Quantile-based Reliability Measures and Some Associated Stochastic Orderings

Abstract

There are several statistical models which have explicit quantile functions, but do not have manageable cumulative distribution functions. For example, Govindarajulu, various forms of lambda, and power-Pareto distributions. Thus, to study the reliability measures for such kind of distributions, a quantile-based tool is essentially required. In this article, we consider quantile version of some well- known reliability measures in the reversed time scale. We study stochastic orders based on the reversed hazard quantile function and the mean inactivity quantile time function. Further, we discuss relative reversed hazard quantile function order, likelihood quantile ratio order, and elasticity quantile order. Connections between the newly proposed orders and the existing stochastic orders are established. AMS 2010 Subject Classification: 60E15, 62E10