Compound Poisson Approximations For Sums Of Random Variables

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Compound Poisson Approximations for Sums of Random Variables

Author : R. F. Serfozo
Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Compound Poisson Approximations for Sums of Random Variables by : R. F. Serfozo

Download or read book Compound Poisson Approximations for Sums of Random Variables written by R. F. Serfozo and published by . This book was released on 1985 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document shows that a sum of dependent random variables is approximately compound Poisson when the variables are rarely nonzero and, given they are nonzero, their conditional distributions are nearly identical. It give several upper bounds on the total-variation distance between the distribution of such a sum and a compund Poisson distribution. Included is an example for Markovian occurrences of a rare event. The bounds are consistent with those that are known for Poisson approximations for sums of uniformly small random variables. (Author).

Compound Poisson Approximation

Author : V. Čekanavičius
Publisher : CRC Press
ISBN 13 : 1040037275
Total Pages : 320 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Compound Poisson Approximation by : V. Čekanavičius

Download or read book Compound Poisson Approximation written by V. Čekanavičius and published by CRC Press. This book was released on 2024-08-21 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Compound Poisson approximation appears naturally in situations where one deals with a large number of rare events. It has important applications in insurance, extreme value theory, reliability theory, mathematical biology, and more. Compound Poisson Approximation synthesizes the most important recent research in the field in a single volume. With an extensive list of references, open problems, and exercises, it will become the standard reference book on the topic. Features • Provides a comprehensive overview of this rapidly expanding field • Synthesizes the most important research results of recent years • Presents an array of special topics • Provides the reader with a set of tools needed for research and education The book is of interest to researchers and postgraduate students from probability, statistics, and mathematics.

Poisson Approximation for Sums of Dependent Bernoulli Random Variables

Author : Louis Hsiao Yun Chen
Publisher :
ISBN 13 :
Total Pages : 256 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Poisson Approximation for Sums of Dependent Bernoulli Random Variables by : Louis Hsiao Yun Chen

Download or read book Poisson Approximation for Sums of Dependent Bernoulli Random Variables written by Louis Hsiao Yun Chen and published by . This book was released on 1971 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Compound Poisson Approximation for Dissociated Random Variables Via Stein'smethod

Author : Peter Eichelsbacher
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (897 download)

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Book Synopsis Compound Poisson Approximation for Dissociated Random Variables Via Stein'smethod by : Peter Eichelsbacher

Download or read book Compound Poisson Approximation for Dissociated Random Variables Via Stein'smethod written by Peter Eichelsbacher and published by . This book was released on 1998 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Compound Poisson Approximation for Nonnegative Random Variables Via Stein's Method

Author : A. D. Barbour
Publisher :
ISBN 13 :
Total Pages : 28 pages
Book Rating : 4.:/5 (897 download)

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Book Synopsis Compound Poisson Approximation for Nonnegative Random Variables Via Stein's Method by : A. D. Barbour

Download or read book Compound Poisson Approximation for Nonnegative Random Variables Via Stein's Method written by A. D. Barbour and published by . This book was released on 1990 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to Stein's Method

Author : A. D. Barbour
Publisher : World Scientific
ISBN 13 : 981256280X
Total Pages : 240 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis An Introduction to Stein's Method by : A. D. Barbour

Download or read book An Introduction to Stein's Method written by A. D. Barbour and published by World Scientific. This book was released on 2005 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: A common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which makes this possible in a wide variety of situations. Traditional approaches, for example using Fourier analysis, become awkward to carry through in situations in which dependence plays an important part, whereas Stein's method can often still be applied to great effect. In addition, the method delivers estimates for the error in the approximation, and not just a proof of convergence. Nor is there in principle any restriction on the distribution to be approximated; it can equally well be normal, or Poisson, or that of the whole path of a random process, though the techniques have so far been worked out in much more detail for the classical approximation theorems.This volume of lecture notes provides a detailed introduction to the theory and application of Stein's method, in a form suitable for graduate students who want to acquaint themselves with the method. It includes chapters treating normal, Poisson and compound Poisson approximation, approximation by Poisson processes, and approximation by an arbitrary distribution, written by experts in the different fields. The lectures take the reader from the very basics of Stein's method to the limits of current knowledge.

