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?
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.