MPIDR Working Paper

On mixture failure rate ordering

Finkelstein, M. S., Esaulova, V.
MPIDR Working Paper WP-2005-019, 18 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 can be observed asymptotically as time tends to infinity. This is due to the fact that the mixture failure rate is ‘bent down’ compared with the corresponding unconditional expectation of the baseline failure rate, which was proved previously for some specific cases. We generalize this result and discuss the “weakest populations are dying first” property, which leads to the change in the failure rate shape. We also consider the problem of mixture failure rate ordering for the ordered mixing distributions. Two types of stochastic ordering are analyzed: ordering in the likelihood ratio sense and ordering in variances when the means are equal.
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.