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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 Cochran's theorem ： ウィキペディア英語版 Cochran's theorem In statistics, Cochran's theorem, devised by William G. Cochran, is a theorem used to justify results relating to the probability distributions of statistics that are used in the analysis of variance. == Statement == Suppose ''U''1, ..., ''U''''n'' are independent standard normally distributed random variables, and an identity of the form :$$ \sum_^n U_i^2=Q_1+\cdots + Q_k can be written, where each ''Q''''i'' is a sum of squares of linear combinations of the ''U''s. Further suppose that :$$ r_1+\cdots +r_k=n where ''r''''i'' is the rank of ''Q''''i''. Cochran's theorem states that the ''Q''''i'' are independent, and each ''Q''''i'' has a chi-squared distribution with ''r''''i'' degrees of freedom.〔 Here the rank of ''Q''''i'' should be interpreted as meaning the rank of the matrix ''B''(''i''), with elements ''B''''j,k''(''i''), in the representation of ''Q''''i'' as a quadratic form: :$Q\_i=\backslash sum\_^n\backslash sum\_^n\; U\_j\; B\_^\; U\_k\; .$ Less formally, it is the number of linear combinations included in the sum of squares defining ''Q''''i'', provided that these linear combinations are linearly independent. 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「Cochran's theorem」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.