Analysis and Estimation of Distributions using Linear Combinations of Order Statistics

Abstract

It is well known that the computation of higher order statistics, like skewness and kurtosis (which we call C-moments) is very dependent on sample size and is highly susceptible to the presence of outliers.  To overcome these difficulties, Hosking (1990) has introduced related statistics called L-moments.   L-moments are expectations of certain linear combinations of order statistics.  They can be defined for any random variable whose mean exists and form the basis of a general theory which covers the summarization and description of theoretical probability distributions and hypothetical tests for probability distributions.  The theory of L-moments parallels the theory of conventional moments as this list of applications might suggest