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Power series generalized nonlinear models

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  • Cordeiro, Gauss M.
  • Andrade, Marinho G.
  • de Castro, Mário

Abstract

We introduce in this paper a new class of discrete generalized nonlinear models to extend the binomial, Poisson and negative binomial models to cope with count data. This class of models includes some important models such as log-nonlinear models, logit, probit and negative binomial nonlinear models, generalized Poisson and generalized negative binomial regression models, among other models, which enables the fitting of a wide range of models to count data. We derive an iterative process for fitting these models by maximum likelihood and discuss inference on the parameters. The usefulness of the new class of models is illustrated with an application to a real data set.

Suggested Citation

  • Cordeiro, Gauss M. & Andrade, Marinho G. & de Castro, Mário, 2009. "Power series generalized nonlinear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1155-1166, February.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:1155-1166
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    References listed on IDEAS

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    1. P.C. Consul & F. Famoye, 1986. "On The Unimodality Of The Generalized Negative Binomial Distribution," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 40(3), pages 141-144, September.
    2. Rigby, R.A. & Stasinopoulos, D.M. & Akantziliotou, C., 2008. "A framework for modelling overdispersed count data, including the Poisson-shifted generalized inverse Gaussian distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 381-393, December.
    3. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    4. Stasinopoulos, D. Mikis & Rigby, Robert A., 2007. "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i07).
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    Cited by:

    1. Katiane S. Conceição & Marinho G. Andrade & Francisco Louzada & Nalini Ravishanker, 2022. "Characterizations and generalizations of the negative binomial distribution," Computational Statistics, Springer, vol. 37(3), pages 1255-1286, July.
    2. Rodríguez-Avi, J. & Conde-Sánchez, A. & Sáez-Castillo, A.J. & Olmo-Jiménez, M.J. & Martínez-Rodríguez, A.M., 2009. "A generalized Waring regression model for count data," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3717-3725, August.
    3. José Rodríguez-Avi & María José Olmo-Jiménez, 2017. "A regression model for overdispersed data without too many zeros," Statistical Papers, Springer, vol. 58(3), pages 749-773, September.
    4. Marinho G. Andrade & Katiane S. Conceição & Nalini Ravishanker, 2024. "Zero-modified count time series modeling with an application to influenza cases," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(3), pages 611-637, September.

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