翻訳と辞書 Words near each other ・ Bennett Strong ・ Bennett Thrasher LLP ・ Bennett Township ・ Bennett Township, Fillmore County, Nebraska ・ Bennett Township, Kingman County, Kansas ・ Bennett Valley ・ Bennett Valley AVA ・ Bennett Valley Fire District ・ Bennett Valley Union School District ・ Bennett Wolf ・ Bennett's Adventure ・ Bennett's Cave ・ Bennett's chinchilla rat ・ Bennett's fracture ・ Bennett's Hole ・ Bennett's inequality ・ Bennett's laws ・ Bennett's Meadow Bridge ・ Bennett's Pond State Park ・ Bennett's stingray ・ Bennett's tree-kangaroo ・ Bennett's woodpecker ・ Bennett, Alpert, and Goldstein’s S ・ Bennett, British Columbia ・ Bennett, California ・ Bennett, Colorado ・ Bennett, Iowa ・ Bennett, North Carolina ・ Bennett, West Virginia ・ Bennett, Wisconsin Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Bennett's inequality ： ウィキペディア英語版 Bennett's inequality In probability theory, Bennett's inequality provides an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount. Bennett's inequality was proved by George Bennett of the University of New South Wales in 1962. Let be independent random variables, and assume (for simplicity but without loss of generality) they all have zero expected value. Further assume almost surely for all , and let :$\backslash sigma^2\; =\; \backslash frac1n\; \backslash sum\_^n\; \backslash operatorname(X\_i).$ Then for any , :$\backslash Pr\backslash left(\; \backslash sum\_^n\; X\_i\; >\; t\; \backslash right)\; \backslash leq$ \exp\left( - \frac h\left(\frac \right)\right), where . See also Freedman (1975) and Fan et al. (2012) for a martingale version of Bennett's inequality and its improvement, respectively. ==See also== * Bernstein inequalities (probability theory) * Hoeffding's inequality * Azuma's inequality * McDiarmid's inequality * Markov inequality * Dvoretzky–Kiefer–Wolfowitz inequality * Chebyshev's inequality * Concentration inequality 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「Bennett'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.