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I'm working with the nataf transformation - AkA Gaussian copula - and trying to establish the range of joint bivariate pdf's it can approximate, and what limitations it puts on those joint pdf's. I've scoured the net and library’s but am unable to find such information. Does anyone know? Or know of a research that looks specifically at this?

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Lack of larger left-tail correlation. – user2763361 Dec 25 '13 at 7:51
I'm not familiar with the term nataf transformation. But as previous commentator said, the gaussian copula has neither lower nor upper tail dependence. To clarify, copulas are used to model dependence between r.v's, in particular different copulas has different tail characteristics. For instance, t-copulas has both lower and upper tail dependence, and clayton copulas only has lower tail dependence. I removed my earlier comment on this because I wasn't sure if this is what you were asking for. – Good Guy Mike Dec 25 '13 at 18:46

The joint pdfs can exhibit whatever the characteristics are of the two random variables. This includes location (mean), spread(sigma), skewness, kurtosis, other moments, etc. As was pointed out above however, you need to ensure that normal is the best fitting distribution for your data. Copulas are used for simulation, which requires knowing the appropriate distribution of the data you are trying to simulate.

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