Hi San
Welcome on UQWorld!
There are two questions, I think. One is "how to define a probabilistic model that includes dependence between random variables of given marginal distributions and given linear correlations? ". The second is “how to do this with UQLab?”.
When writing the reply, I realized there are many aspects. So I moved my reply into this post on Linear correlation, dependence, copulas, Nataf distribution and all that stuff.
thanks for initiating the discussion!
Best regards
Bruno