How to generate multivariate random numbers with different marginal distributions?

Question

I have lost idea how to generate some bivariate random mumbers, say in copula. The marginals are of different distribution, i.e. t, gamma, and the joint structure can be gaussian or t. I will have to fixed their kendall tau. And I want to examine how the pearson rho of those random numbers are different from the presetted tau.

Any suggestion? A piece of prototype in R/Matlab is highly appreciated!

Answer 1

If you have Statistics Toolbox you can generate random numbers from copulas using the function copularnd. There are several examples in the documentation. To convert between using Kendall's tau and Pearson's rho, take a look at copulaparam and copulastat.