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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?