The Total Time on Test Transform and the Excess Wealth Stochastic Orders of Distributions

For nonnegative random variables X and Y we write X ≤ttt Y if TX(p) ≤ TY (p) for all p ∈ (0, 1), where TX(p) ≡ ∫ F−1(p) 0 (1− F (x)) dx and TY (p) ≡ ∫ G−1(p) 0 (1−G(x)) dx; here 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 obtained in the present article as well. Applications in the statistical theory of reliability and in economics are included. AMS Subject Classification: 60E15, 62N05.