Stochastic orders and aging notions based upon the moment generating function order: Theory

The purpose of this paper is to study new notions of stochastic comparisons and aging notions based on the moment generating function order. Two characteristics of the moment generating function order of residual lives are obtained, and some closure properties of the aging classes DRLmg (IRLmg), NBUmg (NWUmg) and EBUmg (EWUmg) under some transformations are developed. As application, some results for random sums with applications to shock models are obtained.