# Poisson approximation - Zurich Open Repository and Archive

Barbour, A D; Holst, L; Janson, S (1992). Poisson approximation. New York: The Clarendon Press Oxford University Press.

## Abstract

The Poisson "law of small numbers" is a central principle in modern theories of reliability, insurance, and the statistics of extremes. It also has ramifications in apparently unrelated areas, such as the description of algebraic and combinatorial structures, and the distribution of prime numbers. Yet despite its importance, the law of small numbers is only an approximation. In 1975, however, a new technique was introduced, the Stein-Chen method, which makes it possible to estimate the accuracy of the approximation in a wide range of situations. This book provides an introduction to the method, and a varied selection of examples of its application, emphasizing the flexibility of the technique when combined with a judicious choice of coupling. It also contains more advanced material, in particular on compound Poisson and Poisson process approximation, where the reader is brought to the boundaries of current knowledge. The study will be of special interest to postgraduate students and researchers in applied probability as well as computer scientists.

## Abstract

The Poisson "law of small numbers" is a central principle in modern theories of reliability, insurance, and the statistics of extremes. It also has ramifications in apparently unrelated areas, such as the description of algebraic and combinatorial structures, and the distribution of prime numbers. Yet despite its importance, the law of small numbers is only an approximation. In 1975, however, a new technique was introduced, the Stein-Chen method, which makes it possible to estimate the accuracy of the approximation in a wide range of situations. This book provides an introduction to the method, and a varied selection of examples of its application, emphasizing the flexibility of the technique when combined with a judicious choice of coupling. It also contains more advanced material, in particular on compound Poisson and Poisson process approximation, where the reader is brought to the boundaries of current knowledge. The study will be of special interest to postgraduate students and researchers in applied probability as well as computer scientists.

## Citations

86 citations in Web of ScienceĀ®

## Altmetrics

Item Type: Monograph 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 1992 17 Nov 2009 09:03 05 Apr 2017 07:32 The Clarendon Press Oxford University Press Oxford Studies in Probability 2 277 0-19-852235-5 Oxford Science Publications https://doi.org/10.1214/aop/1176989531 http://www.oup.com/us/catalog/general/subject/Mathematics/ProbabilityStatistics/?view=usa&ci=9780198522355 http://www.ams.org/mathscinet-getitem?mr=1163825