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On the zero-modified poisson model: Bayesian analysis and posterior divergence measure

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  • Katiane Conceição
  • Marinho Andrade
  • Francisco Louzada

Abstract

In this paper we consider a Bayesian approach for the zero-modified Poisson distribution, which is recommended for fitting count data which shows any modification related to the frequency of zero. However, some loss may occur when we have the knowledge that the datasets show no modification in the zero frequency and has the necessary conditions for the assumption of a Poisson distribution, and still considers the zero-modified Poisson distribution. In this context, we propose the use of the Kullback–Leibler divergence measure to evaluate this loss. The proposed methodology was illustrated in simulated datasets, whose results were able to evaluate the losses and establish its relationship with the Kullback–Leibler divergence measure. Moreover, we exemplify the use of the methodology by considering two real datasets. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Katiane Conceição & Marinho Andrade & Francisco Louzada, 2014. "On the zero-modified poisson model: Bayesian analysis and posterior divergence measure," Computational Statistics, Springer, vol. 29(5), pages 959-980, October.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:5:p:959-980
    DOI: 10.1007/s00180-013-0473-y
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    References listed on IDEAS

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    1. Dalrymple, M. L. & Hudson, I. L. & Ford, R. P. K., 2003. "Finite Mixture, Zero-inflated Poisson and Hurdle models with application to SIDS," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 491-504, January.
    2. Grogger, J T & Carson, Richard T, 1991. "Models for Truncated Counts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(3), pages 225-238, July-Sept.
    3. Dietz, Ekkehart & Bohning, Dankmar, 2000. "On estimation of the Poisson parameter in zero-modified Poisson models," Computational Statistics & Data Analysis, Elsevier, vol. 34(4), pages 441-459, October.
    4. Hassan Bakouch & Miroslav Ristić, 2010. "Zero truncated Poisson integer-valued AR(1) model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(2), pages 265-280, September.
    5. Daniel B. Hall, 2000. "Zero-Inflated Poisson and Binomial Regression with Random Effects: A Case Study," Biometrics, The International Biometric Society, vol. 56(4), pages 1030-1039, December.
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