Stochastic Environmental Research and Risk Assessment

, Volume 14, Issue 1, pp 50–68

L-moments and C-moments

  • T. J. Ulrych
  • D. R. Velis
  • A. D. Woodbury
  • M. D. Sacchi

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.

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • T. J. Ulrych
    • 1
  • D. R. Velis
    • 2
  • A. D. Woodbury
    • 3
  • M. D. Sacchi
    • 4
  1. 1.Department of Earth & Ocean Sciences, University of British Columbia, 2219 Main Mall, Vancouver, BC, Canada V6T 1Z4CA
  2. 2.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, ArgentinaAR
  3. 3.Department of Civil and Geological Engineering, University of Manitoba, 15 Gillson St., Winnipeg, MB, Canada R3T 5V6CA
  4. 4.Department of Physics, University of Alberta, Avadh Bhatia Physics Lab., Edmonton, AB, Canada T6G 2J1CA