For nonnegative random variables \(X\) and \(Y\) we write
\(X\le_{\textup{ttt}}Y\) 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.