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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 stable distribution ： ウィキペディア英語版 Multivariate stable distribution The multivariate stable distribution is a multivariate probability distribution that is a multivariate generalisation of the univariate stable distribution. The multivariate stable distribution defines linear relations between stable distribution marginals. In the same way as for the univariate case, the distribution is defined in terms of its characteristic function. The multivariate stable distribution can also be thought as an extension of the multivariate normal distribution. It has parameter, ''α'', which is defined over the range 0 < ''α'' ≤ 2, and where the case ''α'' = 2 is equivalent to the multivariate normal distribution. It has an additional skew parameter that allows for non-symmetric distributions, where the multivariate normal distribution is symmetric. == Definition == Let $\backslash mathbb$ be the unit sphere in $\backslash mathbb\; R^d\; :\; \backslash mathbb\; =\; \backslash$. A random vector, $X$, has a multivariate stable distribution - denoted as $X\; \backslash sim\; S(\backslash alpha,\; \backslash Lambda,\; \backslash delta)$ -, if the joint characteristic function of $X$ is〔J. Nolan, Multivariate stable densities and distribution functions: general and elliptical case, BundesBank Conference, Eltville, Germany, 11 November 2005. See also http://academic2.american.edu/~jpnolan/stable/stable.html〕 : $\backslash operatorname\; \backslash exp(u^T\; X)\; =\; \backslash exp\; \backslash left\backslash \; \backslash ,\; \backslash Lambda(ds)\; +\; i\; u^T\backslash delta\backslash right\backslash \}$ where 0 < ''α'' < 2, and for $y\backslash in\backslash mathbb\; R$ : (2/\pi)y \ln |y| & \alpha=1. \end This is essentially the result of Feldheim,〔Feldheim, E. (1937). Etude de la stabilité des lois de probabilité . Ph. D. thesis, Faculté des Sciences de Paris, Paris, France.〕 that any stable random vector can be characterized by a spectral measure $\backslash Lambda$ (a finite measure on $\backslash mathbb\; S$) and a shift vector $\backslash delta\; \backslash in\; \backslash mathbb\; R^d$. 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 stable 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.