MPIDR Working Paper

Asymptotic behavior of mixture failure rates

Finkelstein, M. S., Esaulova, V.
MPIDR Working Paper WP-2005-023, 28 pages.
Rostock, Max Planck Institute for Demographic Research (August 2005)
Open Access


Mixtures of increasing failure rate distributions (IFR) can decrease at least in some intervals of time. Usually this property is observed asymptotically as time tends to infinity , 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 distri-bution in the neighborhood of the left end point of its support and not on the whole mixing distribution.
The Max Planck Institute for Demographic Research (MPIDR) in Rostock is one of the leading demographic research centers in the world. It's part of the Max Planck Society, the internationally renowned German research society.