Poisson Approximation for Random Sums of Bernoulli Random Variables

Author : N. Yannaros
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (897 download)

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Book Synopsis Poisson Approximation for Random Sums of Bernoulli Random Variables by : N. Yannaros

Download or read book Poisson Approximation for Random Sums of Bernoulli Random Variables written by N. Yannaros and published by . This book was released on 1989 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Bounds in Poisson Approximation for Random Sums of Bernoulli Random Variables

Author :
Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.:/5 (921 download)

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Book Synopsis Bounds in Poisson Approximation for Random Sums of Bernoulli Random Variables by :

Download or read book Bounds in Poisson Approximation for Random Sums of Bernoulli Random Variables written by and published by . This book was released on 2011 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let X[subscript n] be a sequence of Bernoulli random variables and a positive integer-valued random variable. Define S[subscript N] = X1 +X2 +... X [subscript n]) be random sums. Assume N, X1, X2, ... are independent. In this thesis, we establish uniform and non-uniform bounds in Poisson approximation for S[subscript N].

Approximate Computation of Expectations

Author : Charles Stein
Publisher : IMS
ISBN 13 : 9780940600089
Total Pages : 172 pages
Book Rating : 4.6/5 ( download)

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Book Synopsis Approximate Computation of Expectations by : Charles Stein

Download or read book Approximate Computation of Expectations written by Charles Stein and published by IMS. This book was released on 1986 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Approximation Methods in Probability Theory

Author : Vydas Čekanavičius
Publisher : Springer
ISBN 13 : 3319340727
Total Pages : 283 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Approximation Methods in Probability Theory by : Vydas Čekanavičius

Download or read book Approximation Methods in Probability Theory written by Vydas Čekanavičius and published by Springer. This book was released on 2016-06-16 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a wide range of well-known and less common methods used for estimating the accuracy of probabilistic approximations, including the Esseen type inversion formulas, the Stein method as well as the methods of convolutions and triangle function. Emphasising the correct usage of the methods presented, each step required for the proofs is examined in detail. As a result, this textbook provides valuable tools for proving approximation theorems. While Approximation Methods in Probability Theory will appeal to everyone interested in limit theorems of probability theory, the book is particularly aimed at graduate students who have completed a standard intermediate course in probability theory. Furthermore, experienced researchers wanting to enlarge their toolkit will also find this book useful.

Scientific and Technical Aerospace Reports

Author :
Publisher :
ISBN 13 :
Total Pages : 1160 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Scientific and Technical Aerospace Reports by :

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1986 with total page 1160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Asymptotic Methods in Probability and Statistics with Applications

Author : N. Balakrishnan
Publisher : Springer Science & Business Media
ISBN 13 : 1461202094
Total Pages : 541 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Asymptotic Methods in Probability and Statistics with Applications by : N. Balakrishnan

Download or read book Asymptotic Methods in Probability and Statistics with Applications written by N. Balakrishnan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditions of the 150-year-old St. Petersburg School of Probability and Statis tics had been developed by many prominent scientists including P. L. Cheby chev, A. M. Lyapunov, A. A. Markov, S. N. Bernstein, and Yu. V. Linnik. In 1948, the Chair of Probability and Statistics was established at the Department of Mathematics and Mechanics of the St. Petersburg State University with Yu. V. Linik being its founder and also the first Chair. Nowadays, alumni of this Chair are spread around Russia, Lithuania, France, Germany, Sweden, China, the United States, and Canada. The fiftieth anniversary of this Chair was celebrated by an International Conference, which was held in St. Petersburg from June 24-28, 1998. More than 125 probabilists and statisticians from 18 countries (Azerbaijan, Canada, Finland, France, Germany, Hungary, Israel, Italy, Lithuania, The Netherlands, Norway, Poland, Russia, Taiwan, Turkey, Ukraine, Uzbekistan, and the United States) participated in this International Conference in order to discuss the current state and perspectives of Probability and Mathematical Statistics. The conference was organized jointly by St. Petersburg State University, St. Petersburg branch of Mathematical Institute, and the Euler Institute, and was partially sponsored by the Russian Foundation of Basic Researches. The main theme of the Conference was chosen in the tradition of the St.

