Abstract

In this article, we first study the likelihood ratio ordering of generalized order statistics (GOS) in both one-sample and two-sample problems. Then, we establish the transmission of the increasing hazard rate and decreasing reversed hazard rate aging properties of GOS. To do this, we extend Karlin’s basic composition theorem for the functions of three variables. Then, we settle certain open problems in this regard by providing some counterexamples. We further investigate similar transmission cases which have not been addressed in the literature so far.

中文翻译：

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似然比排序和广义排序统计老化特性的一些新结果

摘要

在本文中，我们首先研究了单样本和双样本问题中广义顺序统计 (GOS) 的似然比排序。然后，我们建立了 GOS 的增加危险率和减少反向危险率老化特性的传递。为此，我们将卡林的基本组合定理扩展为三个变量的函数。然后，我们通过提供一些反例来解决这方面的一些悬而未决的问题。我们进一步调查了迄今为止文献中尚未解决的类似传播案例。