Matrix variate Dirichlet distribution

In statistics, the matrix variate Dirichlet distribution is a generalization of the matrix variate beta distribution and of the Dirichlet distribution. Suppose U 1 , … , U r {\displaystyle U_{1},\ldots ,U_{r}} are p × p {\displaystyle p\times p} positive definite matrices with I p − ∑ i = 1 r U i {\displaystyle I_{p}-\sum _{i=1}^{r}U_{i}} also positive-definite, where I p {\displaystyle I_{p}} is the p × p {\displaystyle p\times p} identity matrix.

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