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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 Cantelli's inequality ： ウィキペディア英語版 Cantelli's inequality In probability theory, Cantelli's inequality, named after Francesco Paolo Cantelli, is a generalization of Chebyshev's inequality in the case of a single "tail".〔''Research and practice in multiple criteria decision making: proceedings of the XIVth International Conference on Multiple Criteria Decision Making (MCDM), Charlottesville, Virginia, USA, June 8–12, 1998'', edited by Y.Y. Haimes and R.E. Steuer, Springer, 2000, ISBN 3540672664.〕〔("Tail and Concentration Inequalities" by Hung Q. Ngo )〕〔("Concentration-of-measure inequalities" by Gábor Lugosi )〕 The inequality states that : $$ \Pr(X-\mu\ge\lambda)\quad\begin \le \frac & \text \lambda > 0, \\() \ge 1 - \frac & \text\lambda < 0. \end where :$X$ is a real-valued random variable, :$\backslash Pr$ is the probability measure, :$\backslash mu$ is the expected value of $X$, :$\backslash sigma^2$ is the variance of $X$. With the same methods one can prove the following variant: : $$ \Pr(|X-\mu|\ge\lambda)\le \frac. The inequality is due to Francesco Paolo Cantelli. The Chebyshev inequality implies that in any data sample or probability distribution, "nearly all" values are close to the mean in terms of the absolute value of the difference between the points of the data sample and the weighted average of the data sample. The Cantelli inequality (sometimes called the "Chebyshev–Cantelli inequality" or the "one-sided Chebyshev inequality") gives a way of estimating how the points of the data sample are bigger than or smaller than their weighted average without the two tails of the absolute value estimate. The Chebyshev inequality has "higher moments versions" and "vector versions", and so does the Cantelli inequality. ==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「Cantelli's inequality」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.