A new bivariate distribution with uniform marginals

Starting from three independent exponential random variables we have generated a bivariate random vector (U, V) having the marginal distributions as standard uniform. The joint distribution function and the survival function have been derived along with the moment generating function. We have also given an expression for the joint moment of order (r, s). The distributions of different functions of U and V have been derived. Different dependence measures between U and V have also been calculated. The reliability of the underlying stress-strength model has been obtained as an application of the distribution. A simulation exercise has been carried out to check for the goodness-of-fit of the model. We have also calculated the relative errors in different reliability measures under the assumption that the variables U and V are independent when actually they are not.