# Dirichlet Distribution

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.

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### Famous quotes containing the word distribution:

In this distribution of functions, the scholar is the delegated intellect. In the right state, he is, Man Thinking. In the degenerate state, when the victim of society, he tends to become a mere thinker, or, still worse, the parrot of other men’s thinking.
Ralph Waldo Emerson (1803–1882)