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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 Generalized multivariate log-gamma distribution ： ウィキペディア英語版 Generalized multivariate log-gamma distribution In probability theory and statistics, the generalized multivariate log-gamma (G-MVLG) distribution is a multivariate distribution introduced by Demirhan and Hamurkaroglu in 2011. The G-MVLG is a flexible distribution. Skewness and kurtosis are well controlled by the parameters of the distribution. This enables one to control dispersion of the distribution. Because of this property, the distribution is effectively used as a joint prior distribution in Bayesian analysis, especially when the likelihood is not from the location-scale family of distributions such as normal distribution. ==Joint probability density function== If $\backslash boldsymbol\; \backslash sim$ \mathrm\text\mathrm(\delta,\nu,\boldsymbol,\boldsymbol), the joint probability density function (pdf) of $\backslash boldsymbol=(Y\_,\backslash dots,Y\_)$ is given as the following: :$f(y\_1,\backslash dots,y\_k)=\; \backslash delta^\backslash sum\_^\backslash infty\; \backslash frac^k\; \backslash mu\_i\; \backslash lambda\_i^\}$ \exp\bigg\^k \frac\exp\\bigg\}, where $\backslash boldsymbol\backslash in\; \backslash mathbb^,\; \backslash nu>0,\; \backslash lambda\_>0,\; \backslash mu\_>0$ for $j=1,\backslash dots,k,\; \backslash delta=\backslash det(\backslash boldsymbol)^\},$ and : $$ \boldsymbol=\left( \begin 1 & \sqrt)} & \cdots & \sqrt)} \\ \sqrt)} & 1 & \cdots & \sqrt)} \\ \vdots & \vdots & \ddots & \vdots \\ \sqrt)} & \sqrt)} & \cdots & 1 \end \right), $\backslash rho\_$ is the correlation between $Y\_i$ and $Y\_j$, $\backslash det(\backslash cdot)$ and $\backslash mathrm(\backslash cdot)$ denote determinant and absolute value of inner expression, respectively, and $\backslash boldsymbol=(\backslash delta,\backslash nu,\backslash boldsymbol^T,\backslash boldsymbol^T)$ includes parameters of the 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「Generalized multivariate log-gamma 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.