Stochastic Comparisons of Sample Spacings

Abstract

AbstractThe differences between order statistics are called sample spacings, the sample range being a special case. They are of great interest in various areas of statistics, in particular, in characterizations of distributions, goodness-of-fit tests, life testing, reliability models, and auction theory. In the reliability context, they correspond to times elapsed between successive failures of components in a system. This chapter is devoted to the study of the stochastic properties of sample spacings. Stochastic order relations between the successive normalized spacings from restricted families of distributions are investigated. The distribution theory of the normalized spacings in the case of heterogeneous exponential random variables is studied in detail. When the observations are not identically distributed, the tools of majorization and Schur convexity are used to see the effect of changes in the parameters of the parent distributions on the stochastic properties of the spacings.KeywordsSchur convexMajorizationSample rangeLikelihood ratio orderingHazard rate orderingStochastic orderingDispersive orderingRight spread ordering