The Mixture Approach for Simulating New Families of Bivariate Distributions with Specified Correlations

The mixture approach is an exact methodology for simulating new families of bivariate distributions with specified correlation coefficients. It accommodates the entire range of correlations, produces bivariate surfaces that are intuitively appealing, and is often remarkably easy to implement. The approach is introduced in a Bayesian context and demonstrated for the conjugate families of beta and gamma distributions, with special attention given to the bivariate uniform. For these distributions, formulas for correlations have simple closed forms and computations are easy.