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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 McKay's approximation for the coefficient of variation ： ウィキペディア英語版 McKay's approximation for the coefficient of variation In statistics, McKay's approximation of the coefficient of variation is a statistic based on a sample from a normally distributed population. It was introduced in 1932 by A. T. McKay. Statistical methods for the coefficient of variation often utilizes McKay's approximation.〔.〕 Let $x\_i$, $i\; =\; 1,\; 2,\backslash ldots,\; n$ be $n$ independent observations from a $N(\backslash mu,\; \backslash sigma^2)$ normal distribution. The population coefficient of variation is $c\_v\; =\; \backslash sigma\; /\; \backslash mu$. Let $\backslash bar$ and $s\; \backslash ,$ denote the sample mean and the sample standard deviation, respectively. Then $\backslash hat\_v\; =\; s/\backslash bar$ is the sample coefficient of variation. McKay’s approximation is :$$ K = \left( 1 + \frac \right) \ \frac Note that in this expression, the first factor includes the population coefficient of variation, which is usually unknown. When $c\_v$ is smaller than 1/3, then $K$ is approximately chi-square distributed with $n\; -\; 1$ degrees of freedom. In the original article by McKay, the expression for $K$ looks slightly different, since McKay defined $\backslash sigma^2$ with denominator $n$ instead of $n\; -\; 1$. McKay's approximation, $K$, for the coefficient of variation is approximately chi-square distributed, but exactly noncentral beta distributed . == References== 〔 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「McKay's approximation for the coefficient of variation」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.