Some discrete exponential dispersion models: poisson-Tweedie and Hinde-Demetrio classes

• Autores: Célestin C. Kokonendji , Clarice Garcia Borges Demétrio, Simplice Dossou-Gbété
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 28, Nº. 2, 2004, págs. 201-214
• Idioma: inglés
• Títulos paralelos:
  • Algunos modelos de dispersión exponencial discretos: las clases de Poisson-Tweedie y de Hinde-Demétrio.
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• Resumen
  • català

    En aquest article investiguem dues classes de models exponencials de dispersi¿o (EDMs) per a dades de recompte sobre-dispersionades respecte a la distribuci¿o de Poisson. La primera ¿es una classe de mixtures de Poisson amb distribuci¿o de mixtura de Tweedie positiva. Com a aproximaci¿o de la primera (en termes de la funci¿o vari`ancia), la segona ¿es una nova classe de EDMs caracteritzada per la seva funci¿o vari`ancia unitat de la forma µ + µp, on p ¿es un ¿index real relacionat amb un model prec¿is. Aquestes dues classes proporcionen alternatives a la distribuci¿o binomial negativa (p = 2) que s'utilitza cl`assicament en models de regressi¿o per a dades de recompte, quan es presenta sobre-dispersi¿o en la bondat d'ajust a un model de regressi¿o de Poisson. Es discuteixen algunes propietats i la utilitat pr`actica. . .

  • English

    In this paper we investigate two classes of exponential dispersion models (EDMs) for overdispersed count data with respect to the Poisson distribution. The first is a class of Poisson mixture with positive Tweedie mixing distributions. As an approximation (in terms of unit variance function) of the first, the second is a new class of EDMs characterized by their unit variance functions of the form µ + µp, where p is a real index related to a precise model. These two classes provide some alternatives to the negative binomial distribution (p = 2) which is classically used in the framework of regression models for count data when overdispersion results in a lack of fit of the Poisson regression model. Some properties are then studied and the practical usefulness is also discussed

• Referencias bibliográficas
  • Castillo, J. and Ṕerez-Casany, M. (2004). Overdispersed and underdispersedPoisson generalizations.J. Statist. Plann. Inference, to appear.
  • Feller, W. (1943). On a general class of contagious distributions.Ann. Math. Statist., 14 (4), 389-400.
  • Hinde, J. and Deḿetrio, C. G. B. (1998).Overdispersion: Models and Estimation.São Paulo: ABE.
  • Hougaard, P., Lee, M-L. T. and Whitmore, G. A. (1997). Analysis of overdispersed count data by mixtures of Poisson variables and Poisson processes,Biometrics,...
  • Johnson, N. L., Kotz, S. and Kemp, A. W. (1992).Univariate Discrete Distributions, 2nd ed.New York: John Wiley & Sons.
  • Jørgensen, B. (1997).The Theory of Dispersion Models.London: Chapman & Hall.
  • Jourdan, A. and Kokonendji, C. C. (2002). Surdispersion et modèle binomial ńegatif ǵeńeraliśe. Rev. Statistique Appliquée, L (3),...
  • Kemp, A. W. and Kemp, C. D. (1966). An alternative derivationof the Hermite distribution.Biometrika, 53, 627-628.
  • Kokonendji, C. C. and Khoudar, M. (2004). On strict arcsine distribution.Commun. Statist.-Theory Meth., 33 (5), 993-1006.
  • Kotz, S., Balakrishnan, N. and Johnson, N. L. (2000).Continuous Multivariate Distributions, vol. 1: Models and Applications, 2nd ed. New York:...
  • Letac, G. and Mora, M. (1990). Natural real exponential families with cubic variance functions.Ann. Statist., 18, 1-37.
  • McCullagh, P. and Nelder, J. A. (1989).Generalized Linear Models, 2nd ed. London: Chapman & Hall.
  • Tweedie, M. C. K. (1984). An index which distinguishes between some important exponential families. In Statistics: Applications and new directions....
  • Willmot, G. E. (1987). The Poisson-inverse Gaussian distribution as an alternative to the negative binomial. Scandinavian Actuarial J., 2,...