# Publications and Preprints

The Total Time on Test Transform and the Excess Wealth Stochastic Orders of Distributions
by
Subhash C. Kochar, Xiaohu Li and Moshe Shaked
For nonnegative random variables $X$ and $Y$ we write $X \le_{ttt} Y$ if $T_X (p) \le T_Y (p)$ for all $p \in (0, 1)$, where $T_X (p) \equiv \int_0^{F^{-1}(p)} (1-F(x)) dx$ and $T_Y (p) \equiv \int_0^{G^{-1}(p)} (1-G(x)) dx$; 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.

isid/ms/2002/27 [fulltext]