Poisson Approximation
Book Details
Format
Hardback or Cased Book
Book Series
Oxford Studies in Probability
ISBN-10
0198522355
ISBN-13
9780198522355
Publisher
Oxford University Press
Imprint
Clarendon Press
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Feb 27th, 1992
Print length
288 Pages
Weight
588 grams
Dimensions
23.40 x 15.30 x 1.60 cms
Product Classification:
Calculus & mathematical analysisProbability & statisticsStochastics
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The modern theories of reliability and insurance are based on the assumption that the occurence of rare events is governed by Poisson processes. This volume provides an introduction to the Stein-Chen method, which makes it possible to assess how much error is introduced by the assumption.
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.The law of small numbers is only an approximation. In 1975, 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.
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