Relations, bounds and approximations for order statistics
type: Item
instance of: scholarly article
title: Relations, bounds and approximations for order statistics
zbMATH Open document ID: 0703.62064
author: Barry C. Arnold
author: Narayanaswamy Balakrishnan
published in: Lecture Notes in Statistics
publication date: 1993-06-05T00:00:00Z
review text: This monograph deals with problems concerning moments of order statistics in case of i.i.d. random variables. Occasionally results for dependent and non-identically distributed r.v.'s are included. The contents of the book may be satisfactorily described by the chapter titles: 1. The distributions of order statistics. 2. Recurrence relations and identities for order statistics. 3. Bounds on expectations of order statistics. 4. Approximations to moments of order statistics. 5. Order statistics from a sample containing a single outlier. 6. Record values. References. Author index. Subject index. The book is well written and the proofs are carefully elaborated. Further material about distributional properties and moments of order statistics are listed in the exercises supplementing each chapter. This book covers to some extent the field of moments of order statistics and provides excellent references to the literature without being exhaustive. Supposedly, many statisticians can contribute further results on moments of order statistics [see e.g. an Edgeworth-type expansion developed by the reviewer, Probability and statistical decision theory, Proc. 4 th Pannonian Symp. Math. Stat., Bad Tatzmannsdorf/Austria 1983, Vol. A, 293- 300 (1985; Zbl 0585.60048), and further references mentioned there].
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 62E15
Mathematics Subject Classification ID: 62-02
Mathematics Subject Classification ID: 62-01
zbMATH DE Number: 194661
zbMATH Keywords: moments of order statistics
zbMATH Keywords: distributions of order statistics
zbMATH Keywords: recurrence relations
zbMATH Keywords: identities
zbMATH Keywords: bounds on expectations
zbMATH Keywords: approximations
zbMATH Keywords: outlier
zbMATH Keywords: record values
zbMATH Keywords: exercises
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 194661