The incorrect notion that kurtosis somehow measures “peakedness” (flatness, pointiness, or modality) of a distribution is remarkably persistent, despite attempts by statisticians to set the record straight. This article puts the notion to rest once and for all. Kurtosis tells you virtually nothing about the shape of the peak—its only unambiguous interpretation is in terms of tail extremity, that is, either existing outliers (for the sample kurtosis) or propensity to produce outliers (for the kurtosis of a probability distribution). To clarify this point, relevant literature is reviewed, counterexample distributions are given, and it is shown that the proportion of the kurtosis that is determined by the central μ ± σ range is usually quite small.

中文翻译：

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峰度作为峰度，1905–2014.RIP

尽管统计学家试图澄清记录，但峰度以某种方式衡量分布的“峰度”（平坦度、尖度或模态）的错误观念非常持久。这篇文章让这个概念一劳永逸。峰度几乎没有告诉您峰的形状——它唯一明确的解释是尾部末端，即现有异常值（对于样本峰度）或产生异常值的倾向（对于概率分布的峰态）。为了澄清这一点，查阅了相关文献，给出了反例分布，表明由中心μ±σ范围决定的峰度的比例通常很小。