Simulating multivariate distributions with specific correlations

The mixture approach for simulating bivariate distributions introduced by Michael, J. R. and Schucany, W. R. (2002). The mixture approach for simulating bivariate distributions with specific correlations. The American Statistician, 56, 48-54, is generalized to generate pseudo-random numbers from multivariate distributions. The simulated joint distributions have identical marginals and equal positive painwise correlations. The approach is illustrated for the p-dimensional families of beta and gamma distributions. For these families the formulas for the correlations have simple closed forms and the computations are quite simple.