Some New Results on Stochastic Comparisons of Spacings of Generalized Order Statistics from One and Two Samples

Abstract

Generalized order statistics (GOSs) are often adopted as a tool for providing a unified approach to several stochastic models dealing with ordered random variables. In this contribution, we first recall various useful results based on the notion of total positivity. Then, some stochastic comparisons between spacings of GOSs from one sample, as well as two samples, are developed under the more general assumptions on the parameters of the model. Specifically, the given results deal with the likelihood ratio order, the hazard rate order and the mean residual life order. Finally, an application is demonstrated for sequential systems.

Keywords

• stochastic orders
• logconvexity/logconcavity
• total positivity
• basic composition theorem
• generalized order statistics