L-moments and C-moments

Citation
Tj. Ulrych et al., L-moments and C-moments, STOCH ENV R, 14(1), 2000, pp. 50-68
Citations number
21
Categorie Soggetti
Environment/Ecology,"Environmental Engineering & Energy
Journal title
STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT
ISSN journal
14363240 → ACNP
Volume
14
Issue
1
Year of publication
2000
Pages
50 - 68
Database
ISI
SICI code
1436-3240(200002)14:1<50:LAC>2.0.ZU;2-O
Abstract
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.