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3 - Halphen Type A Distribution

Published online by Cambridge University Press:  13 April 2022

Vijay P. Singh
Affiliation:
Texas A & M University
Lan Zhang
Affiliation:
University of Akron, Ohio
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Summary

The Halphen type A (Hal-A) frequency distribution has been employed for frequency analyses of hydrometeorological and hydrological extremes. This chapter derives this distribution using entropy theory and discusses the estimation of its parameters using the methods of entropy, moments, probability moments, L-moments, cumulative moments, and maximum likelihood estimation.

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Publisher: Cambridge University Press
Print publication year: 2022

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References

Abramovitz, M. and Stegun, I. (1972). Handbook of Mathematical Functions. With Formulas, Graphs, and Mathematical Tables. Dover Publications, New York.Google Scholar
Dvorak, V., Bobée, B., Boucher, S., and Ashkar, F. (1988). Halphen distributions and related systems of frequency functions research report No. R-236 INRS-Eau.Ste-Foy. Quebec, Canada, 81 pp.Google Scholar
El Adlouni, S. and Bobée, B. (2017). Halphen Distribution Family: With Application in Hydrological Frequency Analysis. Water Resources Publications, LLC, Highland Ranch, CO.Google Scholar
Fateh, C., Salaheddine, E.A., and Bernard, B. (2010). Mixed estimation methods for Halphen distributions with applications in extreme hydrologic events. Stochastic Environmental Research and Risk Assessment, Vol. 24, No. 3, pp. 359376.Google Scholar
Fitzgerald, D.L. (2000). Statistical aspects of Tricomiis function and modified Bessel functions of the second kind. Stochastic Environmental Research and Risk Assessment, Vol. 14, pp. 139158.Google Scholar
Gumbel, E.J. (1958). Statistics of Extremes. Columbia University Press, New York. doi: 10.7312/gumb92958.CrossRefGoogle Scholar
Halphen, E. (1941). Sur un nouveau type de couBRe de fréquence. Comptes Rendus de l’Académie des Sciences, Vol. 213, pp. 633635. Published under the name of “Dugué” due to war constraints.Google Scholar
Halphen, E. (1955). Les fonctions factorielles. Publications de l’Institut de Statistique de l’Université de Paris, Vol. IV, Fascicule I, pp. 2139.Google Scholar
Ouarda, T.B.M.J., Ashkar, F., Ben Said, E.M., and Hourani, L. (1994). Distribution statistiques utilisees on hydrologie: Transformation et proprieties asymptotiques. Rapport de recherché STAT-13. University of Moncton, N.B., Canada.Google Scholar
Perreault, L., Bobée, B., and Rasmussen, P. (1999). Halphen distribution system. I: Mathematical and statistical properties. Journal of Hydrologic Engineering, 4, No. 3, pp. 189199.CrossRefGoogle Scholar
Shannon, C.E. (1948). A mathematical theory of communication. Bell System Technical Journal, Vol. 27, No. 3, pp. 379423.CrossRefGoogle Scholar
Sheshadri, V. (1993). The Inverse Gaussian Distribution. Clarendon Press, Oxford.Google Scholar
Sheshadri, V. (1997). Halphen’s laws. In Kotz, S. and Johnson, N.L. (eds.), Encyclopedia of Statistical Sciences, Update, Vol. 1. John Wiley & Sons, New York, pp. 302306.Google Scholar
Singh, V.P. (1998). Entropy Based Parameter Estimation in Hydrology. Kluwer Academic Publishers, Dordrecht.Google Scholar
Singh, V.P. (2013). Entropy Theory and Its Application in Environmental and Water Engineering. Wiley-Blackwell, Hoboken, NJ.Google Scholar
Watson, G.N.A. (1966). Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge University Press, Cambridge, England, 804 pp.Google Scholar

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  • Halphen Type A Distribution
  • Vijay P. Singh, Texas A & M University, Lan Zhang, University of Akron, Ohio
  • Book: Generalized Frequency Distributions for Environmental and Water Engineering
  • Online publication: 13 April 2022
  • Chapter DOI: https://doi.org/10.1017/9781009025317.004
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  • Halphen Type A Distribution
  • Vijay P. Singh, Texas A & M University, Lan Zhang, University of Akron, Ohio
  • Book: Generalized Frequency Distributions for Environmental and Water Engineering
  • Online publication: 13 April 2022
  • Chapter DOI: https://doi.org/10.1017/9781009025317.004
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Halphen Type A Distribution
  • Vijay P. Singh, Texas A & M University, Lan Zhang, University of Akron, Ohio
  • Book: Generalized Frequency Distributions for Environmental and Water Engineering
  • Online publication: 13 April 2022
  • Chapter DOI: https://doi.org/10.1017/9781009025317.004
Available formats
×