Theoretical Statistics and Mathematics Unit, ISI Delhi

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]

Click here to return to Preprints Page