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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 Wrapped normal distribution ： ウィキペディア英語版 Wrapped normal distribution In probability theory and directional statistics, a wrapped normal distribution is a wrapped probability distribution that results from the "wrapping" of the normal distribution around the unit circle. It finds application in the theory of Brownian motion and is a solution to the heat equation for periodic boundary conditions. It is closely approximated by the von Mises distribution, which, due to its mathematical simplicity and tractability, is the most commonly used distribution in directional statistics. ==Definition== The probability density function of the wrapped normal distribution is :$$ f_(\theta;\mu,\sigma)=\frac_ \exp \left(Expressing the above density function in terms of the characteristic function of the normal distribution yields:〔 :$$ f_(\theta;\mu,\sigma)=\frac\sum_^\infty e^ =\frac\vartheta\left(\frac,\frac\right) , where $\backslash vartheta(\backslash theta,\backslash tau)$ is the Jacobi theta function, given by :$$ \vartheta(\theta,\tau)=\sum_^\infty (w^2)^n q^ \text w \equiv e^ and $q\; \backslash equiv\; e^\; .$ The wrapped normal distribution may also be expressed in terms of the Jacobi triple product: :$f\_(\backslash theta;\backslash mu,\backslash sigma)=\backslash frac\backslash prod\_^\backslash infty\; (1-q^n)(1+q^z)(1+q^/z)\; .$ where $z=e^\backslash ,$ and $q=e^.$ 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「Wrapped 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.