Moments of L-Statistics: A Divided Differences Approach

Owing to their extensive application in the field of robust estimation, the derivation of the distributions of linear combinations of order statistics or L-statistics and the computation of their moments has been approached in several ways. In this paper we use the properties of divided differences to obtain expressions for moments of some order statistics which arise as special cases of L-statistics. Expectations of some well known L-statistics such as trimmed mean and winsorised mean for the pareto distribution are computed. The study also undertakes the computation of L-moments which are expectations of certain linear combinations of order statistics. The algorithms have been implemented using some well known continuous distributions as examples. The results are compared with known values wherever they are available in literature.