In this paper we investigate the characterizations of life distributions under four stochastic orderings, <p, <(p), <(p) and <L, by a unified method. Conditions for the stochastic equality of two non-negative random variables under the four stochastic orderings are derived. Many previous results are consequences. As applications, we provide characterizations of life distributions by a single value of their Laplace transforms under orderings <p and <(p) and their moment generating functions under orderings <p and <(p). Under ordering <L, a characterization is given by the expected value of a strictly completely monotone function. The conditions for the stochastic equality of two non-negative vectors under the stochastic orderings <(p), <(p) and <L are presented in terms of the Laplace transforms and moment generating functions of their extremes and sample means. Characterizations of the exponential distribution among L and &Lmacr; life distribution classes are also given.
