L-moments and C-moments

It is well known that the computation of higher order statistics, like skew ness and kurtosis, (which we call C-moments) is very dependent on sample si ze and is highly susceptible to the presence of outliers. To obviate these difficulties, Hosking (1990) has introduced related statistics called L-mom ents. We have investigated the relationship of these two measures in a numb er of different ways. Firstly, we show that probability density functions ( pdf) that are estimated from L-moments are superior estimates to those obta ined using C-moments and the principle of maximum entropy. C-moments comput ed from these pdf's are not however, contrary to what one may have expected , better estimates than those estimated from sample statistics. L-moment de rived distributions for field data examples appear to be more consistent sa mple to sample than pdf's determined by conventional means. Our observation s and conclusions have a significant impact on the use of the conventional maximum entropy procedure which typically uses C-moments from actual data s ets to infer probabilities.