MPIDR Working Paper

On mixture failure rate ordering

Finkelstein, M. S., Esaulova, V.
MPIDR Working Paper WP-2005-019, 18 pages.
Rostock, Max-Planck-Institut für demografische Forschung (August 2005)
OpenAccess

Abstract

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.
Das Max-Planck-Institut für demografische Forschung (MPIDR) in Rostock ist eines der international führenden Zentren für Bevölkerungswissenschaft. Es gehört zur Max-Planck-Gesellschaft, einer der weltweit renommiertesten Forschungsgemeinschaften.