Characterizations of Probability Distributions.
Author: Janos Galambos
Publisher: Springer
Published: 2006-11-15
Total Pages: 177
ISBN-13: 3540357335
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Characterization of Probability Distributions on Locally Compact Abelian Groups
Author: Gennadiy Feldman
Publisher: American Mathematical Society
Published: 2023-04-07
Total Pages: 253
ISBN-13: 1470472953
DOWNLOAD EBOOKIt 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.
The Normal Distribution
Author: Wlodzimierz Bryc
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 142
ISBN-13: 1461225604
DOWNLOAD EBOOKThis book is a concise presentation of the normal distribution on the real line and its counterparts on more abstract spaces, which we shall call the Gaussian distributions. The material is selected towards presenting characteristic properties, or characterizations, of the normal distribution. There are many such properties and there are numerous rel evant works in the literature. In this book special attention is given to characterizations generated by the so called Maxwell's Theorem of statistical mechanics, which is stated in the introduction as Theorem 0.0.1. These characterizations are of interest both intrin sically, and as techniques that are worth being aware of. The book may also serve as a good introduction to diverse analytic methods of probability theory. We use characteristic functions, tail estimates, and occasionally dive into complex analysis. In the book we also show how the characteristic properties can be used to prove important results about the Gaussian processes and the abstract Gaussian vectors. For instance, in Section 5.4 we present Fernique's beautiful proofs of the zero-one law and of the integrability of abstract Gaussian vectors. The central limit theorem is obtained via characterizations in Section 7.3.
A Modern Course on Statistical Distributions in Scientific Work
Author: Ganapati P. Patil
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 430
ISBN-13: 9401018480
DOWNLOAD EBOOKThese 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.
Probability Distributions Used in Reliability Engineering
Author: Andrew N O'Connor
Publisher: RIAC
Published: 2011
Total Pages: 220
ISBN-13: 1933904062
DOWNLOAD EBOOKThe book provides details on 22 probability distributions. Each distribution section provides a graphical visualization and formulas for distribution parameters, along with distribution formulas. Common statistics such as moments and percentile formulas are followed by likelihood functions and in many cases the derivation of maximum likelihood estimates. Bayesian non-informative and conjugate priors are provided followed by a discussion on the distribution characteristics and applications in reliability engineering.
Arithmetic of Probability Distributions, and Characterization Problems on Abelian Groups
Author: Gennadiĭ Mikhaĭlovich Felʹdman
Publisher: American Mathematical Soc.
Published: 1993
Total Pages: 236
ISBN-13: 9780821845936
DOWNLOAD EBOOKThis 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.
N-distances and Their Applications
Author: Lev B. Klebanov
Publisher: Karolinum Press, Charles University
Published: 2006-04
Total Pages: 0
ISBN-13: 9788024611525
DOWNLOAD EBOOKThe book focuses on probability metrics suitable for the characterization of random variables in Hilbert or Banach space. It provides details of various stochastic processes, such as testing non-deterministic statistical hypotheses, characterization of probability distribution or constructing multidimensional test for two selections. The book is published in the English language.
Arithmetic of Probability Distributions, and Characterization Problems on Abelian Groups
Author: Gennadij M. Fel'dman
Publisher: American Mathematical Soc.
Published:
Total Pages: 236
ISBN-13: 9780821897447
DOWNLOAD EBOOKThis 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.
Queueing Theory 2
Author: Vladimir Anisimov
Publisher: John Wiley & Sons
Published: 2021-04-27
Total Pages: 336
ISBN-13: 1119755220
DOWNLOAD EBOOKThe aim of this book is to reflect the current cutting-edge thinking and established practices in the investigation of queueing systems and networks. This second volume includes eight chapters written by experts wellknown in their areas. The book conducts a stability analysis of certain types of multiserver regenerative queueing systems; a transient evaluation of Markovian queueing systems, focusing on closed-form distributions and numerical techniques; analysis of queueing models in service sectors using analytical and simulation approaches; plus an investigation of probability distributions in queueing models and their use in economics, industry, demography and environmental studies. This book also considers techniques for the control of information in queueing systems and their impact on strategic customer behavior, social welfare and the revenue of monopolists. In addition, applications of maximum entropy methods of inference for the analysis of a stable M/G/1 queue with heavy tails, and inventory models with positive service time - including perishable items and stock supplied using various algorithmic control policies ((s; S); (r;Q), etc.).
Normal and Student ́s t Distributions and Their Applications
Author: Mohammad Ahsanullah
Publisher: Springer Science & Business Media
Published: 2014-02-07
Total Pages: 163
ISBN-13: 9462390614
DOWNLOAD EBOOKThe most important properties of normal and Student t-distributions are presented. A number of applications of these properties are demonstrated. New related results dealing with the distributions of the sum, product and ratio of the independent normal and Student distributions are presented. The materials will be useful to the advanced undergraduate and graduate students and practitioners in the various fields of science and engineering.
