期刊名称：Brazilian Journal of Probability and Statistics
印刷版ISSN：0103-0752
出版年度：2018
卷号：32
期号：2
页码：422-436
DOI：10.1214/16-BJPS348
语种：English
出版社：Brazilian Statistical Association
摘要：The residual life of a random variable $X$ at random time $\Theta$ is defined to be a random variable $X_{\Theta}$ having the same distribution as the conditional distribution of $X-\Theta$ given $X>\Theta$ (denoted by $X_{\Theta}=(X-\Theta|X>\Theta)$). Let $(X,\Theta_{1})$ and $(Y,\Theta_{2})$ be two pairs of jointly distributed random variables, where $X$ and $\Theta_{1}$ (and, $Y$ and $\Theta_{2}$) are not necessarily independent. In this paper, we compare random variables $X_{\Theta_{1}}$ and $Y_{\Theta_{2}}$ by providing sufficient conditions under which $X_{\Theta_{1}}$ and $Y_{\Theta_{2}}$ are stochastically ordered with respect to various stochastic orderings. These comparisons have been made with respect to hazard rate, likelihood ratio and mean residual life orders. We also study various ageing properties of random variable $X_{\Theta_{1}}$. By considering this generalized model, we generalize and unify several results in the literature on stochastic properties of residual lifetimes at random times. Some examples to illustrate the application of the results derived in the paper are also presented.
