Multivariate Birnbaum–Saunders distribution based on a skewed distribution and associated EM-estimation

Abstract

We develop here a multivariate generalization of Birnbaum-Saunders (BS) distribution based on the multivariate skew-normal distribution. Some distributional characteristics and properties are presented, as well as a simple and efficient EM algorithm for the iterative computation of the maximum likelihood (ML) estimates of model parameters, through the hierarchical representation of the proposed model. The standard errors of the maximum likelihood estimates are calculated from the observed Fisher information matrix. Moreover, by using the tools, we present a log-linear regression model, where the the ML estimates are once again obtained using an EM algorithm. Finally, simulation studies and two applications to real data sets are presented for illustrating the model and the inferential results developed here. List of Abbreviations AIC Akaike information criterion BS Birnbaum-Saunders BVBS Bivariate Birnbaum-Saunders cdf cumulative distribution function CI Confidence Interval CM Conditional Maximization ECM Expectation-Conditional Maximization EM Expectation-Maximization LR Likelihood Ratio ML Maximum Likelihood MSE root Mean Squared Error NBS Non-Central Birnbaum-Saunders pdf probability density function RB Relative Bias SD Standard Deviation SE Standard Error SIC Schwarz information criterion SMN Scale Mixtures of Normal SN Skew-Normal SNBS Skew-Normal Birnbaum-Saunders TTT Total Time on Test