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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 Multivariate gaussian distribution ： ウィキペディア英語版 Multivariate normal distribution |\boldsymbol\Sigma|^}\, e^(\mathbf-\boldsymbol\mu)'\boldsymbol\Sigma^(\mathbf-\boldsymbol\mu) }, exists only when Σ is positive-definite | mean = ''μ'' | median = | mode = ''μ'' | variance = Σ | skewness = | kurtosis = | entropy = $\backslash frac\; (1\; +\; \backslash ln\; (2\backslash pi))\; +\; \backslash frac\; \backslash ln\; |\backslash boldsymbol\backslash Sigma\; |$ | mgf = $\backslash exp\backslash !\backslash Big(\; \backslash boldsymbol\backslash mu\text{'}\backslash mathbf\; +\; \backslash tfrac\; \backslash mathbf\text{'}\backslash boldsymbol\backslash Sigma\; \backslash mathbf\backslash Big)$ | char = $\backslash exp\backslash !\backslash Big(\; i\backslash boldsymbol\backslash mu\text{'}\backslash mathbf\; -\; \backslash tfrac\; \backslash mathbf\text{'}\backslash boldsymbol\backslash Sigma\; \backslash mathbf\backslash Big)$ }} In probability theory and statistics, the multivariate normal distribution or multivariate Gaussian distribution, is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. One possible definition is that a random vector is said to be ''k''-variate normally distributed if every linear combination of its ''k'' components has a univariate normal distribution. Its importance derives mainly from the multivariate central limit theorem. The multivariate normal distribution is often used to describe, at least approximately, any set of (possibly) correlated real-valued random variables each of which clusters around a mean value. == Notation and parametrization == The multivariate normal distribution of a ''k''-dimensional random vector can be written in the following notation: : $$ \mathbf\ \sim\ \mathcal(\boldsymbol\mu,\, \boldsymbol\Sigma), or to make it explicitly known that ''X'' is ''k''-dimensional, : $$ \mathbf\ \sim\ \mathcal_k(\boldsymbol\mu,\, \boldsymbol\Sigma). with ''k''-dimensional mean vector :$\backslash boldsymbol\backslash mu\; =\; ,\; \backslash ldots,\; \backslash operatorname()]$ and $k\; \backslash times\; k$ covariance matrix :$\backslash boldsymbol\backslash Sigma\; =\; [\backslash operatorname[X\_i,\; X\_j]],\; i=1,2,\backslash ldots,k;\; j=1,2,\backslash ldots,k$ 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「Multivariate normal 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.