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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 Quasi-arithmetic mean ： ウィキペディア英語版 Quasi-arithmetic mean In mathematics and statistics, the quasi-arithmetic mean or generalised ''f''-mean is one generalisation of the more familiar means such as the arithmetic mean and the geometric mean, using a function $f$. It is also called Kolmogorov mean after Russian scientist Andrey Kolmogorov. ==Definition== If ''f'' is a function which maps an interval $I$ of the real line to the real numbers, and is both continuous and injective then we can define the ''f''-mean of two numbers :$x\_1,\; x\_2\; \backslash in\; I$ as :$M\_f(x\_1,x\_2)\; =\; f^\backslash left(\; \backslash frac2\; \backslash right).$ For $n$ numbers :$x\_1,\; \backslash dots,\; x\_n\; \backslash in\; I$, the f-mean is :$M\_f(x\_1,\; \backslash dots,\; x\_n)\; =\; f^\backslash left(\; \backslash fracn\; \backslash right).$ We require ''f'' to be injective in order for the inverse function $f^$ to exist. Since $f$ is defined over an interval, $\backslash frac2$ lies within the domain of $f^$. Since ''f'' is injective and continuous, it follows that ''f'' is a strictly monotonic function, and therefore that the ''f''-mean is neither larger than the largest number of the tuple $x$ nor smaller than the smallest number in $x$. 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「Quasi-arithmetic mean」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.