翻訳と辞書 Words near each other ・ Stability (short story) ・ Stability 2008 ・ Stability and Growth Pact ・ Stability and support operations ・ Stability conditions ・ Stability constant ・ Stability constants of complexes ・ Stability criterion ・ Stability derivatives ・ Stability group ・ Stability Model ・ Stability of Boolean networks ・ Stability of the Solar System ・ Stability Pact ・ Stability Pact for South Eastern Europe ・ Stability postulate ・ Stability radius ・ Stability spectrum ・ Stability testing ・ Stability theory ・ Stability–instability paradox ・ Stabilization (architecture) ・ Stabilization (medicine) ・ Stabilization (warfare) ・ Stabilization Act of 1942 ・ Stabilization clause ・ Stabilization fund ・ Stabilization Fund of the Russian Federation ・ Stabilization of fragile states ・ Stabilization payments 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 Stability postulate ： ウィキペディア英語版 Stability postulate In probability theory, to obtain a nondegenerate limiting distribution of the extreme value distribution, it is necessary to "reduce" the actual greatest value by applying a linear transformation with coefficients that depend on the sample size. If $X\_1,\; X\_2,\; \backslash dots\; ,\; X\_n\; \backslash ,$ are independent random variables with common probability density function : $p\_(x)=f(x),$ then the cumulative distribution function of $X\text{'}\_n=\backslash max\backslash \; \backslash ,$ is : $F\_=^n\; \backslash ,$ If there is a limiting distribution of interest, the stability postulate states the limiting distribution is some sequence of transformed "reduced" values, such as $(a\_n\; X\text{'}\_n\; +\; b\_n)\; \backslash ,$, where $a\_n,\; b\_n\; \backslash ,$ may depend on ''n'' but not on ''x''. To distinguish the limiting cumulative distribution function from the "reduced" greatest value from ''F''(''x''), we will denote it by ''G''(''x''). It follows that ''G''(''x'') must satisfy the functional equation : $^n\; =\; G\; \backslash ,$ This equation was obtained by Maurice René Fréchet and also by Ronald Fisher. Boris Vladimirovich Gnedenko has shown there are ''no other'' distributions satisfying the stability postulate other than the following: * Gumbel distribution for the ''minimum'' stability postulate * * If $X\_i=\backslash textrm(\backslash mu,\backslash beta)\; \backslash ,$ and $Y=\backslash min\backslash \; \backslash ,$ then $Y\; \backslash sim\; a\_n\; X+b\_n\; \backslash ,$ where $a\_n=1\backslash ,$ and $b\_n=\; \backslash beta\; \backslash log(n)\; \backslash ,$ * * In other words, $Y\; \backslash sim\; \backslash textrm(\backslash mu\; -\; \backslash beta\; \backslash log(n),\backslash beta)\; \backslash ,$ * Extreme value distribution for the maximum stability postulate * * If $X\_i=\backslash textrm(\backslash mu,\backslash sigma)\; \backslash ,$ and $Y=\backslash max\backslash \; \backslash ,$ then $Y\; \backslash sim\; a\_n\; X+b\_n\; \backslash ,$ where $a\_n=1\backslash ,$ and $b\_n=\; \backslash sigma\; \backslash log(\backslash tfrac)\; \backslash ,$ * * In other words, $Y\; \backslash sim\; \backslash textrm(\backslash mu\; -\; \backslash sigma\; \backslash log(\backslash tfrac),\backslash sigma)\; \backslash ,$ * Fréchet distribution for the maximum stability postulate * * If $X\_i=\backslash textrm(\backslash alpha,s,m)\; \backslash ,$ and $Y=\backslash max\backslash \; \backslash ,$ then $Y\; \backslash sim\; a\_n\; X+b\_n\; \backslash ,$ where $a\_n=n^\}\backslash ,$ and $b\_n=\; m\; \backslash left(\; 1-\; n^\}\backslash right)\; \backslash ,$ * * In other words, $Y\; \backslash sim\; \backslash textrm(\backslash alpha,n^\}\; s,m)\; \backslash ,$ 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「Stability postulate」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.