On proportional mean past lifetimes model

ABSTRACT

In this paper, we first investigate some reliability properties in the proportional mean past lifetimes model. Specifically, some implications of stochastic orders and aging notions between random variables which have proportional mean past lifetimes are discussed. Then, as an extension, mixture model arising from the proportional mean past lifetimes model is introduced and preservation properties of some stochastic orders and aging notions concerning this mixture model are studied. We also study some negative dependence properties in the proposed mixture model.

Keywords:

• Aging notion
• Dependence structure
• DRHR, IMPL
• Preservation
• Reversed hazard rate
• Stochastic order

Mathematics Subject Classification:

• 62N05
• 60E15

Acknowledgments

The author is sincerely grateful to anonymous referees for their helpful comments and suggestions on the earlier version of this paper which lead to this improved version.

Funding

This work was partially supported by the University of Birjand, Birjand, Iran.