Question: best approximation of six multivariate normally distributed scores

April 05 2014 Harry Garst 99

Dear Maple experts,

I would like to generate population data that is the best possible approximation of a multivariate normal distribution with a specified covariance matrix and vector of means. I do not want to draw a sample from a multivariate distribution, but I want the population values itself which are approximately multivariate normal distributed. The size of the datamatrix should be limited, otherwise I could draw a huge sample from a multivariate normal distribution. For instance, I would like to generate a 200 by 6 data matrix that is the best (or at least good enough) approximation of a MVN distribution. For a bivariate normal distribution one could calculate the probalities of a grid by integrating the density, but for six variables that seems undoable. 

Before trying the invent the wheel again, I think I will ask this question to experts, because it is unlikely that there is no already existing algorithm that does the job pretty well.

Thanks in advance,

Harry Garst

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