On a bivariate Birnbaum-Saunders distribution parameterized by its means: features, reliability analysis and application

Abstract: Birnbaum-Saunders models have been widely used to model positively skewed data. In this paper, we introduce a bivariate Birnbaum-Saunders distribution which has the means as parameters. We present some properties of the univariate and bivariate Birnbaum-Saunders models. We discuss the maximum likelihood and modified moment estimation of the model parameters and associated inference. A simulation study is conducted to evaluate the performance of the maximum likelihood and modified moment estimators. The probability coverages of confidence intervals are also discussed. Finally, a real-world data analysis is carried out for illustrating the proposed model.