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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 Bates distribution ： ウィキペディア英語版 Bates distribution -e^}) }\right)^n }} In probability and statistics, the Bates distribution, named after Grace Bates, is a probability distribution of the mean of a number of statistically independent uniformly distributed random variables on the unit interval.〔Jonhson, N.L.; Kotz, S.; Balakrishnan (1995) ''Continuous Univariate Distributions'', Volume 2, 2nd Edition, Wiley ISBN 0-471-58494-0(Section 26.9)〕 This distribution is sometimes confused with the Irwin–Hall distribution, which is the distribution of the sum (not mean) of n independent random variables uniformly distributed from 0 to 1. ==Definition== The Bates distribution is the continuous probability distribution of the mean, ''X'', of ''n'' independent uniformly distributed random variables on the unit interval, ''Ui'': :$$ X = \frac\sum_^n U_k. The equation defining the probability density function of a Bates distribution random variable x is :$$ f_X(x;n)=\frac\sum_^\left(-1\right)^k\left(nx-k\right)^\sgn(nx-k) for ''x'' in the interval (0,1), and zero elsewhere. Here sgn(''x − k'') denotes the sign function: :$\backslash sgn\backslash left(nx-k\backslash right)\; =\; \backslash begin$ -1 & nx < k \\ 0 & nx = k \\ 1 & nx > k. \end More generally, the mean of ''n'' independent uniformly distributed random variables on the interval () :$$ X_ = \frac\sum_^n U_k(a,b). would have the probability density function (PDF) of :$g(x;n,a,b)\; =\; f\_X\backslash left(\backslash frac;n\backslash right)\; \backslash text\; a\; \backslash leq\; x\; \backslash leq\; b\; \backslash ,$ Therefore the PDF of the distribution is $PDF\; =\; \backslash begin$ \sum_^n (-1)^k \binom \left( \frac-k/n \right)^ \sgn\left( \frac-k/n \right) & \text x\in()\\ 0 & \text \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「Bates 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.