An absolutely continuous bivariate Topp-Leone distribution: A useful model on a bounded domain

We introduce an absolutely continuous bivariate generalization of the Topp-Leone distribution, which is a special member of the proportional reversed hazard family using a one-parameter bivariate exchangeable distribution. We show that a copula approach could also be used in defining the bivariate Topp-Leone distribution. The marginal distributions of the new bivariate distribution have also Topp-Leone distributions. We study its distributional and dependence properties. We estimate the parameters by maximum-likelihood procedure, perform a simulation study on the estimators, and apply them to a real data set. Furthermore, we give a way of generating bivariate distributions using the proposed distribution.