Generalized Poisson Models and their Applications in Insurance and Finance

Author : Vladimir E. Bening
Publisher : Walter de Gruyter
ISBN 13 : 3110936011
Total Pages : 456 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Generalized Poisson Models and their Applications in Insurance and Finance by : Vladimir E. Bening

Download or read book Generalized Poisson Models and their Applications in Insurance and Finance written by Vladimir E. Bening and published by Walter de Gruyter. This book was released on 2012-06-11 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.

Probability and Statistical Models with Applications

Author : CH. A. Charalambides
Publisher : CRC Press
ISBN 13 : 1420036084
Total Pages : 665 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Probability and Statistical Models with Applications by : CH. A. Charalambides

Download or read book Probability and Statistical Models with Applications written by CH. A. Charalambides and published by CRC Press. This book was released on 2000-09-21 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph of carefully collected articles reviews recent developments in theoretical and applied statistical science, highlights current noteworthy results and illustrates their applications; and points out possible new directions to pursue. With its enlightening account of statistical discoveries and its numerous figures and tables, Probabili

Probability Approximations and Beyond

Author : Andrew Barbour
Publisher : Springer Science & Business Media
ISBN 13 : 1461419662
Total Pages : 166 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Probability Approximations and Beyond by : Andrew Barbour

Download or read book Probability Approximations and Beyond written by Andrew Barbour and published by Springer Science & Business Media. This book was released on 2011-12-08 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: In June 2010, a conference, Probability Approximations and Beyond, was held at the National University of Singapore (NUS), in honor of pioneering mathematician Louis Chen. Chen made the first of several seminal contributions to the theory and application of Stein’s method. One of his most important contributions has been to turn Stein’s concentration inequality idea into an effective tool for providing error bounds for the normal approximation in many settings, and in particular for sums of random variables exhibiting only local dependence. This conference attracted a large audience that came to pay homage to Chen and to hear presentations by colleagues who have worked with him in special ways over the past 40+ years. The papers in this volume attest to how Louis Chen’s cutting-edge ideas influenced and continue to influence such areas as molecular biology and computer science. He has developed applications of his work on Poisson approximation to problems of signal detection in computational biology. The original papers contained in this book provide historical context for Chen’s work alongside commentary on some of his major contributions by noteworthy statisticians and mathematicians working today.

Lectures on the Poisson Process

Author : Günter Last
Publisher : Cambridge University Press
ISBN 13 : 1107088011
Total Pages : 315 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Lectures on the Poisson Process by : Günter Last

Download or read book Lectures on the Poisson Process written by Günter Last and published by Cambridge University Press. This book was released on 2017-10-26 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.

Nonconventional Limit Theorems And Random Dynamics

Author : Yeor Hafouta
Publisher : World Scientific
ISBN 13 : 9813235020
Total Pages : 299 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Nonconventional Limit Theorems And Random Dynamics by : Yeor Hafouta

Download or read book Nonconventional Limit Theorems And Random Dynamics written by Yeor Hafouta and published by World Scientific. This book was released on 2018-04-09 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to limit theorems for nonconventional sums and arrays. Asymptotic behavior of such sums were first studied in ergodic theory but recently it turned out that main limit theorems of probability theory, such as central, local and Poisson limit theorems can also be obtained for such expressions. In order to obtain sufficiently general local limit theorem, we develop also thermodynamic formalism type results for random complex operators, which is one of the novelties of the book.