How does a Matrix be Generalized with Dirichlet distribution?

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Generalized Dirichlet distribution has a more general covariance structure than Dirichlet distribution. This makes the generalized Dirichlet distribution to be more practical and useful.

The concept of complete neutrality will be used to derive the general moment function for the generalized Dirichlet distribution, and then some properties of the generalized Dirichlet distribution will be established. Similar to the Dirichlet distribution, the generalized Dirichlet distribution will be shown to conjugate to multinominal sampling

Could anyone explain How does a Matrix be generalized using Dirichlet distribution