Uso dos modelos gama e normal inverso para a análise de dados positivos assimétricos

Abstract

Generalized linear models consider in their construction the exponential family of dispersion, which has the gamma and inverse normal distribution as members. These distributionsallow modeling data that assume positive real values and with positive asymmetry. The exponential family has several interesting properties that are extended to all its members, which makes it easier to obtain and calculate certain quantities. This work presents the methodology of Generalized Linear Models (GLM), developed by Nelder and Wedderburn (1972), such as definition, estimation, link functions, model selection, residual analysis and diagnosis in GLM’s. An application using real credit limit data will also be presented, in an attempt to describe the average used limit of customers using only the gamma and inverse normal models. In the adjustment of the models and by the analysis of residues, it was possible to observe that for the gamma and inverse normal distributions, using the identity link function, models with good adjustments were obtained after eliminating the observations highlighted in the analysis of residues and diagnosis.