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Kurtosis as Peakedness, 1905-2014. R.I.P

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  • Peter H. Westfall

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, 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.

Suggested Citation

  • Peter H. Westfall, 2014. "Kurtosis as Peakedness, 1905-2014. R.I.P," The American Statistician, Taylor & Francis Journals, vol. 68(3), pages 191-195, April.
    • Handle: RePEc:taf:amstat:v:68:y:2014:i:3:p:191-195
    DOI: 10.1080/00031305.2014.917055
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    References listed on IDEAS

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    1. Kotz, Samuel & Seier, Edith, 2008. "Visualizing Peak and Tails to Introduce Kurtosis," The American Statistician, American Statistical Association, vol. 62(4), pages 348-354.
    2. An, Lihua & Ahmed, S. Ejaz, 2008. "Improving the performance of kurtosis estimator," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2669-2681, January.
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