Poisson Approximation (Oxford Studies in Probability)

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9780198522355: Poisson Approximation (Oxford Studies in Probability)

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.

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About the Author:

A. D. Barbour is at University of Zurich. Lars Holst is at Royal Institute of Technology, Stockholm.

Review:

'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 advance material, in particular on compound Poisson and Poisson
process approximation, where the reader is brought to the boundaries of current knowledge.'
L'Enseignement Mathematique, 1992

'This monograph gives a thorough account of methods for obtaining bounds on the error arising in such approximations.'
International Statistical Institute, Vol. 12 No.3 - December 1992

'The book contains a lot of new or recent results in the fields... At saome points it also shows the limits of what is obtainable by the Stein-Chen resp. coupling methods.'
L. Ruschendorf, Zentralblatter

'All in all this book can be warmly recommended to students and researchers in probability theory and its applications. The reader interested in a deeper insight into the applications touched in the Chapters 4-9 is referred to the more than 120 references at the end of the book.'
L. Heinrich, Biomedical Journal, 35 (1993)4

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Barbour, A. D./ Holst, Lars/ Janson, Svante
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