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

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