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An introduction to statistical modeling of extreme values. (English) Zbl 0980.62043

Springer Series in Statistics. London: Springer. xiv, 210 p. (2001).
This is a truly enjoyable introduction with a collection of 11 highly motivating data sets and an excellent, clear, discussion of the probabilistic framework and associated inferential techniques with minimal use of notations. It has very little overlap with and different emphasis from the recent monograph of S. Kotz and S.Nadarajah, Extreme value distributions. Theory and applications. (2000; Zbl 0960.62051). Chapter 1 introduces the data sets that are generously recalled later. Chapter 2 makes the volume self-contained by providing basic distributional results and discussing the maximum likelihood method that is used as the basic inferential tool. The main body provides a good discussion and illustration of classical extreme value theory (Ch. 3), exceedance models (Ch. 4), and models for stationary (Ch. 5) and some non-stationary (Ch. 6) data. Chapter 7 discusses the powerful point process approach. A light introduction to multivariate extremes is given in Chapter 8 and the last chapter provides a brief discussion of Bayesian analysis and spatial extremes. The appendix provides the web resources for the data sets, and S-PLUS codes relevant for the various analyses given in the book.
Readers, especially non-statisticians, seeking to model the data of extreme values, will find this book a very practical, invaluable resource. Statistician that are new in the area, will find this treatment comprehensive, and rigorous for the most part, even though it is short and quite informal. (The reviewer found techniques for checking goodness-of-fit beyond the plots to be lacking.) In summary, this is a highly welcome monograph recommended for the personal collection of anyone who plans to interact with extreme value data.

MSC:

62G32 Statistics of extreme values; tail inference
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62M99 Inference from stochastic processes

Citations:

Zbl 0960.62051

Software:

ismev; S-PLUS
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