The Dirichlet distribution is a family of continuous multivariate probability distributions parameterized by a vector of positive reals (\alpha = (\alpha_1, …, \alpha_K)). It is commonly used as a prior distribution in Bayesian statistics for variables that are probabilities themselves—i.e., variables that lie on a probability simplex. The Dirichlet distribution is the multivariate generalization of the beta distribution and is notable for being the conjugate prior of categorical and multinomial distributions in Bayesian inference.