Asymptotic behavior of a general class of mixture failure rates
Advances in Applied Probability, 38:1, 244–262 (2006)
Mixtures of increasing failure rate distributions (IFR) can decrease at least in some intervals of time. Usually this property is observed asymptotically, which is due to the fact that a mixture failure rate is ‘bent down’, as the weakest populations are dying out first. We consider a survival model, generalizing a very well known in reliability and survival analysis additive hazards, proportional hazards and accelerated life models. We obtain new explicit asymptotic relations for a general setting and study specific cases. Under reasonable assumptions we prove that asymptotic behavior of the mixture failure rate depends only on the behavior of the mixing distribution in the neighborhood of the left end point of its support and not on the whole mixing distribution.