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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Dirichlet distribution ： ウィキペディア英語版 Dirichlet distribution In probability and statistics, the Dirichlet distribution (after Peter Gustav Lejeune Dirichlet), often denoted $\backslash operatorname(\backslash boldsymbol\backslash alpha)$, is a family of continuous multivariate probability distributions parameterized by a vector $\backslash boldsymbol\backslash alpha$ 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 $\backslash alpha\_i-1$ times. The infinite-dimensional generalization of the Dirichlet distribution is the ''Dirichlet process''. ==Probability density function== The Dirichlet distribution of order ''K'' ≥ 2 with parameters ''α''1, ..., ''α''''K'' > 0 has a probability density function with respect to Lebesgue measure on the Euclidean space R''K''−1 given by :$f\; \backslash left(x\_1,\backslash cdots,\; x\_;\; \backslash alpha\_1,\backslash cdots,\; \backslash alpha\_K\; \backslash right)\; =\; \backslash frac\; \backslash prod\_^K\; x\_i^,$ on the open (''K'' − 1)-dimensional simplex defined by: :$\backslash begin$ &x_1, \cdots, x_ > 0 \\ &x_1 + \cdots + x_ < 1 \\ &x_K = 1 - x_1 - \cdots - x_ \end and zero elsewhere. The normalizing constant is the multinomial Beta function, which can be expressed in terms of the gamma function: :$\backslash mathrm(\backslash boldsymbol\backslash alpha)\; =\; \backslash frac,\backslash qquad\backslash boldsymbol=(\backslash alpha\_1,\backslash cdots,\backslash alpha\_K).$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Dirichlet distribution」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.