(Received June 23, 1993; revised February 10, 1994)
Abstract. We investigate the equivalence of weak convergence and moment convergence of life distributions in a family which is larger than the HNBUE family. Also, we point out that within the HNBUE family the exponential distribution can be characterized by one value of its Laplace-Stieltjes transform.
Key words and phrases: Weak convergence, moment convergence, HNBUE family, convex order, characterization of distribution.