On the hazard rate of α-mixture of survival functions

The alpha-mixture model, as a flexible family of distributions, is an effective tool for modeling heterogeneity inS population. This article investigates the hazard rate of alpha-mixture in terms of hazard rates of mixed baseline distributions. In particular, when the baseline hazard rate follows either additive or multiplicative models an inverse problem to obtain the baseline hazard is solved. We, also, study the alpha-mixture hazard rate ordering for the ordered mixing distributions in the sense of likelihood ratio order. Sufficient conditions to order two finite alpha-mixtures in the sense of dispersive ordering are provided. Finally, it is shown that the hazard rate of the finite alpha-mixture in the multiplicative model tends to the hazard rate of the strongest (weakest) population as alpha ->+infinity (-infinity). Several examples are presented to illustrate theoretical findings.