Admissible mixing distributions for a general class of mixture survival models with known asymptotics

Statistical analysis of data on the longest living humans leaves room for speculation whether the human force of mortality is actually leveling off. Based on this uncertainty, we study a mixture failure model, introduced by Finkelstein and Esaulova (2006) that generalizes, among others, the proportional hazards and accelerated failure time models. In this paper we first, extend the Abelian theorem of these authors to mixing distributions, whose densities are functions of regular variation. In addition, taking into account the asymptotic behavior of the mixture hazard rate prescribed by this Abelian theorem, we prove three Tauberian-type theorems that describe the class of admissible mixing distributions. We illustrate our findings with examples of popular mixing distributions that are used to model unobserved heterogeneity.