Algumas extensões da distribuição Birnbaum-Saunders: uma abordagem bayesiana

Abstract

The Birnbaum-Saunders Distribution is based on an physical damage that produces the cumulative fatigue materials, This fatigue was identified as an important cause of failure in engineering structures. Recently, this model has been applied in other areas such as health sciences, environmental measures, forestry, demographic, financial, among others. Due to it s importance several distributions have been proposed to describe the behavior of fatigue resistance. However there is not an argument about which is more effective for the analysis of data from fatigue. A major problem to choose a statistical distribution, is that often several models fit the data well in the central, but, however, the extremes of distribution raise questions about the decision to select some of their models. The lack of data at the extremes distribution is justified to consider other arguments like the use of a specific statistical distribution, and thus reject other models. In this work we study some extensions of the distribution Birnbaum-Saunders with a mixture of normal scale, in which the procedure will for obtaining inferences will be considered from a Bayesian perspective based on the methods Monte Carlo Markov Chain (MCMC). to detect possible observations influential in the models considered, we used the Bayesian method of analysis influence in each case based on the Kullback-Leibler divergence. Moreover, the geometric Birnbaum-Saunders model is proposed , for data survival.