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首页> 外文期刊>Journal of applied statistics >Normality testing: two new tests using L-moments
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Normality testing: two new tests using L-moments

机译：正态性测试：使用L矩的两个新测试

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Establishing that there is no compelling evidence that some population is not normally distributed is fundamental to many statistical inferences, and numerous approaches to testing the null hypothesis of normality have been proposed. Fundamentally, the power of a test depends on which specific deviation from normality may be presented in a distribution. Knowledge of the potential nature of deviation from normality should reasonably guide the researcher's selection of testing for non-normality. In most settings, little is known aside from the data available for analysis, so that selection of a test based on general applicability is typically necessary. This research proposes and reports the power of two new tests of normality. One of the new tests is a version of the R-test that uses the L-moments, respectively, L-skewness and L-kurtosis and the other test is based on normalizing transformations of L-skewness and L-kurtosis. Both tests have high power relative to alternatives. The test based on normalized transformations, in particular, shows consistently high power and outperforms other normality tests against a variety of distributions.
机译：确定没有令人信服的证据表明某些人群不是正态分布是许多统计推论的基础，并且已经提出了许多方法来检验正态性的零假设。从根本上说，测试的功效取决于分布中可能呈现出哪些与正态性的特定偏差。了解偏离正态性的潜在性质应该合理地指导研究人员选择非正态性检验。在大多数情况下，除了可用于分析的数据外，人们所知甚少，因此通常需要根据通用性选择测试。这项研究提出并报告了两种新的正态性检验的功效。一种新的测试是使用L矩分别为L偏度和L峰度的R检验的版本，另一项测试基于归一化L偏度和L峰度的变换。相对于替代方案，这两种测试均具有较高的功效。特别是，基于归一化转换的测试始终显示出高功率，并且在各种分布情况下均优于其他正态性测试。

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