>  the simulated variable correlation are not quite close to the correlation calculated from original dataset Yes. The original data is not even close to being multivariate normal. The model does not fit the data.   > when simulating in PROC COPULA, which correlation matrix is used Spearman    It sounds like you are trying to understand copulas better before you start using them for modeling. The math is not simple. When I looked at copulas a number of years ago, I did not find any simple presentations, so I wrote one for my 2013 book, Simulating Data with SAS (Section 9.5). Maybe some good intros have been written in the intervening years. If you find a good introduction, I'd be interested in learning about it.   For learning about the procedure, there is the PROC COPULA documentation and the 2011 SGF paper by Chvosta, Erdman, Little, which introduces PROC COPULA.   ... View more