Dirichlet distribution

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In probability and statistics, the Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted Dir ⁡ ( α ) {\displaystyle \operatorname {Dir} ({\boldsymbol {\alpha }})} , is a family of continuous multivariate probability distributions parameterized by a vector α of positive reals. It is a multivariate generalization of the beta distribution, hence its alternative name of multivariate beta distribution (MBD). Dirichlet distributions are commonly used as prior distributions in Bayesian statistics, and in fact, the Dirichlet distribution is the conjugate prior of the categorical distribution and multinomial distribution. The infinite-dimensional generalization of the Dirichlet distribution is the Dirichlet process.

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