The Dirichlet distribution refers to a family of multivariate distributions, which are the generalization of the univariate beta distribution.
The Dirichlet distribution refers to a family of multivariate distributions, which are the generalization of the univariate beta distribution. The probability density function of an $n$ dimensional Dirichlet distribution is:
$$p(x_1,x_2,\ldots,x_n;\alpha_1,\alpha_2,\ldots,\alpha_n) = \frac{\Gamma(\sum_{i=1}^n \alpha_i)}{\prod_{i=1}^n \Gamma (\alpha_i)} \prod_{i=1}^n x_i^{\alpha_i-1}$$
The support of the function is $x_i \in (0,1)$ for all $i = 1, ..., n$, with the additional condition $\sum_{i=1}^n x_i = 1$. Note that $n \geq 2$, where $n$ is the number of categories.
The distribution is mostly used in Bayesian statistics as a prior for multinomial likelihood functions.
