Water Resources

, Volume 37, Issue 4, pp 437–445 | Cite as

Estimating distribution parameters of extreme hydrometeorological characteristics by L-moments method

  • T. S. Gubareva
  • B. I. Gartsman
Water Resources and the Regime of Water Bodies


L-moments method is briefly described and compared with classical methods of moments and maximal likelihood. Algorithms are given for calculating parameters of some distributions widely used in engineering hydrology, meteorology, etc. The advantages of L-moments method relative to alternative methods are analyzed for several examples.


L-moments coefficients of L-variation L-asymmetry L-kurtosis distribution parameters GEV GPD lognormal distribution III-type Pearson distribution 


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  1. 1.
    Bolgov, M.V., Mishon, V.M., and Sentsova, N.I., Sovremennye problemy otsenki vodnykh resursov i vodoobespecheniya (Current Problems in Estimating Water Resources and Water Availability), Moscow: Nauka, 2005.Google Scholar
  2. 2.
    Vinogradov, Yu.B., Matematicheskoe modelirovanie protsessov formirovaniya stoka (Mathematical Modeling Runoff Formation Processes), Leningrad: Gidrometeoizdat, 1988.Google Scholar
  3. 3.
    Kichigina, N.V., Maximal Runoff and Floods in Rivers of the Southern East Siberia, in Geograficheskie zakonomernosti gidrologicheskikh protsessov yuga Vostochnoi Sibiri (Geographic Regularities in Hydrological Processes in the Southern East Siberia), Snytko, V.A., and Korytnii, L.M., Eds., Irkutsk: Inst. Geografii, SO RAN, 2003.Google Scholar
  4. 4.
    Kozhevnikova, I.A., Distribution Parameter Estimation for Small Samples by L-moments, Zavod. Labor. Diagn. Mater., 2005, vol. 71, no. 3, pp. 64–68.Google Scholar
  5. 5.
    Naidenov, V.I., Nelineinaya dinamika poverkhnostnykh vod sushi (Nonlinear Dynamics of Surface Continental Waters), Moscow: Nauka, 2004.Google Scholar
  6. 6.
    Pisarenko, V.F., Bolgov, M.V., Osipova, N.V., and Rukavishnikova, T.A., Application of the Theory of Extreme Events to Problems of Approximating Probability Distributions of Water Flow Peaks, Vodn. Resur., 2002, vol. 29, no. 6, pp. 645–657 [Water Resour. (Engl. Transl.), vol. 25, no. 3, pp. 593–694].Google Scholar
  7. 7.
    Raschety rechnogo stoka (metody prostranstvennogo obobshcheniya) (River Runoff Calculation (Methods of Spatial Generalization) Bykov, V.D., Evstigneev, V.M., and Zhuk, V.A., Eds., Moscow: Mosk. Gos. Univ., 1984.Google Scholar
  8. 8.
    Rozhdestvenskii, A.V. and Chebotarev, A.I., Statisticheskie metody v gidrologii (Statistical Methods in Hydrology), Leningrad: Gidrometeoizdat, 1974.Google Scholar
  9. 9.
    Greenwood, J.A., Landwehr, J.M., Matalas, N.C., and Wallis, J.R., Probability Weighted Moments: Definition and Relation to Parameters of Several Distributions Expressable in Inverse Form, Water Res. Research, 1979, vol. 15, no. 5, pp. 1049–1054.CrossRefGoogle Scholar
  10. 10.
    Gubareva, T.S. and Gartsman, B.I., Flood Discharges Estimation in the Amur Basin: Alternative Approach and Spatial Relations, Flood, from Defense to Management, London: Taylor & Francis Group, 2005.Google Scholar
  11. 11.
    Gubareva, T., van Nooijen, R., Kolechkina, A., et al., Extreme Flood Estimation by Different Probability Distribution Laws in Different Climatic Conditions, Geophysical Research Abstracts, 2008,
  12. 12.
    Hideo, Hirose., Maximum Likelihood Parameter Estimation in the Three-Parameter Gamma Distribution, Computational Statistics & Data Analysis, 1995, vol. 20, no. 4, pp. 343–354.CrossRefGoogle Scholar
  13. 13.
    Hosking, J.R.M., L-Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics, J. Royal Statistical Soc. Ser. B, 1990, vol. 52, pp. 105–124.Google Scholar
  14. 14.
    Hosking, J.R.M. and Wallis, J.R., Regional Frequency Analysis. An Approach Based On L-Moments, Cambridge: Cambridge Univer. Press, 1997.CrossRefGoogle Scholar
  15. 15.
    Landwehr, J.M., Matalas, N.C., and Wallis, J.R., Probability-Weighted Moments Compared with Some Traditional Techniques in Estimating Gumbel Parameters and Quantiles, Water Res. Research, 1979, vol. 15, no. 5, pp. 1055–1064.CrossRefGoogle Scholar
  16. 16.
    R: A Language and Environment for Statistical Computing. 2007.
  17. 17.
    Ramachandra, Rao A. and Khaled, H., Hamed, Flood Frequency Analysis, Boca Raton: CRC, 2000.Google Scholar
  18. 18.
    Stedinger, J.R, Vogel, R.M, and Foufoula-Georgiou, E, in Handbook of Hydrology, Maidment, D.R., Ed., London: McGraw-Hill, 1993.Google Scholar
  19. 19.
    Van Gelder, P.H.A.J.M., Statistical Estimation Methods in Hydrological Engineering, Proc. Intern. Semin. “Analysis and Stochastic Modeling of Extreme Runoff in Eurasian Rivers Under Conditions of Climate Change,” Irkutsk: Publishing House of the Institute of Geography SB RAS, 2004, pp. 11–57.Google Scholar
  20. 20.
    Van Nooijen, R., Gubareva, T., Kolechkina, A., and Gartsman, B., Interval Analysis and the Search for Local Maxima of the Log Likelihood for the Pearson III Distribution, Geophysical Research Abstracts, 2008.
  21. 21.
    Vogel, R.M., and Fennessey, N.M., L-Moment Diagrams Should Replace Product-Moment Diagrams, Water Res. Research, 1993, vol. 29, no. 6, pp. 1745–1752.CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • T. S. Gubareva
    • 1
  • B. I. Gartsman
    • 1
  1. 1.Pacific Institute of Geography, Far East DivisionRussian Academy of SciencesVladivostokRussia

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