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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 Fisher–Tippett–Gnedenko theorem ： ウィキペディア英語版 Fisher–Tippett–Gnedenko theorem In statistics, the Fisher–Tippett–Gnedenko theorem (also the Fisher–Tippett theorem or the extreme value theorem) is a general result in extreme value theory regarding asymptotic distribution of extreme order statistics. The maximum of a sample of iid random variables after proper renormalization can only converge in distribution to one of 3 possible distributions, the Gumbel distribution, the Fréchet distribution, or the Weibull distribution. Credit for the extreme value theorem (or convergence to types theorem) is given to Gnedenko (1948), previous versions were stated by Ronald Fisher and Leonard Henry Caleb Tippett in 1928 and Fréchet in 1927. The role of the extremal types theorem for maxima is similar to that of central limit theorem for averages, except that the central limit theorem applies to the average of a sample from any distribution with finite variance, while the Fisher-Tippet-Gnedenko theorem only states that ''if'' the distribution of a normalized maximum converges, ''then'' the limit has to be one of a particular class of distributions. It does not state that the distribution of the normalized maximum does converge. ==Statement== Let $X\_1,X\_2\backslash ldots,\; X\_n\backslash ldots$ be a sequence of independent and identically-distributed random variables, and $M\_n=\backslash max\backslash$. If a sequence of pairs of real numbers $(a\_n,\; b\_n)$ exists such that each $a\_n>0$ and $\backslash lim\_P\backslash left(\backslash frac\backslash leq\; x\backslash right)\; =\; F(x)$, where $F$ is a non degenerate distribution function, then the limit distribution $F$ belongs to either the Gumbel, the Fréchet or the Weibull family. These can be grouped into the generalized extreme value distribution. 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「Fisher–Tippett–Gnedenko theorem」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.