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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 Skew normal distribution ： ウィキペディア英語版 Skew normal distribution \int_^\right)} e^}\ dt| cdf =$\backslash Phi\backslash left(\backslash frac\backslash right)-2T\backslash left(\backslash frac,\backslash alpha\backslash right)$ $T(h,a)$ is Owen's T function| mean =$\backslash xi\; +\; \backslash omega\backslash delta\backslash sqrt\}$ where $\backslash delta\; =\; \backslash frac\backslash right)$| skewness =$\backslash gamma\_1\; =\; \backslash frac\; \backslash frac\backslash right)^4\}$| entropy =| mgf =$M\_X\backslash left(t\backslash right)=2\backslash exp\backslash left(\backslash xi\; t+\backslash frac\backslash right)\backslash Phi\backslash left(\backslash omega\backslash delta\; t\backslash right)$| cf =$M\_X\backslash left(i\backslash delta\backslash omega\; t\backslash right)$| char =| }} In probability theory and statistics, the skew normal distribution is a continuous probability distribution that generalises the normal distribution to allow for non-zero skewness. ==Definition== Let $\backslash phi(x)$ denote the standard normal probability density function :$\backslash phi(x)=\backslash frac\}$ with the cumulative distribution function given by :$\backslash Phi(x)\; =\; \backslash int\_^\; \backslash phi(t)\backslash \; dt\; =\; \backslash frac\; \backslash left(1\; +\; \backslash operatorname\; \backslash left(\backslash frac$. One can verify that the normal distribution is recovered when $\backslash alpha\; =\; 0$, and that the absolute value of the skewness increases as the absolute value of $\backslash alpha$ increases. The distribution is right skewed if $\backslash alpha>0$ and is left skewed if . The probability density function with location $\backslash xi$, scale $\backslash omega$, and parameter $\backslash alpha$ becomes :$f(x)\; =\; \backslash frac\backslash phi\backslash left(\backslash frac\backslash right)\backslash Phi\backslash left(\backslash alpha\; \backslash left(\backslash frac\backslash right)\backslash right).\; \backslash ,$ Note, however, that the skewness of the distribution is limited to the interval $(-1,1)$. 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「Skew 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.