Relations, bounds and approximations for order statistics
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].
scientific article; zbMATH DE number 194661