaretos and published by . This book was released on 1977 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let X and Y be two non-negative, integer-valued random variables, such that X > Y, and let Z=X-Y. When the conditional distribution of Y/X=n is used for making inferences about the distribution of X or the distribution of Y, this model is called a conditionality model. Rao (Classical and Contagious discrete distributions 1963), introduced a new version of the conditionality model; he called this a damage model. In this model X represents an observation which is produced by some natural process and which may be partially damaged; Y/X=n is the destructive process. Thus Y stands for what we actually observe of X (the remaining part of X). Rao and Rubin (Sankhya 1964) obtained a characterization for the Poisson distribution using damage model theory and a condition which has come to be known as the Rao-Rubin condition. In this thesis an extension of the Rao-Rubin characterization which has been suggested by the work of Shanbhag (J.A.P. 1977) has been used to characterize many well-known discrete distributions as the distribution of X or as the distribution of Y/X=n when the other one of the two is given. This model is extended to provide characterizations for truncated distributions. A new model is suggested enabling us to characterize finite discrete distributions, truncated and untruncated. Bivariate and Multivariate extensions of all the results obtained in the Univariate case are derived. Finally, the damage model is examined in the more general situation where either the distribution of X or the distribution of Y/X=n is a compound distribution. Some interesting characterizations are provided by this situation. Many of the results existing in the literature in this field are found to be special cases of our results.
Download or read book Univariate Discrete Distributions written by Norman L. Johnson and published by John Wiley & Sons. This book was released on 2005-08-30 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Set Contains: Continuous Multivariate Distributions, Volume 1, Models and Applications, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Continuous Univariate Distributions, Volume 1, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Continuous Univariate Distributions, Volume 2, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Discrete Multivariate Distributions by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Univariate Discrete Distributions, 3rd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Discover the latest advances in discrete distributions theory The Third Edition of the critically acclaimed Univariate Discrete Distributions provides a self-contained, systematic treatment of the theory, derivation, and application of probability distributions for count data. Generalized zeta-function and q-series distributions have been added and are covered in detail. New families of distributions, including Lagrangian-type distributions, are integrated into this thoroughly revised and updated text. Additional applications of univariate discrete distributions are explored to demonstrate the flexibility of this powerful method. A thorough survey of recent statistical literature draws attention to many new distributions and results for the classical distributions. Approximately 450 new references along with several new sections are introduced to reflect the current literature and knowledge of discrete distributions. Beginning with mathematical, probability, and statistical fundamentals, the authors provide clear coverage of the key topics in the field, including: Families of discrete distributions Binomial distribution Poisson distribution Negative binomial distribution Hypergeometric distributions Logarithmic and Lagrangian distributions Mixture distributions Stopped-sum distributions Matching, occupancy, runs, and q-series distributions Parametric regression models and miscellanea Emphasis continues to be placed on the increasing relevance of Bayesian inference to discrete distribution, especially with regard to the binomial and Poisson distributions. New derivations of discrete distributions via stochastic processes and random walks are introduced without unnecessarily complex discussions of stochastic processes. Throughout the Third Edition, extensive information has been added to reflect the new role of computer-based applications. With its thorough coverage and balanced presentation of theory and application, this is an excellent and essential reference for statisticians and mathematicians.
Download or read book A Modern Course on Statistical Distributions in Scientific Work written by Ganapati P. Patil and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: These three volumes constitute the edited Proceedings of the NATO Advanced Study Institute on Statistical Distributions in Scientific Work held at the University of Calgary from July 29 to August 10, ~. 974. The general title of the volumes is "Statistical Distributions in Scientific Work". The individual volumes are: Volume 1 - Models and Structures; Volume 2 - Model Building and Model Selection; and Volume 3 - Characterizations and Applications. These correspond to the three advanced seminars of the Institute devoted to the respective subject areas. The planned activities of the Institute consisted of main lectures and expositions, seminar lectures and study group dis cussions, tutorials and individual study. The activities included meetings of editorial committees to discuss editorial matters for these proceedings which consist of contributions that have gone through the usual refereeing process. A special session was organized to consider the potential of introducing a course on statistical distributions in scientific modeling in the curriculum of statistics and quantitative studies. This session is reported in Volume 2. The overall perspective for the Institute is provided by the Institute Director, Professor G. P. Pati1, in his inaugural address which appears in Volume 1. The Linnik Memorial Inaugural Lecture given by Professor C. R. Rao for the Characterizations Seminar is included in Volume 3. As discussed in the Institute inaugural address, not mL.
