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I am not sure about this:

In the 2 dimensional case, if I consider the Gaussian copula, is this identical to the bivariate normal distribution, in the case I choose the normal distribution for the margins?

Does this hold for multidemsionality? So is a d-dimensional Gaussian copula with normal margins identical to the multivariate normal distribution?

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  • $\begingroup$ Since the Gaussian copula results from taking a multivariate normal and transforming the margins to uniformity, a multivariate distribution with Gaussian copula and normal margins is multivariate normal. $\endgroup$ – Glen_b -Reinstate Monica Jul 2 '13 at 11:00
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Since the Gaussian copula results from taking a multivariate normal and transforming the margins to uniformity, a multivariate distribution with Gaussian copula and normal margins is multivariate normal.

Transforming the margins to normality merely undoes the original transform to uniform margins to obtain the copula.

See the second sentence at the Gaussian copula section of the Wikipedia article on Copulas for confirmation.

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