A new characterization and global properties of esary-marshall-proschan shock models with applications

Abstract

The Esary-Marshall-Proschan (EMP) shock model survival distributions are shown to be equivalent to the class of hitting time distributions in continuous time uniformizable absorbing Markov chains and the class of generalized Erlang mixtures. In contrast to the usual aging-preservation results, we consider some global properties of these shock models which are shown to strictly iclude the class of Phase type distributions introduced by Neuts and which are of increasing importance in contemporary computational approach to stochastic modelling. Our methodology provides an alternative approach as well as some new results for such distributions and processes, using a duality between discrete and continuous Phase type distributions via the EMP-shock models. In addition to such applications to Phase type distributions, other applications of our results for EMP-shock models are considered including renewal processes generated by such survival distributions