In probability and statistics, the Dirichlet distribution (after Johann Peter Gustav Lejeune Dirichlet), often denoted, is a family of continuous multivariate probability distributions parametrized by a vector of positive reals. It is the multivariate generalization of the beta distribution. 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. That is, its probability density function returns the belief that the probabilities of K rival events are given that each event has been observed times.
The infinite-dimensional generalization of the Dirichlet distribution is the Dirichlet process.
Read more about Dirichlet Distribution: Probability Density Function, Related Distributions, Applications
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