Statistical Modelling 20 (5) (2020), 467–501
A Bayesian approach for some zero-modified Poisson mixture models
Wesley Bertoli,
Department of Statistics,
Federal University of Technology–Paraná,
Curitiba, PR,
Brazil.
e-mail: wbsilva@utfpr.edu.br
Katiane S Conceição,
Department of Applied Mathematics and Statistics,
Institute of Mathematical and Computer Sciences,
University of São Paulo,
São Carlos, SP,
Brazil.
Marinho G Andrade,
Department of Applied Mathematics and Statistics,
Institute of Mathematical and Computer Sciences,
University of São Paulo,
São Carlos, SP,
Brazil.
Francisco Louzada,
Department of Applied Mathematics and Statistics,
Institute of Mathematical and Computer Sciences,
University of São Paulo,
São Carlos, SP,
Brazil.
Abstract:
In this article, we propose a class of zero-modified Poisson mixture models as an alternative to model overdispersed count data exhibiting inflation or deflation of zeros. A relevant feature of this class is that the zero modification can be incorporated using a zero truncation process and consequently, the proposed models can be expressed in the hurdle version. This procedure leads to the fact that the proposed models can be fitted without any previous information about the zero modification present in agiven dataset. A fully Bayesian approach has been considered for estimation and inference concerns. Three different simulation studies have been conducted to illustrate the performance of the developed methodology. The usefulness of the proposed class of models has been assessed by using three real datasets provided by the literature. A general model comparison with some well-known discrete distributions has been presented.
Keywords:
Bayesian inference, model comparison, Poisson mixture distributions, zero-inflated/deflated data, zero-modified models
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