A general family of univariate stochastic orders

In this paper we introduce and study a family of univariate stochastic orders parameterized by a function h  . The usual stochastic order ⩽st⩽st, and the total time on test transform order ⩽ttt⩽ttt, are special cases of this new family. We study some properties of the new family, and we give some applications of it in actuarial science, reliability theory, and statistics.