Abstract

The aim of this article is to extend the inactivity probability order, defined by Abouelmagd et al. (Communications in Statistics-Theory and Methods 47, 3293–3304, 2018), to the case of non independent random variables. It is done by defining a new stochastic order based on the inactivity times of two non negative dependent random variables and the stochastic precedence order. Some characterizations and preservation properties of the new stochastic order have been developed. Also, some of its reliability properties and its relation with the other existing well known stochastic orders have been studied. We also discuss some applications of the derived results.

摘要

本文的目的是扩展 Abouelmagd 等人定义的不活动概率顺序。（Communications in Statistics-Theory and Methods 47, 3293–3304, 2018），以非独立随机变量为例。它是通过根据两个非负相关随机变量的不活动时间和随机优先顺序定义一个新的随机顺序来完成的。已经开发了新随机顺序的一些表征和保存特性。此外，还研究了它的一些可靠性属性及其与其他现有的众所周知的随机顺序的关系。我们还讨论了导出结果的一些应用。