On the characterization of distributions by their L-moments

Abstract

A distribution with finite mean is uniquely determined by the set of expectations of the largest (or smallest) order statistics from samples of size 1, 2,.... However, this characterization contains some redundancy; some of the expectations can be dropped from the set and the remaining elements of the set still suffice to characterize the distribution. The rth L-moment of a distribution is a linear combination of the expectations of the largest (or smallest) order statistics from samples of size 1, 2,..., r. We show that a wide range of distributions can be characterized by their L-moments with no redundancy; a set that contains all of the L-moments except one no longer suffices to characterize the distribution. © 2004. Published by Elsevier B.V. All rights reserved.