Stochastic Environmental Research and Risk Assessment

, Volume 14, Issue 1, pp 50–68

L-moments and C-moments


  • T. J. Ulrych
    • Department of Earth & Ocean Sciences, University of British Columbia, 2219 Main Mall, Vancouver, BC, Canada V6T 1Z4
  • D. R. Velis
    • Formerly Department of Earth & Ocean Sciences, University of British Columbia; presently Observatorio Astronómico, Universidad Nacional de La Plata, Paseo del Bosque s/n, La Plata 1900, Argentina
  • A. D. Woodbury
    • Department of Civil and Geological Engineering, University of Manitoba, 15 Gillson St., Winnipeg, MB, Canada R3T 5V6
  • M. D. Sacchi
    • Department of Physics, University of Alberta, Avadh Bhatia Physics Lab., Edmonton, AB, Canada T6G 2J1

DOI: 10.1007/s004770050004

Cite this article as:
Ulrych, T., Velis, D., Woodbury, A. et al. Stochastic Environmental Research and Risk Assessment (2000) 14: 50. doi:10.1007/s004770050004


 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.

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© Springer-Verlag Berlin Heidelberg 2000