Stochastic orders and aging classes based on quantile residual life in a proportional context

Abstract

A new proportional stochastic order is defined based on the concept of quantile residual life. In addition, a new aging class of life distributions, namely, decreasing proportional failure rate distributions, was defined. Moreover, two other aging classes based on the proposed stochastic ordering are defined and investigated: decreasing proportional α-quantile residual life and its dual increasing proportional α-quantile residual life. The relationship between the proportional failure rate and proportional α-quantile residual life has been discussed. Some well-known and useful models are classified in terms of the proportional α-quantile residual life function. Finally, a new modified Pareto distribution with a decreasing proportional failure rate and an increasing proportional α-quantile residual life function was presented and studied.

Keywords

• Quantile residual life
• Stochastic order
• Proportional order
• Reliability theory
• Survival analysis
• Pareto distribution