Distribuições discretas zero-modificadas para modelar dados de contagem zeros faltantes

Abstract

The analysis of count data takes an important place in applied statistics, since many real problems are expressed in terms of counts. Frequently, count data sets have discrepancies in the frequency of the zero observation, which may be high or low, and in these cases the set is referred as zero-inflated or zero-deflated, respectively. Besides, there are situations where the zero observation does not occur in the data set, and often zero-truncated models are inadequately considered, since there is a positive probability (and not a null one) for such event, although it has not occurred. The main aim of this dissertation is to present the procedure for parameter estimation of the zero-modified distributions in situations where the frequency of zero observation in the data set is zero and the occurrence probability of this same value is positive (zero-deflated). The proposed methodology considers the estimation of missing zeros in the data set consisting only of positive observations, such that the increased data set (with the estimated zeros included) can be explained by a traditional distribution. Moments and maximum likelihood methods are considered for the estimation procedure using the estimation-maximization algorithm. Simulation and artificial data studies are used to evaluate the properties of the estimators and estimates obtained. Real data sets with different cases of zero-modification are also analyzed.