General frailty model and stochastic orderings

In this paper, we propose a general frailty model and develop its properties including some results for stochastic comparisons. More specifically, our main results lie in seeing how the well known stochastic orderings between distributions of two frailties translate into the orderings between the corresponding survival functions. These results are used to obtain the properties of the classical multiplicative frailty model and the additive frailty model. Several of the results, in the literature, are obtained as special cases.