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In statistics, the matrix variate Dirichlet distribution is a generalization of the matrix variate beta distribution and of the Dirichlet distribution. Suppose are positive definite matrices with also positive-definite, where is the identity matrix. Then we say that the have a matrix variate Dirichlet distribution, , if their joint probability density function is where and is the . If we write then the PDF takes the simpler form on the understanding that .
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