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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 Inverted Dirichlet distribution ： ウィキペディア英語版 Inverted Dirichlet distribution In statistics, the inverted Dirichlet distribution is a multivariate generalization of the beta prime distribution, and is related to the Dirichlet distribution. It was first described by Tiao and Cuttman in 1965. The distribution has a density function given by :$$ p\left(x_1,\ldots, x_k\right) = \frac\Gamma\left(\nu_j\right)} x_1^\cdots x_k^\times\left(1+\sum_^k x_i\right)^\nu_j},\qquad x_i>0. The distribution has applications in statistical regression and arises naturally when considering the multivariate Student distribution. It can be characterized by its moment generating function: :$$ E\left() = \frac^k\nu_j\right)}\prod_^k\frac provided that $q\_j>-\backslash nu\_j,\; 1\backslash leqslant\; j\backslash leqslant\; k$ and $\backslash nu\_>q\_1+\backslash ldots+q\_k$. The inverted Dirichlet distribution is conjugate to the negative multinomial distribution if a generalized form of odds ratio is used instead of the categories' probabilities. T. Bdiri et al. have developed several models that use the inverted Dirichlet distribution to represent and model non-Gaussian data. They have introduced finite and infinite mixture models of inverted Dirichlet distributions using the Newton–Raphson technique to estimate the parameters and the Dirichlet process to model infinite mixtures. T. Bdiri et al. have also used the inverted Dirichlet distribution to propose an approach to generate Support Vector Machine kernels basing on Bayesian inference and another approach to establish hierarchical clustering. ==References== 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「Inverted 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.