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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 elliptical distribution ： ウィキペディア英語版 elliptical distribution In probability and statistics, an elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively, in the simplified two and three dimensional case, the joint distribution forms an ellipse and an ellipsoid, respectively, in iso-density plots. ==Definition== Elliptical distributions can be defined using characteristic functions. A multivariate distribution is said to be elliptical if its characteristic function is of the form :$e^\; \backslash Psi(t\text{'}\; \backslash Sigma\; t)\; \backslash ,$ for a specified vector $\backslash mu$, positive-definite matrix $\backslash Sigma$, and characteristic function $\backslash Psi$. The function $\backslash Psi$ is known as the characteristic generator of the elliptical distribution.〔Härdle and Simar (2012), p. 178.〕 Elliptical distributions can also be defined in terms of their density functions. When they exist, the density functions ''f'' have the structure: :$f(x)=\; k\; \backslash cdot\; g((x-\backslash mu)\text{'}\backslash Sigma^(x-\backslash mu))$ where $k$ is the scale factor, $x$ is an $n$-dimensional random vector with median vector $\backslash mu$ (which is also the mean vector if the latter exists), $\backslash Sigma$ is a positive definite matrix which is proportional to the covariance matrix if the latter exists, and $g$ is a function mapping from the non-negative reals to the non-negative reals giving a finite area under the curve.〔Frahm, G., Junker, M., & Szimayer, A. (2003). Elliptical copulas: applicability and limitations. Statistics & Probability Letters, 63(3), 275-286.〕 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「elliptical 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.