What Properties Should a Frailty Distribution Possess?
Trifon I. Missov, Max Planck Institute for Demographic Research
The article studies a mixture model, proposed in Finkelstein and Esaulova (2006), which generalizes many popular models, most notably proportional hazards and accelerated life. In this framework we derive that a crucial feature of the frailty distribution is its regular variation at 0. Among the popular distributions to model unobserved heterogeneity, the gamma, beta, Weibull, and truncated normal densities have this property, as opposed to the inverse Gaussian and lognormal distributions.