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

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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.

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Acknowledgments

This work was partially funded by the Brazilian institutions, São Paulo Research Foundation—FAPESP and National Counsel of Technological and Scientific Development—CNPq.

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Authors and Affiliations

  1. Departamento de Estatística, Universidade Federal de São Carlos, São Carlos, São Paulo, Brazil

    Katiane S. Conceição

  2. Departamento de Matemática Aplicada e Estatística, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos, São Paulo, Brazil

    Marinho G. Andrade & Francisco Louzada

Authors
  1. Katiane S. Conceição
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  2. Marinho G. Andrade
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  3. Francisco Louzada
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Correspondence to Marinho G. Andrade.

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Conceição, K.S., Andrade, M.G. & Louzada, F. On the zero-modified poisson model: Bayesian analysis and posterior divergence measure. Comput Stat 29, 959–980 (2014). https://doi.org/10.1007/s00180-013-0473-y

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  • DOI: https://doi.org/10.1007/s00180-013-0473-y

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