翻訳と辞書 Words near each other ・ Algebraic code-excited linear prediction ・ Algebraic combinatorics ・ Algebraic connectivity ・ Algebraic curve ・ Algebraic cycle ・ Algebraic data type ・ Algebraic definition ・ Algebraic differential equation ・ Algebraic differential geometry ・ Algebraic element ・ Algebraic enumeration ・ Algebraic equation ・ Algebraic Eraser ・ Algebraic expression ・ Algebraic extension ・ Algebraic formula for the variance ・ Algebraic fraction ・ Algebraic function ・ Algebraic function field ・ Algebraic geometry ・ Algebraic Geometry (book) ・ Algebraic geometry and analytic geometry ・ Algebraic geometry of projective spaces ・ Algebraic graph theory ・ Algebraic group ・ Algebraic holography ・ Algebraic independence ・ Algebraic integer ・ Algebraic interior ・ Algebraic K-theory 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 Algebraic formula for the variance ： ウィキペディア英語版 Algebraic formula for the variance In probability theory and statistics, there are several algebraic formulae for the variance available for deriving the variance of a random variable. The usefulness of these depends on what is already known about the random variable; for example a random variable may be defined in terms of its probability density function or by construction from other random variables. The context here is that of deriving algebraic expressions for the theoretical variance of a random variable, in contrast to questions of estimating the variance of a population from sample data for which there are special considerations in implementing computational algorithms. ==In terms of raw moments== If the raw moments E(''X'') and E(''X'' 2) of a random variable ''X'' are known (where E(''X'') is the expected value of ''X''), then Var(''X'') is given by :$\backslash operatorname(X)\; =\; \backslash operatorname(X^2)\; -\; ()^2\; .$ The result is called the König–Huygens formula in French-language literature〔In French: formule de Koenig–Huygens. See e.g. 〕 and known as Steiner translation theorem in Germany.〔In German: Verschiebungssatz von Steiner. See e.g. .〕 There is a corresponding formula for use in estimation of the variance from sample data, that can be of use in hand calculations. This is a closely related identity that is structured to create an unbiased estimate of the population variance :$$ \hat^2 = \frac\sum_^N(x_i-\bar)^2 = \frac\left(\frac\left(\sum_^N x_i^2\right) - \bar^2\right) \equiv \frac\left(\left(\sum_^N x_i^2\right) - N \left(\bar\right)^2\right) . However, use of these formulas can be unwise in practice when using floating point arithmetic with limited precision: subtracting two values having a similar magnitude can lead to catastrophic cancellation,〔Donald E. Knuth (1998). ''The Art of Computer Programming'', volume 2: ''Seminumerical Algorithms'', 3rd edn., p. 232. Boston: Addison-Wesley.〕 and thus causing a loss of significance when $\backslash operatorname(X)^2\; \backslash gg\; \backslash operatorname(X)$. There exist other numerically stable algorithms for calculating variance for use with floating point numbers. 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「Algebraic formula for the variance」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.