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Abstract <p>We show that the univariate Khattree–Bahuguna measure of skewness cannot exceed <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12004_2025_5078_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\frac{1}{2},\)</EquationSource> <!--MMStat2570007Lun-m1--> </InlineEquation> thereby reducing the range of feasible values stated by original authors by a factor of two. This substantially changes the interpretation of the magnitude of this measure especially for the highly skewed data. We also show that this bound cannot be improved further. A similar change in the upper bound occurs also for the two multivariate measures of skewness defined by Khattree and Bahuguna.</p>

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A Comment on a Skewness Coefficient

  • 期刊论文

  • 发表日期：

    2025年9月25日

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  • Zhixin Lun,
  • Ravindra Khattree

摘要

Abstract

We show that the univariate Khattree–Bahuguna measure of skewness cannot exceed \(\frac{1}{2},\) thereby reducing the range of feasible values stated by original authors by a factor of two. This substantially changes the interpretation of the magnitude of this measure especially for the highly skewed data. We also show that this bound cannot be improved further. A similar change in the upper bound occurs also for the two multivariate measures of skewness defined by Khattree and Bahuguna.