Compound Poisson Approximation

V. ?ekanavi?ius, S. Y. Novak, V. ?ekanavi?ius, V. ?ekanavi?ius, V. ?ekanavi?ius

• Publisher: Chapman and Hall/CRC
• Year: 2024
• ISBN:
  9781040037294
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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.

Table of contents

• Cover Page
• Half-Title Page
• Title Page
• Copyright Page
• Dedication Page
• Contents
• Preface
• Authors
• Notation and abbreviations
• 1 Preliminaries
• 2 Poisson limit theorem
• 3 Accuracy of Poisson approximation
• 4 Applications
• 5 Compound Poisson limit theorem
• 6 Accuracy of CP approximation: rare events
• 7 Accuracy of CP approximation: discrete random variables
• 8 Sums of m-dependent integer-valued random variables
• 9 Markov Binomial distribution
• 10 Compound Poisson approximations related to Kolmogorov's problem
• 11 Compound Poisson approximation for sequences of random variables
• 12 Multivariate compound Poisson approximation
• 13 Compound Poisson process approximation
• 14 Appendix
• Hints and solutions to selected exercises
• Bibliography
• Index