The asymptotic theory of extreme order statistics. 2nd ed. (English) Zbl 0634.62044

Galambos, Janos

Malabar, Florida: Robert E. Krieger Publishing Company. XV, 414 p.; $ 49.50 (1987).

In reviewing the first edition of this book, see Zbl 0381.62039, we described the structure of the book, noticed some misprints and even errors, but said that it was a good book in the field of statistical extremes, beginning to grow at that time.
Nine years elapsed and we have now a corrected and enlarged edition, with the same structure and updated references until 1986. The dimension of the added material can be measured by the increase of the text from 330 p. (first ed.) to 378 p. (this ed.). Although there are other smaller modifications, we can stress the reorganization and enlargement of section 2.7 (around von Mises conditions), the various error estimates on the speed of convergence (section 2.10), the chapter 5 on multivariate extreme value distributions (essentially sections 5.3 and 5.4), and the enlargement of the surveys on literature at the end of the chapters, reflecting the growing of this field.
This is a good book. And we can conclude, as for the first edition, that it will surely be used by students and researchers interested in the probalistic theory of statistical extremes because it gives a good, balanced and clear perspective of the field.

Reviewer: J.Tiago de Oliveira

MSC:

62G30	Order statistics; empirical distribution functions
62E20	Asymptotic distribution theory in statistics
62-02	Research exposition (monographs, survey articles) pertaining to statistics
60-02	Research exposition (monographs, survey articles) pertaining to probability theory
60E05	Probability distributions: general theory
60F99	Limit theorems in probability theory
62H10	Multivariate distribution of statistics

Keywords:

statistical extremes; von Mises conditions; error estimates on the speed of convergence; multivariate extreme value distributions

Citations:

Zbl 0564.60023; Zbl 0381.62039