The total time on test transform and the excess wealth stochastic orders of distributions

Abstract

For nonnegative random variables X and Y we write X ≤ TTT Y if ∫ 0 F -1 ( p ) (1- F ( x ))d x ≤ ∫ 0 G -1 ( p ) (1- G ( x ))d x all p ∈ (0,1), where F and G denote the distribution functions of X and Y respectively. The purpose of this article is to study some properties of this new stochastic order. New properties of the excess wealth (or right-spread) order, and of other related stochastic orders, are also obtained. Applications in the statistical theory of reliability and in economics are included.