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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 D'Agostino's K-squared test ： ウィキペディア英語版 D'Agostino's K-squared test In statistics, D’Agostino’s ''K''2 test, named for Ralph D'Agostino, is a goodness-of-fit measure of departure from normality, that is the test aims to establish whether or not the given sample comes from a normally distributed population. The test is based on transformations of the sample kurtosis and skewness, and has power only against the alternatives that the distribution is skewed and/or kurtic. == Skewness and kurtosis == In the following, let denote a sample of ''n'' observations, ''g''1 and ''g''2 are the sample skewness and kurtosis, ''mj''’s are the ''j''-th sample central moments, and $\backslash bar$ is the sample mean. (Note that quite frequently in the literature related to normality testing the skewness and kurtosis are denoted as √''β''1 and ''β''2 respectively. Such notation is less convenient since for example √''β''1 can be a negative quantity). The sample skewness and kurtosis are defined as : $\backslash begin$ & g_1 = \frac = \frac \sum_^n \left( x_i - \bar \right)^3} \sum_^n \left( x_i - \bar \right)^2 \right)^}\ , \\ & g_2 = \frac-3 = \frac \sum_^n \left( x_i - \bar \right)^4} \sum_^n \left( x_i - \bar \right)^2 \right)^2} - 3\ . \end These quantities consistently estimate the theoretical skewness and kurtosis of the distribution, respectively. Moreover, if the sample indeed comes from a normal population, then the exact finite sample distributions of the skewness and kurtosis can themselves be analysed in terms of their means ''μ''1, variances ''μ''2, skewnesses ''γ''1, and kurtoses ''γ''2. This has been done by , who derived the following expressions: : $\backslash begin$ & \mu_1(g_1) = 0, \\ & \mu_2(g_1) = \frac, \\ & \gamma_1(g_1) \equiv \frac. \end and : $\backslash begin$ & \mu_1(g_2) = - \frac, \\ & \mu_2(g_2) = \frac, \\ & \gamma_1(g_2) \equiv \frac \sqrt}, \\ & \gamma_2(g_2) \equiv \frac. \end For example, a sample with size drawn from a normally distributed population can be expected to have a skewness of and a kurtosis of , where SD indicates the standard deviation. 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「D'Agostino's K-squared 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.