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Order statistics: An introduction. (English) Zbl 0908.62060
Balakrishnan, N. (ed.) et al., Order statistics: theory & methods. Amsterdam: North Holland/ Elsevier. Handb. Stat. 16, 3-24 (1998).
The first chapter of the book, written by the well-known specialists in the theory and applications of order statistics, gives an excellent introduction to this important and rapidly developing branch of mathematical statistics. According to the authors opinion their task was to give an elementary introduction to order statistics which can be regarded as “a bare essential description of the subject that would facilitate the reader to follow all other chapters in the handbook”. This chapter includes 17 sections devoted to such important topics as marginal and joint distributions of order statistics, properties of single and product moments, recurrence relations, identities, bounds and series approximations for moments, characterizations of various distributions based on order statistics, asymptotic behaviour and extreme value theory.
The authors reviewed the main results connected with applications in estimation, prediction and hypothesis testing for full and censored samples with emphasis on robustness of procedures based on order statistics. Schemes with type-I and type-II censoring as well as hybrid, random and progressive censoring are discussed. Several facts about related statistics (records, spacings, concomitants) are presented. Undoubtedly, this article is a good starting point for the whole volume.
For the entire collection see [Zbl 0894.00024].

MSC:
62G30 Order statistics; empirical distribution functions
62E10 Characterization and structure theory of statistical distributions
62G35 Nonparametric robustness
60G70 Extreme value theory; extremal stochastic processes
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