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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 Jarque–Bera test ： ウィキペディア英語版 Jarque–Bera test In statistics, the Jarque–Bera test is a goodness-of-fit test of whether sample data have the skewness and kurtosis matching a normal distribution. The test is named after Carlos Jarque and Anil K. Bera. The test statistic ''JB'' is defined as : $$ \mathit = \frac \left( S^2 + \frac14 (C-3)^2 \right) where ''n'' is the number of observations (or degrees of freedom in general); ''S'' is the sample skewness, ''C'' is the sample kurtosis, and k is the number of regressors: : $$ S = \frac = \frac)^3} )^2 \right)^} , : $$ C = \frac = \frac)^4} )^2 \right)^} , where $\backslash hat\_3$ and $\backslash hat\_4$ are the estimates of third and fourth central moments, respectively, $\backslash bar$ is the sample mean, and $\backslash hat^2$ is the estimate of the second central moment, the variance. If the data come from a normal distribution, the ''JB'' statistic asymptotically has a chi-squared distribution with two degrees of freedom, so the statistic can be used to test the hypothesis that the data are from a normal distribution. The null hypothesis is a joint hypothesis of the skewness being zero and the excess kurtosis being zero. Samples from a normal distribution have an expected skewness of 0 and an expected excess kurtosis of 0 (which is the same as a kurtosis of 3). As the definition of ''JB'' shows, any deviation from this increases the JB statistic. For small samples the chi-squared approximation is overly sensitive, often rejecting the null hypothesis when it is in fact true. Furthermore, the distribution of ''p''-values departs from a uniform distribution and becomes a right-skewed uni-modal distribution, especially for small ''p''-values. This leads to a large Type I error rate. The table below shows some ''p''-values approximated by a chi-squared distribution that differ from their true alpha levels for small samples. : (These values have been approximated by using Monte Carlo simulation in Matlab) In MATLAB's implementation, the chi-squared approximation for the JB statistic's distribution is only used for large sample sizes (> 2000). For smaller samples, it uses a table derived from Monte Carlo simulations in order to interpolate ''p''-values.〔(【引用サイトリンク】title=Analysis of the JB-Test in MATLAB )〕 ==History== Considering normal sampling, and √''β''1 and ''β''2 contours, noticed that the statistic ''JB'' will be asymptotically ''χ''2(2)-distributed; however they also noted that “large sample sizes would doubtless be required for the ''χ''2 approximation to hold”. Bowman and Shelton did not study the properties any further, preferring D’Agostino’s K-squared test. 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「Jarque–Bera test」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.