L-moments and C-moments

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 obviate these difficulties, Hosking (1990) has introduced related statistics called L-moments. We have investigated the relationship of these two measures in a number of different ways. Firstly, we show that probability density functions (pdf ) that are estimated from L-moments are superior estimates to those obtained using C-moments and the principle of maximum entropy. C-moments computed from these pdf's are not however, contrary to what one may have expected, better estimates than those estimated from sample statistics. L-moment derived distributions for field data examples appear to be more consistent sample to sample than pdf 's determined by conventional means. Our observations and conclusions have a significant impact on the use of the conventional maximum entropy procedure which typically uses C-moments from actual data sets to infer probabilities.