Extreme value and related models with applications in engineering and science.

*(English)*Zbl 1072.62045
Wiley Series in Probability and Statistics. Hoboken, NJ: John Wiley & Sons (ISBN 0-471-67172-X/hbk). xiv, 362 p. (2005).

This volume presents an elementary introduction to models and methods for extreme value data with a special emphasis on engineering applications. It provides a self-contained treatment of the area with 11 chapters (10 with exercises) divided into 5 parts.

Part 1, containing Chapter 1, discusses many applications of extreme values and introduces several univariate and multivariate data sets. These data sets are used in subsequent chapters for illustrating the many statistical models and methods. Part 2 (Chapters 2–4) contains a basic introduction to relevant univariate and multivariate (discrete and continuous) distributions. Part 3 (Chapters 5 and 6) explains a variety of techniques of parametric estimation and model selection with an emphasis on the Probability Paper, P-P, and Q-Q plots. All these plots are based on functions of uniform order statistics and sample order statistics. Distributions of order statistics and point process models that lead to extremes are discussed in Part 4 (Chapters 7 and 8).

Part 5, the longest with 134 pages that make up Chapters 9 - 11, contains the core material on asymptotic models for univariate and multivariate extremes and associated inference procedures. Generalized extreme-value distributions, generalized Pareto distributions, and dependence function of multivariate extremes are discussed there.

The associated website, http://personales.unican.es/castie/extremes/, provides necessary software downloads, data sets and corrections. With exercises and many attractive graphs, this self-contained volume can serve well for an introductory course in statistics of extremes for students majoring in several engineering disciplines. Some supplementary material on basic properties of probability would be needed. Researchers and practitioners looking for advanced material on the theory and methods would be better served by another recent multi-authored volume by J. Beirlant et al. [Statistics of Extremes. Theory and Applications. (2004; Zbl 1070.62036)].

Part 1, containing Chapter 1, discusses many applications of extreme values and introduces several univariate and multivariate data sets. These data sets are used in subsequent chapters for illustrating the many statistical models and methods. Part 2 (Chapters 2–4) contains a basic introduction to relevant univariate and multivariate (discrete and continuous) distributions. Part 3 (Chapters 5 and 6) explains a variety of techniques of parametric estimation and model selection with an emphasis on the Probability Paper, P-P, and Q-Q plots. All these plots are based on functions of uniform order statistics and sample order statistics. Distributions of order statistics and point process models that lead to extremes are discussed in Part 4 (Chapters 7 and 8).

Part 5, the longest with 134 pages that make up Chapters 9 - 11, contains the core material on asymptotic models for univariate and multivariate extremes and associated inference procedures. Generalized extreme-value distributions, generalized Pareto distributions, and dependence function of multivariate extremes are discussed there.

The associated website, http://personales.unican.es/castie/extremes/, provides necessary software downloads, data sets and corrections. With exercises and many attractive graphs, this self-contained volume can serve well for an introductory course in statistics of extremes for students majoring in several engineering disciplines. Some supplementary material on basic properties of probability would be needed. Researchers and practitioners looking for advanced material on the theory and methods would be better served by another recent multi-authored volume by J. Beirlant et al. [Statistics of Extremes. Theory and Applications. (2004; Zbl 1070.62036)].

Reviewer: H. N. Nagaraja (Columbus/Ohio)

##### MSC:

62G32 | Statistics of extreme values; tail inference |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

62P30 | Applications of statistics in engineering and industry; control charts |

62F10 | Point estimation |

62G30 | Order statistics; empirical distribution functions |