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Bivariate Hofmann distributions

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  • J. F. Walhin

Abstract

The aim of this paper is to develop some bivariate generalizations of the Hofmann distribution. The Hofmann distribution is known to give nice fits for overdispersed data sets. Two bivariate models are proposed. Recursive formulae are given for the evaluation of the probability function. Moments, conditional distributions and marginal distributions are studied. Two data sets are fitted based on the proposed models. Parameters are estimated by maximum likelihood.

Suggested Citation

  • J. F. Walhin, 2003. "Bivariate Hofmann distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(9), pages 1033-1046.
    • Handle: RePEc:taf:japsta:v:30:y:2003:i:9:p:1033-1046
    DOI: 10.1080/0266476032000076155
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    References listed on IDEAS

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    1. Hurlimann, Werner, 1990. "On maximum likelihood estimation for count data models," Insurance: Mathematics and Economics, Elsevier, vol. 9(1), pages 39-49, March.
    2. Walhin, J.F. & Paris, J., 2000. "Recursive Formulae for Some Bivariate Counting Distributions Obtained by the Trivariate Reduction Method," ASTIN Bulletin, Cambridge University Press, vol. 30(1), pages 141-155, May.
    3. Felix Famoye & P. Consul, 1995. "Bivariate generalized Poisson distribution with some applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 42(1), pages 127-138, December.
    4. S. Kocherlakota, 1988. "On the compounded bivariate Poisson distribution: A unified treatment," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(1), pages 61-76, March.
    5. Panjer, Harry H., 1981. "Recursive Evaluation of a Family of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 22-26, June.
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    Cited by:

    1. Bermúdez i Morata, Lluís, 2009. "A priori ratemaking using bivariate Poisson regression models," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 135-141, February.
    2. Lluis Bermúdez i Morata, 2008. "A priori ratemaking using bivariate poisson regression models," Working Papers XREAP2008-09, Xarxa de Referència en Economia Aplicada (XREAP), revised Jul 2008.

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