Modelos série de potência com excesso de zeros observáveis e latentes

Abstract

The present work's main objective is to study the significance of zeros in an observable and latent data. In observable data set that occur excess of zeros, its common to have sobredispersion. In this sense, the models zero-inflated power series (ZISP) were proposed to accommodate these excesses. Specifically for the analysis of observed data, it was made a study of gradient statistic, proposed by Terrell (2002), to test the hypotheses in relation to inflation parameter ZISP models. This test is based on evaluation of the performance of gradient statistic compared with the classical likelihood ratio (Wilks, 1938), score (Rao, 1948) and Wald (Wald, 1943) statistics. In addition, recently, fragility has being modeled by discrete distributions using non-negative integers values that allows zero fragility, which means, individuals who do not present the event of interest (fraction of zero risk). For this type of latent data, we have proposed a new survival model induced by discrete frailty with ZISP distribution. This proposal brings a real description of individuals without risk, because individuals cured due to genetic factors (immune) are modeled by fraction of deterministic zero risk, while the cured by treatment are modeled by fraction of random zero risk. In this context, we also developed the gradient statistic to verify parameter significance of zero risk for data modeled by fraction of deterministic zero risk. To show our proposals, we present the results of simulation studies and applications using real data.