Extreme value theory in engineering. (English) Zbl 0657.62004

Statistical Modeling and Decision Science. Boston, MA etc.: Academic Press, Inc. xv, 389 p. $ 59.95 (1988).
The aim of this book, as is described in the introduction, is “to bring to engineers and applied scientists some selected results of extreme value theory which can be useful in application”. The mathematical details are kept to a minimum but throughout the book a large number of illustrative applications are presented. Many of these are taken from areas of recent research interest. Some theoretical parts of the book are completely original, i.e. chapter 9 and parts of chapters 3, 4 and 6. The book is well written in an easy, accessible style and it can be used as a textbook or as a consulting book.
Table of Contents: 1. Introduction and motivation; 2. Order statistics; 3. Asymptotic distributions of maxima and minima (i.i.d. case); 4. Shortcut procedures: probability papers and least-squares methods; 5. The Gumbel, Weibull and Fréchet distributions; 6. Selection of limit distributions from data; 7. Limit distributions of k-th order statistics; 8. Limit distributions in the case of dependence; 9. Multivariate and regression models related to extremes; 10. Multivariate extremes; Appendix A. The orthogonal inverse expansion method; Appendix B. Computer codes; Appendix C. Data examples.
Reviewer: W.Dziubdziela


62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62E20 Asymptotic distribution theory in statistics
62G30 Order statistics; empirical distribution functions
62N99 Survival analysis and censored data
60F05 Central limit and other weak theorems