Multivariate Birnbaum-Saunders power-normal model and associated inference

The univariate Birnbaum-Saunders distribution is quite useful for modeling lifetime data, reliability problems, and times to failure for materials subject to fatigue. On the other hand, multivariate extensions of this univariate distribution are not common in the statistic literature. In this paper, based on the multivariate power-normal distribution and univariate Birnbaum-Saunders power-normal distribution, we extended the univariate Birnbaum-Saunders distribution to the multivariate setup. Structural properties of the new multivariate Birnbaum-Saunders distribution are established. We consider the maximum likelihood method to estimate the unknown parameters, as well as the two-stage estimation procedure, which is defined for multivariate copula-based models. Monte Carlo simulation experiments are carried out to investigate the performance of these estimation methods. An empirical application of the proposed multivariate distribution to real data is provided for illustrative purposes.