I am reading about Metaelliptical copulas but I don't know the difference between elliptical Gaussian and multivariate Gaussian distributions I would appreciate if somebody can explain the difference in a simple way. This is the paper that I was reading in case if you need more clarification. http://onlinelibrary.wiley.com/doi/10.1029/2006WR005275/abstract
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No difference -- all multivariate Gaussian distributions are necessarily elliptical.
However, not all elliptical distributions are Gaussian.
As the article you point to says "... the well-known family of elliptical distributions, [...] is itself an extension of the classical multivariate normal distribution".
