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Asymptotic Distribution of Probabilities of Misclassification for Edgeworth Series Distribution (ESD)

机译:EdgeWorth系列分布(ESD)错误分类概率的渐近分布

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The exact distribution of the test statistics in multivariate case is quite complicated in many situations, even when the underlying distribution is multivariate normal. This is due to the complex nature of the expression and therefore, there is a need to derive the asymptotic expression for the distribution. In this study, the asymptotic distribution of errors of misclassification for Edgeworth Series is derived by using Taylor's expansion. The error of misclassification for the conditional probability of misclassification was expanded around the means emanating from populations one and two using approximated mean and variance of the errors of misclassification. The distribution of error of misclassification of the conditional probability of misclassification for ESD is approximately normal with mean zero and variance one.
机译:在许多情况下,多变量案例中的测试统计的确切分布在许多情况下,即使基本分布是多变量正常的情况。这是由于表达的复杂性,因此,需要导出分布的渐近表达。在这项研究中,通过使用泰勒的扩张来得出边缘Worth系列错误分类误差的渐近分布。使用近似平均值和错误分类误差的差异和变化,将错误分类错误分类错误分类错误分类概率扩展。错误分类错误分类误差的分配概率对于ESD的分类概率大致正常,其平均零和方差1。

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