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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 beta distribution ： ウィキペディア英語版 Noncentral beta distribution | cdf = (type I) $\backslash sum\_^\; e^\; \backslash frac\backslash right)^j\}\; I\_x\; \backslash left(\backslash alpha\; +\; j,\backslash beta\backslash right)$| mean = (type I) $e^\}\backslash frac\; \backslash frac\; \backslash right)$ (see Confluent hypergeometric function)| variance = (type I) $e^\}\backslash frac\; \backslash frac\; \backslash right)\; -\; \backslash mu^2$ where $\backslash mu$ is the mean. (see Confluent hypergeometric function) }} In probability theory and statistics, the noncentral beta distribution is a continuous probability distribution that is a generalization of the (central) beta distribution. The noncentral beta distribution (Type I) is the distribution of the ratio :$$ X = \frac, where $\backslash chi^2\_m(\backslash lambda)$ is a noncentral chi-squared random variable with degrees of freedom ''m'' and noncentrality parameter $\backslash lambda$, and $\backslash chi^2\_n$ is a central chi-squared random variable with degrees of freedom ''n'', independent of $\backslash chi^2\_m(\backslash lambda)$. In this case, $X\; \backslash sim\; \backslash mbox\backslash left(\backslash frac,\backslash frac,\backslash lambda\backslash right)$ A Type II noncentral beta distribution is the distribution of the ratio :$Y\; =\; \backslash frac,$ where the noncentral chi-squared variable is in the denominator only.〔 If $Y$ follows the type II distribution, then $X\; =\; 1\; -\; Y$ follows a type I distribution. == Cumulative distribution function == The Type I cumulative distribution function is usually represented as a Poisson mixture of central beta random variables:〔 :$$ F(x) = \sum_^\infty P(j) I_x(\alpha+j,\beta), where λ is the noncentrality parameter, ''P''(.) is the Poisson(λ/2) probability mass function, ''\alpha=m/2'' and ''\beta=n/2'' are shape parameters, and $I\_x(a,b)$ is the incomplete beta function. That is, :$$ F(x) = \sum_^\infty \frac\left(\frac\right)^je^I_x(\alpha+j,\beta). The Type II cumulative distribution function in mixture form is :$$ F(x) = \sum_^\infty P(j) I_x(\alpha,\beta+j). Algorithms for evaluating the noncentral beta distribution functions are given by Posten and Chattamvelli.〔 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 beta 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.