Poisson Approximation
Published on 27. February 1992
Book
Hardback
288 pages
978-0-19-852235-5 (ISBN)
Description
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.
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.
Reviews / Votes
'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
More details
Series
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Oxford University Press
Target group
Professional and scholarly
Dimensions
Height: 234 mm
Width: 153 mm
Thickness: 16 mm
Weight
588 gr
ISBN-13
978-0-19-852235-5 (9780198522355)
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Schweitzer Classification
Persons
Content
Introduction; Upper bounds; Lower bounds; Random permutations; Random graphs; Occupancy and urn models; Spacings; Exceedances and extremes; Independent and dissociated terms; Poisson process approximation; Appendices; References; Index.