STOCHASTIC PROPERTIES OF GENERALIZED FINITE MIXTURE MODELS WITH DEPENDENT COMPONENTS

In this paper we consider a new generalized finite mixture model formed by dependent and identically distributed (d.i.d.) components. We then establish results for the comparisons of lifetimes of two such generalized finite mixture models in two different cases: (i) when the two mixture models are formed from two random vectors X and Y but with the same weights, and (ii) when the two mixture models are formed with the same random vectors but with different weights. Because the lifetimes of k-out-of-n systems and coherent systems are special cases of the mixture model considered, we use the established results to compare the lifetimes of k-out-of-n systems and coherent systems with respect to the reversed hazard rate and hazard rate orderings.

Automated summary

This paper considers a new generalized finite mixture model and establishes comparisons for the lifetimes of two such models under different scenarios. The established results are used to compare the lifetimes of k-out-of-n systems and coherent systems in terms of reversed hazard rate and hazard rate orderings.