Abstract
Stochastic comparisons and ageing properties of residual life (inactivity time) of a random variable X at random time Y (RLRT/ITRT) taking X and Y independent have been investigated in the literature. In this article, we consider X and Y not necessarily independent and obtain stochastic comparison results for RLRT and ITRT based on variance residual life (VRL) order. We also study various ageing properties of RLRT/ITRT based on the associated classes of life distributions of VRL. An application of one of the results derived in this paper is also illustrated.
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