Relative stochastic comparisons of additive frailty models

Abstract

Abstract This article is devoted to the proposal of two relative stochastic orders namely the relative hazard rate and relative mean residual life orders. These stochastic orders are applied to provide some stochastic comparisons between two additive frailty models. Some closure properties of the model with respect to these relative stochastic orders are presented. In addition, we demonstrate how the variation of the baseline variable and the variation of the additive variable in the additive frailty model, each in one time, has an effect on the model. Finally, a possible extension of the concept of relative orders to the multivariate case is discussed.

Keywords

• stochastic order
• hazard rate
• mean residual life
• additive hazards model
• mixture
• multivariate mean residual life