I have a question regarding generaton of correlated random variables, where each component can have a different distribution (e.g. in <x1,x2,x3> x1 could be normal, x2 uniform and x3 beta).
One of papers (not a statistical journal mind you, so could be wrong) mentions the following procedure to proceed about it.
1) From the covariance matrix generate desired number of random vectors from multivariate normal distribution.
2) Evaluate cummulative distribution function (assuming the marginal distribution is normal) for each observation in each random vector. This step will produce vectors of correlated observations distributed uniformly between 0,1 U(0,1).
3) Now substitute each component of the U(0,1) vector from step 3, into the appropriate inverse marginal distribution function to get vectors with observations of random variables, that have the desired marginal distributions and similar correlation structure.
Even the procedure looks right, I haven't come across many instances of usage of this kind of procedure. Is the above procedure correct, if not is there a alternative method? Please reply. I would greatly appreciate any comments in this regards.
Thanks in advance Sudhakar
-- Sudhakar Mamillapalli Dept Of Agricultural Engineering Purdue University firstname.lastname@example.org