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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 Wilks' lambda distribution ： ウィキペディア英語版 Wilks's lambda distribution In statistics, Wilks's lambda distribution (named for Samuel S. Wilks), is a probability distribution used in multivariate hypothesis testing, especially with regard to the likelihood-ratio test and multivariate analysis of variance (MANOVA). It is a multivariate generalization of the univariate ''F''-distribution, generalizing the ''F''-distribution in the same way that the Hotelling's ''T''-squared distribution generalizes Student's ''t''-distribution. Wilks's lambda distribution is related to two independent Wishart distributed variables, and is defined as follows,〔 〕 given :$A\; \backslash sim\; W\_p(\backslash Sigma,\; m)\; \backslash qquad\; B\; \backslash sim\; W\_p(\backslash Sigma,\; n)$ independent and with $m\; \backslash ge\; p$ :$\backslash lambda\; =\; \backslash frac\; =\; \backslash frac\; \backslash sim\; \backslash Lambda(p,m,n)$ where ''p'' is the number of dimensions. In the context of likelihood-ratio tests ''m'' is typically the error degrees of freedom, and ''n'' is the hypothesis degrees of freedom, so that $n+m$ is the total degrees of freedom.〔 The distribution can be related to a product of independent beta-distributed random variables :$u\_i\; \backslash sim\; B\backslash left(\backslash frac,\backslash frac\backslash right)$ :$\backslash prod\_^p\; u\_i\; \backslash sim\; \backslash Lambda(p,m,n).$ For large ''m'', Bartlett's approximation〔 〕 allows Wilks's lambda to be approximated with a chi-squared distribution :$\backslash left(\backslash frac-m\backslash right)\backslash log\; \backslash Lambda(p,m,n)\; \backslash sim\; \backslash chi^2\_.$〔 == See also == * Chi-squared distribution * ''F''-distribution * Gamma distribution * Hotelling's ''T''-squared distribution * Student's ''t''-distribution * Wishart distribution 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「Wilks's lambda 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.