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Poisson approximation


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.

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

83 citations in Web of Science®

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Additional indexing

Item Type:Monograph
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1992
Deposited On:17 Nov 2009 09:03
Last Modified:05 Apr 2016 13:28
Publisher:The Clarendon Press Oxford University Press
Series Name:Oxford Studies in Probability
Volume:2
Number of Pages:277
ISBN:0-19-852235-5
Additional Information:Oxford Science Publications
Publisher DOI:10.1214/aop/1176989531
Official URL:http://www.oup.com/us/catalog/general/subject/Mathematics/ProbabilityStatistics/?view=usa&ci=9780198522355
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1163825

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