what's a copula
A copula can be extracted from any joint distribution F(): C(u 1;u 2;:::;u p) = F F 1 1 (u 1);F 1 2 (u 2);:::F 1 p (u p) Unlike the Pearson (or linear) correlation, the copula is invariant under monotone increasing transformations of the random variables. If F() is a multivariate normal distribution N p( ; ), then C() is a Gaussian copula. If the location or scale of the distribution is changed, the copula does not change, so conventionally = 0 and = R, a