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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 Directional statistics ： ウィキペディア英語版 Directional statistics Directional statistics (also circular statistics or spherical statistics) is the subdiscipline of statistics that deals with directions (unit vectors in R''n''), axes (lines through the origin in R''n'') or rotations in R''n''. More generally, directional statistics deals with observations on compact Riemannian manifolds. The fact that 0 degrees and 360 degrees are identical angles, so that for example 180 degrees is not a sensible mean of 2 degrees and 358 degrees, provides one illustration that special statistical methods are required for the analysis of some types of data (in this case, angular data). Other examples of data that may be regarded as directional include statistics involving temporal periods (e.g. time of day, week, month, year, etc.), compass directions, dihedral angles in molecules, orientations, rotations and so on. ==Circular and higher-dimensional distributions== Any probability density function $p(x)$ on the line can be "wrapped" around the circumference of a circle of unit radius.〔Bahlmann, C., (2006), Directional features in online handwriting recognition, Pattern Recognition, 39〕 That is, the pdf of the wrapped variable : $$ \theta = x_w=x \mod 2\pi\ \ \in (-\pi,\pi] is : $$ p_w(\theta)=\sum_^. This concept can be extended to the multivariate context by an extension of the simple sum to a number of $F$ sums that cover all dimensions in the feature space: : $$ p_w(\vec\theta)=\sum_^\cdots \sum_^\infty_F)} where $\backslash mathbf\_k=(0,\backslash dots,0,1,0,\backslash dots,0)^\{\backslash mathsf\{T\}\}$ is the $k$th Euclidean basis vector. The following sections show some relevant circular distributions. 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「Directional statistics」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.