Galambos, Janos The asymptotic theory of extreme order statistics. 2nd ed. (English) Zbl 0634.62044 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 Cited in 14 ReviewsCited in 274 Documents 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 PDF BibTeX XML Cite \textit{J. Galambos}, The asymptotic theory of extreme order statistics. 2nd ed. Melbourne, FL: Krieger Publishing Co., Inc. (1987; Zbl 0634.62044) OpenURL