Dirichlet Distribution - Probability Density Function

Probability Density Function

The Dirichlet distribution of order K ≥ 2 with parameters α1, ..., αK > 0 has a probability density function with respect to Lebesgue measure on the Euclidean space RK-1 given by

for all x1, ..., xK–1 > 0 satisfying x1 + ... + xK–1 < 1, and where xK = 1 – x1 – ... – xK–1. The density is zero outside this open (K − 1)-dimensional simplex.

The normalizing constant is the multinomial Beta function, which can be expressed in terms of the gamma function:

Read more about this topic:  Dirichlet Distribution

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