O Modelo de Regressão Potência-Normal Logística, Cauchy, Normal e Gumbel para resposta no intervalo unitário

Abstract

In this research a new statistical model is introduced to model data restricted in the continuous interval (0,1) . The new model is the composition of the power-normal distribution and the quantile of another family of distributions with the same support. The new proposal is a generalization of the model proposed by Johnson (Johnson (1949)). In addition, the new family is extended to regression models as an alternative to the regression model with a unit interval response. Also for the proposed class of models, we developed inference procedures from the classical perspective, based on the likelihood theory. Specifically, the maximum likelihood estimates are obtained numerically and we study the asymptotic properties via stochastic simulation and we develop hypothesis testing procedures for the model parameters and a simulation study is performed to study the asymptotic behavior of the gradient, wald, score and likelihood ratio statistics. An application for real data to illustrate the use of the new family is considered.