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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 chi-squared distribution ： ウィキペディア英語版 Noncentral chi-squared distribution \left( \sqrt, \sqrt \right) with Marcum Q-function $Q\_M(a,b)$ | mean =$k+\backslash lambda\backslash ,$| median =| mode =| variance =$2(k+2\backslash lambda)\backslash ,$| skewness =$\backslash frac$| entropy =| mgf =| char =$\backslash frac\backslash right)\}\}$ In probability theory and statistics, the noncentral chi-squared or noncentral $\backslash chi^2$ distribution is a generalization of the chi-squared distribution. This distribution often arises in the power analysis of statistical tests in which the null distribution is (perhaps asymptotically) a chi-squared distribution; important examples of such tests are the likelihood ratio tests. ==Background== Let ($X\_1$, $X\_2,\; \backslash ldots,$$X\_i,\; \backslash ldots,$ $X\_k$) be ''k'' independent, normally distributed random variables with means $\backslash mu\_i$ and unit variances. Then the random variable : $\backslash sum\_^k\; X\_i^2$ is distributed according to the noncentral chi-squared distribution. It has two parameters: $k$ which specifies the number of degrees of freedom (i.e. the number of $X\_i$), and $\backslash lambda$ which is related to the mean of the random variables $X\_i$ by: : $\backslash lambda=\backslash sum\_^k\; \backslash mu\_i^2.$ $\backslash lambda$ is sometimes called the noncentrality parameter. Note that some references define $\backslash lambda$ in other ways, such as half of the above sum, or its square root. This distribution arises in multivariate statistics as a derivative of the multivariate normal distribution. While the central chi-squared distribution is the squared norm of a random vector with $N(0\_k,I\_k)$ distribution (i.e., the squared distance from the origin of a point taken at random from that distribution), the non-central $\backslash chi^2$ is the squared norm of a random vector with $N(\backslash mu,I\_k)$ distribution. Here $0\_k$ is a zero vector of length ''k'', $\backslash mu\; =\; (\backslash mu\_1,\; \backslash ldots,\; \backslash mu\_k)$ and $I\_k$ is the identity matrix of size ''k''. 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 chi-squared 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.