Some Properties And Applications Of Shifted Proportional Stochastic Orders

Abstract

The purpose of this paper is to study shifted versions of the proportional likelihood ratio order, proportional (reversed) hazard rate order and some related aging classes. We give some properties and relationships to other stochastic comparisons which are known in the literature and we study some applications in the reliability theory. Furthermore, conditions for preservation of this orderings under weighted distributions are given.

Keywords

• Up (Down) proportional likelihood ratio order,Up (Down) proportional hazard rate order,Preservation,Shock models,Coherent system

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