The Dirichlet distribution

tags
Probability distribution

Is it to proportions what Multinomial is to number in categories?

Interpretation

Let us consider an urn with \(K\) different colors. There are \(\alpha_1\) balls of the first colors, …, \(\alpha_K\) balls of the $K$th color. We draw \(N\) balls from this urn using the following protocol:

  1. Pick one ball
  2. Return the ball to the urn
  3. Add another ball of the same color to the urn

When \(N\) is very large, the proportions of balls of different colors are distributed according to \(\operatorname{Dirichlet}(\mathbf{\alpha})\).

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