峰度作为峰值，1905 - 2014 年。
Kurtosis as Peakedness, 1905 - 2014. .
作者信息
Westfall Peter H
机构信息
Peter H. Westfall is Horn Professor in the Area of Information Systems and Quantitative Sciences, Texas Tech University, Lubbock, TX 79409 (
出版信息
Am Stat. 2014;68(3):191-195. doi: 10.1080/00031305.2014.917055.
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; i.e., 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.
尽管统计学家们试图澄清事实，但认为峰度以某种方式衡量分布的“尖峰程度”（平坦度、尖锐度或模态）这一错误观念却异常顽固。本文将彻底消除这一观念。峰度实际上几乎无法告诉你关于峰值形状的任何信息——它唯一明确的解释是关于尾部极值；即，要么是现有异常值（对于样本峰度而言），要么是产生异常值的倾向（对于概率分布的峰度而言）。为了阐明这一点，回顾了相关文献，给出了反例分布，并表明由中心μ±σ范围所决定的峰度比例通常相当小。
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