Copula theory

A copula from two, independent standard Gaussian variables; from 0 standard deviations for each variable from the center:

A copula from two, independent standard Gaussian variables; from 2 standard deviations for each variable from the center:

Note that Guassian copulas suffer from a lack of tail dependence.  Also the difference between the copulas shows a pattern that is more minimal, the further from the center one begins their analysis.  For example, the copula from the shifted center shows a much weaker marginal tail distribution.  Notice the surface plot below, which differences the second distribution chart above, from the first distribution chart above: