# Copula generation (Gaussian, t and Gumbel) with the help of correlation matrix using R

I have a set of data of 2 variates. I have generated correlation matrix between the variates. Using copula package of R, I computed t-copula using correlation matrix. I used the following technique for that:

1. With the help of correlation matrix for example let it be corr_mat, I computed parameter vector, lets say param_vect.
2. Then I computed tcopula object, let it be t_object, using tCopula(param_vect, dim =..., dispstr="un", df =...)

3. Lastly I simulated 1000 sample from the copula using rcopula(1000,t_object).

The above procedure works fine for t-copula. Can someone please suggest me amethod to simulate samples from the Gaussian and Gumbell copulas? I tried with the gumbelcopula function, but it fails with errors. Could anyone one suggest the method to simulate copula using correlation matrix?

The correlation matrix that is an input to a t-copula doesn't define the correlation of the resulting variables that have that copula, so you may not be achieving what you think you are when you use the t-copula function. Similarly with the correlation in a Gaussian copula - you can specify the value of the parameter $\rho$, but that doesn't mean that the correlation of the variables you generate with that Gaussian copula is $\rho$. If they also have Gaussian margins, then the correlation is $\rho$, otherwise it will generally not be $\rho$, but some function of it that depends on what the margins are.
• I didn't mention any approach. You could use the relationship between the copula and the nonparametric correlation to infer a parameter value, but that's not necessarily the best choice. So for example, with the Gumbel, the parameter $\alpha = \frac{1}{1-\tau}$, so the sample value $\hat\tau$ could be used to back out an estimate of $\alpha$, but I believe that's not the most common way to do it with the Gumbel. – Glen_b -Reinstate Monica May 14 '14 at 10:21