In this work, we present a family of distributions for count data, the so called Zero- Modified Power Series, which is an extension of the Power Series distributions family whose support starts at zero. This extension consists in modifying the probability of observing zero of each Power Series distribution, allowing the new zero-modified distribution appro- priately accommodate datasets which have any amount of zero observations (for instance, zero-inflated or zero-deflated datasets). Power Series distributions included in the Zero- Modified Power Series family are: Poisson, Generalized Poisson, Geometric, Binomial, Negative Binomial and Generalized Negative Binomial. We introduce the Zero-Modified Power Series regression models and propose a Bayesian approach considering information matrix priori. Two real datasets, corresponding to leptospirosis notifications in cities of Bahia State at Brazil, are analyzed. We emphasize that the proposed Zero-Modified Power Series family distributions and their regression versions can accommodate sets of count data without any previous knowledge about the characteristic of zero-inflation (-deflation) present in the dataset.

http://www.icmc.usp.br/e/df257