Download or read book Univariate Discrete Distributions written by Norman L. Johnson and published by John Wiley & Sons. This book was released on 2005-10-03 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Set Contains: Continuous Multivariate Distributions, Volume 1, Models and Applications, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Continuous Univariate Distributions, Volume 1, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Continuous Univariate Distributions, Volume 2, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Discrete Multivariate Distributions by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Univariate Discrete Distributions, 3rd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Discover the latest advances in discrete distributions theory The Third Edition of the critically acclaimed Univariate Discrete Distributions provides a self-contained, systematic treatment of the theory, derivation, and application of probability distributions for count data. Generalized zeta-function and q-series distributions have been added and are covered in detail. New families of distributions, including Lagrangian-type distributions, are integrated into this thoroughly revised and updated text. Additional applications of univariate discrete distributions are explored to demonstrate the flexibility of this powerful method. A thorough survey of recent statistical literature draws attention to many new distributions and results for the classical distributions. Approximately 450 new references along with several new sections are introduced to reflect the current literature and knowledge of discrete distributions. Beginning with mathematical, probability, and statistical fundamentals, the authors provide clear coverage of the key topics in the field, including: Families of discrete distributions Binomial distribution Poisson distribution Negative binomial distribution Hypergeometric distributions Logarithmic and Lagrangian distributions Mixture distributions Stopped-sum distributions Matching, occupancy, runs, and q-series distributions Parametric regression models and miscellanea Emphasis continues to be placed on the increasing relevance of Bayesian inference to discrete distribution, especially with regard to the binomial and Poisson distributions. New derivations of discrete distributions via stochastic processes and random walks are introduced without unnecessarily complex discussions of stochastic processes. Throughout the Third Edition, extensive information has been added to reflect the new role of computer-based applications. With its thorough coverage and balanced presentation of theory and application, this is an excellent and essential reference for statisticians and mathematicians.
Download or read book Arithmetic of Probability Distributions and Characterization Problems on Abelian Groups written by Gennadiĭ Mikhaĭlovich Felʹdman and published by American Mathematical Soc.. This book was released on 1993 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the problem of the decomposition of a given random variable introduction a sum of independent random variables (components). The central feature of the book is Feldman's use of powerful analytical techniques.
Download or read book Characterization of Probability Distributions on Locally Compact Abelian Groups written by Gennadiy Feldman and published by American Mathematical Society. This book was released on 2023-04-07 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that if two independent identically distributed random variables are Gaussian, then their sum and difference are also independent. It turns out that only Gaussian random variables have such property. This statement, known as the famous Kac-Bernstein theorem, is a typical example of a so-called characterization theorem. Characterization theorems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions of these random variables. The first results in this area are associated with famous 20th century mathematicians such as G. Pólya, M. Kac, S. N. Bernstein, and Yu. V. Linnik. By now, the corresponding theory on the real line has basically been constructed. The problem of extending the classical characterization theorems to various algebraic structures has been actively studied in recent decades. The purpose of this book is to provide a comprehensive and self-contained overview of the current state of the theory of characterization problems on locally compact Abelian groups. The book will be useful to everyone with some familiarity of abstract harmonic analysis who is interested in probability distributions and functional equations on groups.
Download or read book Characterizations of Probability Distributions written by Janos Galambos and published by . This book was released on 2014-09-01 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
