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Characterization And Identification Of Probability Distributions

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Characterization And Identification Of Probability Distributions

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Author : Md. Shafiqur Rahman
language : en
Publisher:
Release Date : 1991

Characterization And Identification Of Probability Distributions written by Md. Shafiqur Rahman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.

Characterization And Identification Of Probability Distributions

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Author : Shafiqur Rahman
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2012-02

Characterization And Identification Of Probability Distributions written by Shafiqur Rahman and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-02 with categories.

This book introduces three new criteria (a) moment relations, (b) moment ratios and (c) ratios of the coefficients of the recurrence relations to characterize and indentify probability distributions. In general moment relations criteria are effective but there are some special situations, where the moment relations of two or more suspected distributions are same or one particular moment function takes same value for two or more distributions. In such a situation two moment ratios as extra criteria are proposed for deciding among them. This book also discussed the identification of a distribution by using the ratios of the coefficients of the recurrence relations obtained from its generating function. The significant contribution of this research is to introduce a new special class of exponential family of distributions named 'transformed Chi-square family." Explicit expressions for the MVUE with MV of a function of the parameter of this family are given. The critical region and the power function for various tests of hypotheses for the parameter of this family are also obtained. An identification procedure with probability of correct identification is discussed in detail.

Partial Identification Of Probability Distributions

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Author : Charles F. Manski
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-29

Partial Identification Of Probability Distributions written by Charles F. Manski and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-29 with Mathematics categories.

The book presents in a rigorous and thorough manner the main elements of Charles Manski's research on partial identification of probability distributions. The approach to inference that runs throughout the book is deliberately conservative and thoroughly nonparametric. There is an enormous scope for fruitful inference using data and assumptions that partially identify population parameters.

Characterizations Of Probability Distributions

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Author : Janos Galambos
language : en
Publisher: Springer
Release Date : 2006-11-15

Characterizations Of Probability Distributions written by Janos Galambos and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Characterization Of Probability Distributions On Locally Compact Abelian Groups

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Author : Gennadiy Feldman
language : en
Publisher: American Mathematical Society
Release Date : 2023-04-07

Characterization Of Probability Distributions On Locally Compact Abelian Groups written by Gennadiy Feldman and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-07 with Mathematics categories.

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.