Families of Life Distributions Characterized by Two Moments

摘要

The authors consider several classical notions of partial orderings among life distributions which have been used to describe aging properties, tail domination, etc. They show that if a distribution G dominates another distribution F in one of these partial orderings, and if two moments of G agree with those of F, including the moment that describes the partial ordering, then G = F. This leads to a characterization of the exponential distribution among HNBUE and HNWUE life distribution classes, and thus extends the results of Basu and Bhattacharjee (1984) and rectifies an error in that paper. Keywords: Non-negative random variables. (KR)