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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 Fieller's theorem ： ウィキペディア英語版 Fieller's theorem In statistics, Fieller's theorem allows the calculation of a confidence interval for the ratio of two means. ==Approximate confidence interval== Variables ''a'' and ''b'' may be measured in different units, so there is no way to directly combine the standard errors as they may also be in different units. The most complete discussion of this is given by Fieller (1954). Fieller showed that if ''a'' and ''b'' are (possibly correlated) means of two samples with expectations $\backslash mu\_a$ and $\backslash mu\_b$, and variances $\backslash nu\_\backslash sigma^2$ and $\backslash nu\_\backslash sigma^2$ and covariance $\backslash nu\_\backslash sigma^2$, and if $\backslash nu\_,\; \backslash nu\_,\; \backslash nu\_$ are all known, then a (1 − ''α'') confidence interval (''m''L, ''m''U) for $a/b$ is given by : $(m\_L,\; m\_)\; =\; \backslash frac\; \backslash left(-\; \backslash frac\}\; \backslash mp\; \backslash frac\; \backslash sqrt\backslash nu\_\; +\; \backslash frac\; \backslash nu\_\; -\; g\backslash left(\backslash nu\_\; -\; \backslash frac\; \backslash right)$ where :$g=\backslash fracs^2\backslash nu\_\}.$ Here $s^2$ is an unbiased estimator of $\backslash sigma^2$ based on r degrees of freedom, and $t\_$ is the $\backslash alpha$-level deviate from the Student's t-distribution based on ''r'' degrees of freedom. Three features of this formula are important in this context: a) The expression inside the square root has to be positive, or else the resulting interval will be imaginary. b) When ''g'' is very close to 1, the confidence interval is infinite. c) When ''g'' is greater than 1, the overall divisor outside the square brackets is negative and the confidence interval is exclusive. 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「Fieller's theorem」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.