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Extended Truncated Tweedie-Poisson Model

Author

Listed:
  • Jordi Valero

    (Technical University of Catalonia)

  • Josep Ginebra

    (Universitat Politècnica de Catalunya
    Technical University of Catalonia)

  • Marta Pérez-Casany

    (Technical University of Catalonia)

Abstract

It has been argued that by truncating the sample space of the negative binomial and of the inverse Gaussian-Poisson mixture models at zero, one is allowed to extend the parameter space of the model. Here that is proved to be the case for the more general three parameter Tweedie-Poisson mixture model. It is also proved that the distributions in the extended part of the parameter space are not the zero truncation of mixed Poisson distributions and that, other than under the negative binomial, they are not mixtures of zero truncated Poisson distributions either. By extending the parameter space one can improve the fit when the frequency of one is larger and the right tail is heavier than is allowed by the unextended model. Extending the model also allows one to use the maximum likelihood based inference tools when the m.l.e. does not exist under the unextended model. The extended model is proved useful in the analysis of frequency count data.

Suggested Citation

  • Jordi Valero & Josep Ginebra & Marta Pérez-Casany, 2012. "Extended Truncated Tweedie-Poisson Model," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 811-829, September.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:3:d:10.1007_s11009-012-9277-8
    DOI: 10.1007/s11009-012-9277-8
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    References listed on IDEAS

    as
    1. Puig, Pedro & Valero, Jordi, 2006. "Count Data Distributions: Some Characterizations With Applications," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 332-340, March.
    2. Xavier Puig & Josep Ginebra & Marti Font, 2010. "The Sichel model and the mixing and truncation order," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1585-1603.
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    5. Ginebra, Josep & Puig, Xavier, 2010. "On the measure and the estimation of evenness and diversity," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2187-2201, September.
    6. Willmot, Gordon E., 1988. "A remark on the poisson-pascal and some other contagious distributions," Statistics & Probability Letters, Elsevier, vol. 7(3), pages 217-220, December.
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    Cited by:

    1. L. Beghin & P. Vellaisamy, 2018. "Space-Fractional Versions of the Negative Binomial and Polya-Type Processes," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 463-485, June.

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