Stochastic properties of a time change random effects model

In this paper we develop time change models. In these models the frailty random variable enters the baseline hazard function to change the time scale which is also the case in scale change model available in literature. We investigate, when the frailty random variables are ordered then how are the corresponding population variables ordered in terms of various stochastic orders. Stochastic orders namely the usual stochastic, the likelihood ratio, the hazard rate and the mean residual life ordering between overall population variables are studied.