Construction of two new general classes of bivariate distributions based on stochastic orders

In this paper, based on the concepts of stochastic orders, we propose two new general classes of bivariate distributions. The usual stochastic order and likelihood ratio order are applied to construct the classes. The joint distributions in each class are derived. It will be seen that the obtained formulas for the joint distributions are very simple and easy to apply. Then, the relationships between the classes are discussed and characterized. We illustrate the practical usefulness of the proposed classes by showing that a number of new families of bivariate distributions can be generated from the classes. Furthermore, to illustrate practical relevance, we apply several developed models to analyze a real bivariate failure time data set.