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Method of moments of the Halphen distribution parameters

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Abstract

Halphen laws have been proposed as a complete system of distributions with sufficient statistics that lead to estimation with minimum variance. The Halphen system provides a flexibility to fit a large variety of data sets from natural events. In this paper we present the method of moments (MM) to estimate the Halphen type B and IB distribution parameters. Their computation is very fast when compared to those given by the maximum likelihood method (ML). Furthermore, this estimation method is very easy to implement since the formulae are explicit. Some simulations show the equivalence of both methods when estimating the quantiles for finite sample size.

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Acknowledgments

The authors acknowledge the financial support of Natural Sciences and Engineering Research Council (NSERC) of Canada.

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Authors and Affiliations

  1. INRS-ETE, Chair in Statistical Hydrology, 490 rue de la Couronne, G1K 9A9, Quebec, QC, Canada

    F. Chebana, S. El Adlouni & B. Bobée

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  1. F. Chebana
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  2. S. El Adlouni
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  3. B. Bobée
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Correspondence to F. Chebana.

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Chebana, F., El Adlouni, S. & Bobée, B. Method of moments of the Halphen distribution parameters. Stoch Environ Res Risk Assess 22, 749–757 (2008). https://doi.org/10.1007/s00477-007-0184-4

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  • DOI: https://doi.org/10.1007/s00477-007-0184-4

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