 in probability and statistics, the dirichlet distribution (after peter gustav lejeune dirichlet), often denoted \operatorname{dir}(\boldsymbol\alpha), is a family of continuous multivariate probability distributions parameterized by a vector \boldsymbol\alpha of positive reals. it is the multivariate generalization of the beta distribution. (chapter 49: dirichlet and inverted dirichlet distributions) 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 x_i given that each event has been observed \alpha_i-1 times. the infinite-dimensional generalization of the dirichlet distribution is the dirichlet process. ==probability density function== [[image:logdirichletdensity-alpha 0.3 to alpha 2.0.gif|thumb|right|250px|illustrating how the log of the density function changes when k=3 as we change the vector Î± from Î±=(0.3,&nbsp;0.3,&nbsp;0.3) to (2.0,&nbsp;2.0
Conjugate_prior_distributions Continuous_distributions Exponential_family_distributions Multivariate_continuous_distributions Probability_distributions