Bivariate Log Birnbaum-Saunders Distribution

Univariate Birnbaum-Saunders distribution has received a considerable amount of attention in recent years. Rieck and Nedelman (1991, ’A log-linear model for the Birnbaum-Saunders distribution’, Technometrics, 51-60) introduced a log BirnbaumSaunders distribution. The main aim of this paper is to introduce bivariate log Birnbaum-Saunders distribution. The proposed model is symmetric and it has five parameters. It can be obtained using Gaussian copula. Different properties can be obtained using copula structure. It is observed that the maximum likelihood estimators cannot be obtained explicitly. Two dimensional profile likelihood approach may be adopted to compute the maximum likelihood estimators. We propose some alternative estimators also, which can be obtained quite conveniently. The analysis of one data set is performed for illustrative purposes. Finally, it is observed that this model can be used as a bivariate log-linear model, and its multivariate generalization is also quite straight forward.