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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 Cauchy distribution ： ウィキペディア英語版 Wrapped Cauchy distribution In probability theory and directional statistics, a wrapped Cauchy distribution is a wrapped probability distribution that results from the "wrapping" of the Cauchy distribution around the unit circle. The Cauchy distribution is sometimes known as a Lorentzian distribution, and the wrapped Cauchy distribution may sometimes be referred to as a wrapped Lorentzian distribution. The wrapped Cauchy distribution is often found in the field of spectroscopy where it is used to analyze diffraction patterns (e.g. see Fabry–Pérot interferometer) == Description == The probability density function of the wrapped Cauchy distribution is: :$$ f_(\theta;\mu,\gamma)=\sum_^\infty \frac where $\backslash gamma$ is the scale factor and $\backslash mu$ is the peak position of the "unwrapped" distribution. Expressing the above pdf in terms of the characteristic function of the Cauchy distribution yields: :$$ f_(\theta;\mu,\gamma)=\frac\sum_^\infty e^ =\frac\,\,\frac In terms of the circular variable $z=e^$ the circular moments of the wrapped Cauchy distribution are the characteristic function of the Cauchy distribution evaluated at integer arguments: :$\backslash langle\; z^n\backslash rangle=\backslash int\_\backslash Gamma\; e^\backslash ,f\_(\backslash theta;\backslash mu,\backslash gamma)\backslash ,d\backslash theta\; =\; e^.$ where $\backslash Gamma\backslash ,$ is some interval of length $2\backslash pi$. The first moment is then the average value of ''z'', also known as the mean resultant, or mean resultant vector: :$$ \langle z \rangle=e^ The mean angle is :$$ \langle \theta \rangle=\mathrm\langle z \rangle = \mu and the length of the mean resultant is :$$ R=|\langle z \rangle| = 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 Cauchy 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.