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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 Samuelson's inequality ： ウィキペディア英語版 Samuelson's inequality In statistics, Samuelson's inequality, named after the economist Paul Samuelson,〔Paul Samuelson, "How Deviant Can You Be?", ''Journal of the American Statistical Association'', volume 63, number 324 (December, 1968), pp. 1522–1525 〕 also called the Laguerre–Samuelson inequality,〔Jensen, Shane Tyler (1999) (The Laguerre–Samuelson Inequality with Extensions and Applications in Statistics and Matrix Theory ) MSc Thesis. Department of Mathematics and Statistics, McGill University.〕 after the mathematician Edmond Laguerre, states that every one of any collection ''x''1, ..., ''x''''n'', is within √(''n'' − 1) sample standard deviations of their sample mean. ==Definition== If we let : $\backslash overline\; =\; \backslash frac$ be the sample mean and : $s\; =\; \backslash sqrt\; \backslash sum\_^n\; (x\_i\; -\; \backslash overline)^2\; \}$ be the standard deviation of the sample, then : $\backslash overline\; -\; s\backslash sqrt\; \backslash le\; x\_i\; \backslash le\; \backslash overline\; +\; s\backslash sqrt\backslash qquad\; \backslash texti\; =\; 1,\backslash dots,n.$〔''Advances in Inequalities from Probability Theory and Statistics'', by Neil S. Barnett and Sever Silvestru Dragomir, Nova Publishers, 2008, page 164〕 Equality holds on the left if and only if the ''n'' − 1 smallest of the ''n'' numbers are equal to each other, and on the right iff the ''n'' − 1 largest ones are equal. Samuelson's inequality may be considered a reason why studentization of residuals should be done externally. 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「Samuelson'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.