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.
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