Stochastic Properties of Inactivity Lifetimes at Random Times: Some Unified Results

Abstract

SYNOPTIC ABSTRACTIn this article, we consider the inactivity times and of two random variables X and Y at random times Θ1 and Θ2, respectively, and make stochastic comparisons of and with respect to likelihood ratio, hazard rate and mean residual life orders. Here, X and Θ1 (and Y and Θ2) may be dependent random variables. We also study various ageing properties of random variable . The results derived here unify and extend several existing results. An application of the results derived in this paper is also illustrated.