Modelos não-lineares da família exponencial

Abstract

The exponential family nonlinear models are an extension of the generalized models, opening various options for the distribution of the variable answer and allowing larger flexibility for the connection between the average and the systematic component. These models, for being less restrictive, having been used to model several phenomena in the nature. To estimate the parameters of these models, several procedures are proposed. Usually, the method of maximum likelihood, that has asymptotic properties of order n-1, where n is the size of the sample, it is the used. In this work we will make a general approach to the no-linear models of the exponential family. The theory of the exponential family will be introduced presenting the function of density of probability, function cumulantes geratriz, likelihood function, likelihood ratio and deviation of the model; such presented results will facilitate and/or they will be necessary in the understanding of what will be done for the nonlinear models of the exponential family. The exponential family nonlinear models will be defined by presenting the suppositions of the model, its likelihood function and the algorithm for the estimate of the parameters. We will make the approach of the diagnosis analysis and of influence of the exponential family nonlinear models. Finally, we will present some applications and we will show the efficiency and importance in the use of this class, once several phenomena present nonlinear behavior.