A bivariate Birnbaum–Saunders regression model

In this work, we propose a bivariate Birnbaum–Saunders regression model through the use of bivariate Sinh-normal distribution. The proposed regression model has its marginal as the Birnbaum–Saunders regression model of Rieck and Nedelman (1991), which has been discussed extensively by various authors with natural applications in survival and reliability studies. This bivariate regression model can be used to analyze correlated log-lifetimes of two units, in which the dependence structure between observations arises from the bivariate normal distribution.The main aim of this paper is to propose a bivariate Birnbaum–Saunders regression model and discuss some of its properties. Specifically, we have developed the moment estimation, the maximum likelihood estimation and the observed Fisher information matrix. Hypothesis testing is also performed by the use of the asymptotic normality of the maximum-likelihood estimators. Finally, the results of simulation studies as well as an application to a real data set are presented to illustrate the model and all the inferential methods developed here.