This paper studies a family of stochastic orders of random variables defined via the comparison of their percentile inactivity time functions. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are...

If the random variable T denotes the lifetime (T 0, with probability one) of a unit, then the random variable T <Subscript> (t) </Subscript>=[t − T|T ⩽ t],, for a fixed t, is known as the inactivity time or the reversed residual lifetime. In this paper, we define a new class of life distributions based on the...</subscript>