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A comparison between two simple measures of skewness

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  • I. H. Tajuddin

Abstract

In 1995, Arnold and Groeneveld introduced the measure of skewness gammaM in terms of F(mode)-the cumulative probability of a random variable less than or equal to the mode of the distribution. They assumed that the mode of a distribution exists and is unique. Independently, in 1996, the present author arrived at the measure of skewness T, which is given in terms of F(mean). This measure possesses desirable properties and is equally simple. The measure gammaM satisfies - 1 gammaM 1 , with 1 (- 1) indicating extreme right (left) skewness. However, the measure T can take on any value on the real line; hence, an equivalent measure gammaT is considered and is compared with gammaM. We consider a variety of families of distributions and include in our study other measures of skewness of interest. Skewness values are easily obtained using MINITAB programs.

Suggested Citation

  • I. H. Tajuddin, 1999. "A comparison between two simple measures of skewness," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(6), pages 767-774.
    • Handle: RePEc:taf:japsta:v:26:y:1999:i:6:p:767-774
    DOI: 10.1080/02664769922205
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    References listed on IDEAS

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    1. R.A. Groeneveld, 1986. "Skewness For The Weibull Family," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 40(3), pages 135-140, September.
    2. Xiaojun, Li & Morris, Joel M., 1991. "On measuring asymmetry and the reliability of the skewness measure," Statistics & Probability Letters, Elsevier, vol. 12(3), pages 267-271, September.
    3. I. H. Tajuddin, 1996. "A simple measure of skewness," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 50(3), pages 362-366, November.
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    Cited by:

    1. Andreas Eberl & Bernhard Klar, 2022. "Expectile‐based measures of skewness," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 373-399, March.
    2. Giovanni Campisi & Luca La Rocca & Silvia Muzzioli, 2023. "Assessing skewness in financial markets," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(1), pages 48-70, February.
    3. Eberl, Andreas & Klar, Bernhard, 2020. "Asymptotic distributions and performance of empirical skewness measures," Computational Statistics & Data Analysis, Elsevier, vol. 146(C).

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