# Publications and Preprints

On Stochastic Comparisons of Residual Life Time at Random Time
by
Isha Dewan and Baha-Eldin Khaledi
Let $X_1, X_2,\Theta$ and $\Theta^{\prime}$ be independent non-negative random variables. The residual life of $X_i$ at random time $\Theta$, that is, $X_i^{\Theta}= X_i - \Theta | X_i > {\Theta}$ is considered. Some sufficient conditions which lead to the likelihood ratio ordering, the failure rate ordering, the reverse failure rate ordering and the mean residual life ordering between $X_1^{\Theta}$ and $X_2^{\Theta}$ are obtained and an application in queuing theory is explained. A set of conditions which lead to the same stochastic orderings between $X_1^{\Theta}$ and $X_1^{\Theta^{\prime}}$ are also derived.

isid/ms/2014/05 [fulltext]