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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 Raised cosine distribution ： ウィキペディア英語版 Raised cosine distribution In probability theory and statistics, the raised cosine distribution is a continuous probability distribution supported on the interval $()$. The probability density function (PDF) is :$f(x;\backslash mu,s)=\backslash frac$ \left()\,=\frac\operatorname\left(\frac\,\pi\right)\, for $\backslash mu-s\; \backslash le\; x\; \backslash le\; \backslash mu+s$ and zero otherwise. The cumulative distribution function (CDF) is : for $\backslash mu-s\; \backslash le\; x\; \backslash le\; \backslash mu+s$ and zero for and unity for $x>\backslash mu+s$. The moments of the raised cosine distribution are somewhat complicated, but are considerably simplified for the standard raised cosine distribution. The standard raised cosine distribution is just the raised cosine distribution with $\backslash mu=0$ and $s=1$. Because the standard raised cosine distribution is an even function, the odd moments are zero. The even moments are given by: :$E(x^)=\backslash frac\backslash int\_^1\; ()x^\backslash ,dx\; =\backslash frac\backslash int\_^1\; x^\backslash operatorname(x\backslash pi)\backslash ,dx$ :$=\; \backslash frac+\backslash frac\backslash ,\_1F\_2$ \left(n\!+\!\frac;\frac,n\!+\!\frac;\frac\right) where $\backslash ,\_1F\_2$ is a generalized hypergeometric function. == Differential equation == The pdf of the raised cosine distribution is a solution to the following differential equation: :$\backslash left\backslash$ 2 s^3 f''(x)-2 \pi ^2 s f(x)+\pi ^2 = 0,\\ f(0) = \frac \cosh^2\left(\frac\right),\\ f'(0) = -\frac \sinh \left(\frac\right) \end\right\} 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「Raised cosine 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.