Theoretical Statistics and Mathematics Unit, ISI Delhi

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]

Click here to return to Preprints Page