Relations, bounds, and approximations for order statistics

de Barry C. Arnold

This book describes in great length some relations satisfied by moments of order statistics and some methods of deriving bounds and approximations for these moments. The main purpose of the book is to present various old, as well as recent, developments in the above-mentioned three topics in order statistics and also to illustrate some of their uses. Statisticians working in the areas of order statistics, approximation theory, robust inference, goodness-of-fit, outliners, etc., will find this book quite useful. Various new results, particularly involving order statistics from outliner models, have been presented and their uses in robustness studies have been demonstrated. Some inter-relationships between various results are pointed out; some cautionary notes are given regarding their use. These will be of interest to those who are working on theoretical as well as computational, problems in order statistics and related areas. Some generalizations of well-known results are presented and these will be of interest to researchers working in the area of order statistics and also to those who are applying the theory of order statistics to other fields, including quality control, reliability, control theory, etc.