Distribuição Birnbaum-Saunders: aspectos clássicos e bayesianos

Abstract

The Birnbaum-Saunders distribution is a model used to analyze lifetime of objects that suffer from a cyclic cumulative damage, consisting in an example of fatigue lifetime distribution. The distribution has received great attention lately, serving as theme of many works, including one proposal of reparametrization used in modeling, where the mean is used as one of its parameters. This allows the regression model with the Birnbaum-Saunders distribution to be fitted in a similar manner as a generalized linear model (GLM). The objective of this work is to discuss some properties of the Birnbaum-Saunders distribution, also estimation procedures: the maximum likelihood, moments method and modified moments method. Birnbaum-Saunders regression models (BSRM) are presented, with its development and estimation methods. Besides the classical version, the Bayesian approach is discussed in the work, presenting priori distributions of the parameters and estimatives obtained with posteriori distributions, for both univariate case and Bayesian regression models. An application example is done in a dataset about the lifetime of patients with leukemia, analyzing the adjustment of Birnbaum-Saunders regression models for this data. With the concern to handle a sensitive analyses for the models, influence diagnostic methods in the classic BSRM and the Bayesian model are compared, verifying the similarities and differences of both methodologies in evaluating influential observations, obtaining then more information to decide which model to use.