Overview
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.
Full Product Details
Author: A. D. Barbour (Professor of Biomathematics, Professor of Biomathematics, University of Zurich) ,
Lars Holst (Professor of Mathematical Statistics, Professor of Mathematical Statistics, Royal Institute of Technology, Stockholm) ,
Svante Janson (Professor of Mathematics, Professor of Mathematics, Uppsala University) ,
Svante Janson (Professor of Mathematics, Uppsala University, Sweden)
Publisher: Oxford University Press
Imprint: Clarendon Press
Volume: 2
Dimensions:
Width: 15.30cm
, Height: 1.60cm
, Length: 23.40cm
Weight: 0.588kg
ISBN: 9780198522355
ISBN 10: 0198522355
Pages: 288
Publication Date: 27 February 1992
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Hardback
Publisher's Status: Active
Availability: To order
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Reviews
'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
