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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 Cramér–von Mises criterion ： ウィキペディア英語版 Cramér–von Mises criterion In statistics the Cramér–von Mises criterion is a criterion used for judging the goodness of fit of a cumulative distribution function $F^$ * compared to a given empirical distribution function $F\_n$, or for comparing two empirical distributions. It is also used as a part of other algorithms, such as minimum distance estimation. It is defined as : *(x) In one-sample applications $F^$ * is the theoretical distribution and $F\_n$ is the empirically observed distribution. Alternatively the two distributions can both be empirically estimated ones; this is called the two-sample case. The criterion is named after Harald Cramér and Richard Edler von Mises who first proposed it in 1928–1930.〔H. Cramér, On the composition of elementary errors, Scandinavian Actuarial Journal 1928〕 〔R. E. von Mises, Wahrscheinlichkeit, Statistik und Wahrheit, Julius Springer 1928〕 The generalization to two samples is due to Anderson. The Cramér–von Mises test is an alternative to the Kolmogorov–Smirnov test. ==Cramér–von Mises test (one sample)== Let $x\_1,x\_2,\backslash cdots,x\_n$ be the observed values, in increasing order. Then the statistic is〔〔Pearson, E.S., Hartley, H.O. (1972) ''Biometrika Tables for Statisticians, Volume 2'', CUP. ISBN 0-521-06937-8 (page 118 and Table 54)〕 :$T\; =\; n\; \backslash omega^2\; =\; \backslash frac\; +\; \backslash sum\_^n\; \backslash left(\backslash frac-F(x\_i)\; \backslash right)^2.$ If this value is larger than the tabulated value, then the hypothesis that the data come from the distribution $F$ can be rejected. 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「Cramér–von Mises criterion」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.