Dynamic mixing probability measures of mixtures

Abstract

Lifetime of heterogeneous population can be modeled as mixture of a family of lifetime distributions according to a mixing probability measure. With the help of dynamic mixing measure, the hazard rate of the mixture can also be expressed as the mixture of the hazard rates of the lifetime distributions. Various local stochastic orderings are defined in this article. Applying these local stochastic orderings, we can explore the behavior of the dynamic mixing measures locally and then compare the hazard rates of two heterogeneous populations in both the local and global ways.