A distribuição normal-valor extremo generalizado para a modelagem de dados limitados no intervalo unitário (0, 1)

Abstract

In this research a new statistical model is introduced to model data restricted in the continuous interval (0,1). The proposed model is constructed under a transformation of variables, in which the transformed variable is the result of the combination of a variable with standard normal distribution and the cumulative distribution function of the generalized extreme value distribution. For the new model its structural properties are studied. The new family is extended to regression models, in which the model is reparametrized in the median of the response variable and together with the dispersion parameter are related to covariables through a link function. Inferential procedures are developed from a classical and Bayesian perspective. The classical inference is based on the theory of maximum likelihood, and the Bayesian inference is based on the Markov chain Monte Carlo method. In addition, simulation studies were performed to evaluate the performance of the classical and Bayesian estimates of the model parameters, in which the maximum likelihood estimators of the model parameters satisfy the asymptotic properties. Finally a set of colorectal cancer data is considered to show the applicability of the model, in which, compared to other models, the proposed model best fits this dataset.