Dirichlet distribution

In probability and statistics, the Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted {\displaystyle \operatorname {Dir} ({\boldsymbol {\alpha }})} \operatorname {Dir} ({\boldsymbol {\alpha }}), is a family of continuous multivariate probability distributions parameterized by a vector {\displaystyle {\boldsymbol {\alpha }}} {\boldsymbol {\alpha }} of positive reals. It is a multivariate generalization of the beta distribution.[1] Dirichlet distributions are very often used as prior distributions in Bayesian statistics, and in fact the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial distribution.