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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 Matrix t-distribution ： ウィキペディア英語版 Matrix t-distribution In statistics, the matrix t-distribution (or matrix variate t-distribution) is the generalization of the multivariate t-distribution from vectors to matrices.〔Zhu, Shenghuo and Kai Yu and Yihong Gong (2007). ("Predictive Matrix-Variate ''t'' Models." ) In J.C. Platt, D. Koller, Y. Singer, and S. Roweis, editors, ''NIPS '07: Advances in Neural Information Processing Systems'' 20, pages 1721-1728. MIT Press, Cambridge, MA, 2008. The notation is changed a bit in this article for consistency with the matrix normal distribution article.〕 The matrix t-distribution shares the same relationship with the multivariate t-distribution that the matrix normal distribution shares with the multivariate normal distribution. For example, the matrix t-distribution is the compound distribution that results from sampling from a matrix normal distribution having sampled the covariance matrix of the matrix normal from an inverse Wishart distribution. In a Bayesian analysis of a multivariate linear regression model based on the matrix normal distribution, the matrix t-distribution is the posterior predictive distribution. ==Definition== |\boldsymbol\Sigma|^} :$\backslash times\; \backslash left|\backslash mathbf\_n\; +\; \backslash boldsymbol\backslash Sigma^(\backslash mathbf\; -\; \backslash mathbf)\backslash boldsymbol\backslash Omega^(\backslash mathbf-\backslash mathbf)^\backslash right|^\}$ | cdf =No analytic expression| mean =$\backslash mathbf$ if $\backslash nu\; +\; p\; -\; n\; >\; 1$, else undefined| mode =$\backslash mathbf$| variance =$\backslash frac$ if $\backslash nu\; >\; 2$, else undefined| kurtosis =| entropy =| mgf =| char =see below| }} For a matrix t-distribution, the probability density function at the point $\backslash mathbf$ of an $n\backslash times\; p$ space is :$f(\backslash mathbf\; ;\; \backslash nu,\backslash mathbf,\backslash boldsymbol\backslash Sigma,\; \backslash boldsymbol\backslash Omega)\; =\; K$ \times \left|\mathbf_n + \boldsymbol\Sigma^(\mathbf - \mathbf)\boldsymbol\Omega^(\mathbf-\mathbf)^\right|^}, where the constant of integration ''K'' is given by :$K\; =$ \frac\right)} \Gamma_p\left(\frac\right)} |\boldsymbol\Omega|^} |\boldsymbol\Sigma|^}. Here $\backslash Gamma\_p$ is the multivariate gamma function. The characteristic function and various other properties can be derived from the generalized matrix t-distribution (see below). 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「Matrix t-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.