{"title":"Kurtosis as Peakedness, 1905 - 2014. <i>R.I.P.</i>","authors":"Peter H Westfall","doi":"10.1080/00031305.2014.917055","DOIUrl":null,"url":null,"abstract":"<p><p>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.</p>","PeriodicalId":50801,"journal":{"name":"American Statistician","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00031305.2014.917055","citationCount":"370","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Statistician","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/00031305.2014.917055","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 370
Abstract
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.
期刊介绍：
Are you looking for general-interest articles about current national and international statistical problems and programs; interesting and fun articles of a general nature about statistics and its applications; or the teaching of statistics? Then you are looking for The American Statistician (TAS), published quarterly by the American Statistical Association. TAS contains timely articles organized into the following sections: Statistical Practice, General, Teacher''s Corner, History Corner, Interdisciplinary, Statistical Computing and Graphics, Reviews of Books and Teaching Materials, and Letters to the Editor.
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