A family of cumulative hazard functions and their frailty connections

Anaya-Izquierdo, Karim; Jones, M. C. and Davis, Alice (2021). A family of cumulative hazard functions and their frailty connections. Statistics & Probability Letters, 172, article no. 109059.

DOI: https://doi.org/10.1016/j.spl.2021.109059

Abstract

We consider a novel family of cumulative hazard functions (CHFs) controlled by a single shape parameter, which corresponds to proportionality on a certain scale, in such a way that the family is closed under inversion of the CHF and under frailty mixing using an appropriate mixing distribution. The latter leads to natural shared frailty models in the bivariate case. We also suggest how best to incorporate a second, complementary, shape parameter in order to obtain especially useful parametric models for survival and reliability analysis.

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