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4 - Halphen Type B 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 B (Hal-B) 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 with the use of the constraints used for their derivation. The distribution i+L13s tested using entropy and the methods of moments and maximum likelihood estimation.

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Publisher: Cambridge University Press
Print publication year: 2022

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References

Abramowitz, M. and Stegun, I.A. (1972). Handbook of Mathematical Functions. Dover, New York.Google Scholar
El Adlouni, S. and Bobée, B. (2017). Halphen Distribution Family: With Application in Hydrological Frequency Analysis. Water Resources Publications, LLC, Highlands 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
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
Perreault, L., Bobée, B., and Rasmussen, P. (1999). Halphen distribution system. I: Mathematical and statistical properties. Journal of Hydrologic Engineering, Vol. 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
Singh, V.P. (1998). Entropy Based Parameter Estimation in Hydrology. Kluwer Academic Publishers, Dordrecht, the Netherlands.CrossRefGoogle Scholar
Singh, V.P. (2013). Entropy Theory and Its Application in Environmental and Water Engineering. Wiley-Blackwell, Hoboken, NJ.Google Scholar

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  • Halphen Type B 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/10.1017/9781009025317.005
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  • Halphen Type B 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/10.1017/9781009025317.005
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 B 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/10.1017/9781009025317.005
Available formats
×