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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 Noncentral F-distribution ： ウィキペディア英語版 Noncentral F-distribution In probability theory and statistics, the noncentral ''F''-distribution is a continuous probability distribution that is a generalization of the (ordinary) ''F''-distribution. It describes the distribution of the quotient (''X''/''n''1)/(''Y''/''n''2), where the numerator ''X'' has a noncentral chi-squared distribution with ''n''1 degrees of freedom and the denominator ''Y'' has a central chi-squared distribution ''n''2 degrees of freedom. It is also required that ''X'' and ''Y'' are statistically independent of each other. It is the distribution of the test statistic in analysis of variance problems when the null hypothesis is false. The noncentral ''F''-distribution is used to find the power function of such a test. == Occurrence and specification == If $X$ is a noncentral chi-squared random variable with noncentrality parameter $\backslash lambda$ and $\backslash nu\_1$ degrees of freedom, and $Y$ is a chi-squared random variable with $\backslash nu\_2$ degrees of freedom that is statistically independent of $X$, then :$$ F=\frac is a noncentral ''F''-distributed random variable. The probability density function (pdf) for the noncentral ''F''-distribution is〔S. Kay, Fundamentals of Statistical Signal Processing: Detection Theory, (New Jersey: Prentice Hall, 1998), p. 29.〕 :$$ p(f) =\sum\limits_^\infty\frac,\frac+k\right) k!} \left(\frac\right)^+k} \left(\frac\right)^+k}f^ when $f\backslash ge0$ and zero otherwise. The degrees of freedom $\backslash nu\_1$ and $\backslash nu\_2$ are positive. The noncentrality parameter $\backslash lambda$ is nonnegative. The term $B(x,y)$ is the beta function, where :$$ B(x,y)=\frac. The cumulative distribution function for the noncentral ''F''-distribution is :$$ F(x|d_1,d_2,\lambda)=\sum\limits_^\infty\left(\frac\lambda\right)^j}e^}\right)I\left(\frac\bigg|\frac+j,\frac\right) where $I$ is the regularized incomplete beta function. The mean and variance of the noncentral ''F''-distribution are :$$ \operatorname\left()= \begin \frac &\nu_2>2\\ \text &\nu_2\le2\\ \end and :$$ \operatorname\left()= \begin 2\frac\left(\frac\right)^2 &\nu_2>4\\ \text &\nu_2\le4.\\ \end 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「Noncentral F-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.