Modelos multivariados para dados de contagem com excesso de zeros

Abstract

In this thesis we present two new distributions for modeling multivariate counting data with overdispersion or underdispersion, zeros excess and correlation. Named the zero-inflated multivariate COM-Poisson (ZICOMP Type I) and (ZICOMP Type III) distributions, their constructs were based on the extent in of the zero-inflated multivariate Poisson distributions ZIP Type I and ZIP Type III in ((LIU; TIAN, 2015); (TIAN et al., 2014)). We developed important theoretical properties of the two distributions, their regression models, likelihood ratio hypothesis testing to help choose the best model, and a diagnostic analysis for the ZICOMP Type I distribution regression model. The proposed distributions showed in both simulation study good results and real data analysis. In a real data analysis the proposed distributions showed better adjustments when compared to the ZIP Type I and ZIP Type III distributions, according to the Akaike (AIC) and Bayesian (BIC) information criteria.