After finding a few unanswered requests for a solution of this problem in the web (including my own…) I’d like to share the final results of my work.

The problem:

Suppose you have two random variables, Z and T.

Z is N(0,1) distributed.

T is t(3) distributed.

Now you are supposed to produce four contour plots of the random variables’ joint pdf for the cases that the variables’ dependence structure is given by the

- Gaussian,
- Clayton,
- Frank- and
- Gumbel copula.

With the copula and the marginal distributions given the (bivariate) joint distribution of Z and T can be constructed. And this post is about doing exactly this in R and MatLab (and drawing the corresponding contour-plots).