Dirichlet Distribution

Definition

$X\sim \mathrm{Dir}(a_1,a_2,\dots ,a_K)$ where $K\in \mathbb{N}$ is the number of categories, and $a_i\in {\mathbb{R}}^{+}$‘s are the concentration parameters

A multivariate generalization of the Beta Distribution

Properties

PDF

$f(x)=\frac{\Gamma ({\sum }_{i=1}^K{\alpha }_i)}{{\prod }_{i=1}^K\Gamma ({\alpha }_i)}{\prod }_{i=1}^K{x}_i^{{\alpha }_i-1}$

Facts

If $K=1$, then the Dirichlet distribution is a beta distribution.