Question about copularnd

[Jeff Sun]

I have a very basic question: I'm under the impression that the copularnd() function simply returns several sets of uniformly distributed random variables that maintains the same dependency structure specified by the corrleation matrix, so what is the difference between a Gaussian-copula and a t-copula? Thanks

[Peter Perkins]

Jeff Sun wrote:
> I have a very basic question: I'm under the impression that the copularnd() function simply returns several sets of uniformly distributed random variables that maintains the same dependency structure specified by the corrleation matrix, so what is the difference between a Gaussian-copula and a t-copula? Thanks

The Gaussian copula is, in effect, a t copula with infinite degrees of freedom. You are correct in thinking that COPULARND generates values on the unit hypercube, whose marginal distributions are uniform. And you are correct in thinking that those values have the dependency structure specified by the correlation matrix. But that doesn't uniquely determine a mutivariate distribution, any more than specifying a mean and variance determines a univariate distribution.

Try using COPULARND in 2D, for t with degrees of freedom 1,2,3,5,10,25, and for Gaussian, all with the same correlation matrix. For low degrees of freedom, you'll see a sort of vaguely "X" shaped pattern, while for higher d.f or Gaussian, it's much more cigar shaped.

Actually, you can see all of that here:

<http://www.mathworks.com/products/statistics/demos.html?file=/products/demos/shipping/stats/copulademo.html>

Hope this helps.

- Peter Perkins
The MathWorks, Inc.