An introduction to order statistics
type: Item
instance of: scholarly article
title: An introduction to order statistics
zbMATH Open document ID: 1276.62029
DOI: 10.2991/978-94-91216-83-1
author: M. Shakil
author: M. Ahsanullah
author: V. B. Nevzorov
published in: Atlantis Studies in Probability and Statistics
publication date: 2013-04-08T00:00:00Z
review text: This book is an original instructional exposition of the general theory of order statistics, as an alternative to the well-known monographs due to \textit{H.A. David} [Order statistics. NY: Wiley (1970; Zbl 0223.62057)], \textit{J. Galambos} [The asymptotic threory of extreme order statistics. NY: Wiley (1978; Zbl 0381.62039)], \textit{B.C. Arnold} et al. [A first course in order statistics. NY: Wiley (1992; Zbl 0850.62008)], \textit{U. Kamps} [A concept of generalized order statistics. Stuttgart: Teubner (1995; Zbl 0851.62035)], \textit{V.B. Nevzorov} [Records. Mathematical theory. (Russian) Moscow: (2000; Zbl 0989.62029)]), among other treatments of this subject. The work brings together, in an elegant way, the most important results of this topic. The authors mainly refer to the case of independent and identically distributed random variables. The richness of theoretical results is supplemented by appropriate comments. The theory is grouped in 21 chapters, in an interesting presentation. Thus, each chapter begins with a short exposition of the basic definitions and fundamental results corresponding to the studied problem; then, the readers are urged to solve a lot of exercises. In fact, all significant theoretical developments and suggestive examples are contained in these sets of proposed exercises. The readers can find detailed solutions at the end of each chapter. These solutions are carefully written and filled with suitable remarks. Another feature of this paper is the attention given to the connection between the theory of order statistics and the theories of extreme values and record values, respectively. Also to mention the comprehensive treatment of the properties of estimators and predictors based on order statistics. The book is organized as follows. The first three chapters present the basic definitions of order statistics and related notions. The distributions of order statistics, sample quantiles and ranges of different kind are discussed. Chapter 4…
reviewed by: Eugen Paltanea
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 62G32
Mathematics Subject Classification ID: 62-01
Mathematics Subject Classification ID: 62N02
Mathematics Subject Classification ID: 62N01
zbMATH DE Number: 6151705
zbMATH Keywords: extreme values
zbMATH Keywords: record values
zbMATH Keywords: exponential distributions
zbMATH Keywords: uniform distributions
zbMATH Keywords: normal distributions
zbMATH Keywords: estimators
zbMATH Keywords: predictors
zbMATH Keywords: censored samples
zbMATH Keywords: generalized order statistics
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2991/978-94-91216-83-1
OpenAlex ID: W323503293
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description: scientific article; zbMATH DE number 6151705