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In statistics Hotelling's ''T''-squared distribution is a univariate distribution proportional to the F-distribution and arises importantly as the distribution of a set of statistics which are natural generalizations of the statistics underlying Student's ''t''-distribution. In particular, the distribution arises in multivariate statistics in undertaking tests of the differences between the (multivariate) means of different populations, where tests for univariate problems would make use of a ''t''-test. The distribution is named for Harold Hotelling, who developed it as a generalization of Student's ''t''-distribution. ==The distribution== If the vector ''p''d''1'' is Gaussian multivariate-distributed with zero mean and unit covariance matrix N(''p''0''1'',''p''I''p'') and ''m''M''p'' is a ''p x p'' matrix with a Wishart distribution with unit scale matrix and ''m'' degrees of freedom W(''p''I''p'',''m'') then ''m''(''1''d' ''p''M−1''p''d''1'') has a Hotelling ''T2'' distribution with dimensionality parameter ''p'' and ''m'' degrees of freedom.〔Eric W. Weisstein, ''(CRC Concise Encyclopedia of Mathematics, Second Edition )'', Chapman & Hall/CRC, 2003, p. 1408〕 If the notation is used to denote a random variable having Hotelling's ''T''-squared distribution with parameters ''p'' and ''m'' then, if a random variable ''X'' has Hotelling's ''T''-squared distribution, : then〔 : where is the ''F''-distribution with parameters ''p'' and ''m−p+1''. 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「Hotelling's T-squared distribution」の詳細全文を読む スポンサード リンク
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