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Creating beta multivariate random variables


I have a problem where I need to generate a series of
n-vectors of correlated random variables each with a univariate beta
distribution.
I have a correlation matrix that defines how the variables will be
correlated.

This problem is straight forward for the case when the data is Gaussian
distributed
since the invariance property applies (linear combinations of Gaussian
variables
are again Gaussian) and I can apply the appropriate matrix to
uncorrelated Gaussian data to
obtain the desired correlation.

But applying such a transformation to beta distributed data will create
variables that are no longer beta distributed.
Anyone suggestions?


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