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Errors of Misclassification Associated with Edgeworth Series Distribution (ESD)

机译：Edgeworth系列分布（ESD）带来的错误分类错误

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This study investigates the errors of misclassification associated with Edgeworth Series Distribution (ESD) with a view to assessing the effects of sampling from non-normality. The effects of applying a normal classificatory rule when it is actually a persistent non-normal distribution were examined. These were achieved by comparing the errors of misclassification for ESD with ND using small sample sizes at every level of skewness factor. The simulation procedure for the experiment of the study was implemented using numerical inverse interpolation method in R program to generate a uniformly distributed random variable N. A configuration size of 1000 was obtained for the two training samples drawn at every level of skewness factor (λ_3), in the range (0.00625, 0.4). This was repeated for different small sample sizes by comparing errors of misclassification of ESD with ND. The simulation results showed that the optimum probabilities of misclassification by ESD: (E_(12E)) decreases and (E_(12E)) increases, as the skewness factor (λ_3) increases. The optimum total probability of misclassification is stable as λ_3 also increases. The probability of misclassification E_(12E) ≥ E_(12N) and E_(21E) ≥ E_(21N) at every level of λ_3. Thus, the total probabilities of misclassification are not greatly affected by the skewness factor. This asserts that the normal classification procedure is robust against departure from normality.
机译：这项研究调查了与Edgeworth系列分布（ESD）相关的错误分类错误，以评估非正态采样的影响。检验了应用正常分类规则实际上是持续的非正态分布时的效果。通过比较在每个偏度因子水平上使用小样本量的ESD与ND的误分类误差，可以实现这些目标。在R程序中使用数值逆插值方法实施了用于研究实验的模拟程序，以生成均匀分布的随机变量N。在每个偏度因子（λ_3）级别绘制的两个训练样本的配置大小为1000 ，范围为（0.00625，0.4）。通过比较ESD和ND的误分类误差，对不同的小样本量重复进行此操作。仿真结果表明，随着偏度因子（λ_3）的增加，通过ESD进行错误分类的最佳概率为（E_（12E））减小而（E_（12E））增大。当λ_3也增加时，错误分类的最佳总概率是稳定的。在每个λ_3级别上，错误分类E_（12E）≥E_（12N）和E_（21E）≥E_（21N）的概率。因此，错误分类的总概率不会受到偏度因素的很大影响。这断言，正常分类程序对抵制偏离正常性具有鲁棒性。

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