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A Simple Class of Measures of Skewness

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  • ALTINAY, Galip

Abstract

In this paper, a simple class of measures for detecting skewness in samples is introduced. The new class of measures is based on a new definition of skewness that takes midrange into consideration. The proposed coefficients of skewness can be computed easily with only three of the summary statistics, i.e., the minimum value, the maximum value and the median (or the mode, or the mean). Another advantage of the new statistics is that they are bounded by -1 and +1, hence, the coefficients of skewness can be interpreted easily. The powers of the proposed statistics to detect skewness are investigated by a limited Monte Carlo simulation in order to have an idea. The preliminary results indicate that the performances of the new statistics look generally good in a limited simulation. However, a more comprehensive investigation is needed.

Suggested Citation

  • ALTINAY, Galip, 2016. "A Simple Class of Measures of Skewness," MPRA Paper 72353, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:72353
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    File URL: https://mpra.ub.uni-muenchen.de/72353/1/MPRA_paper_72353.pdf
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    References listed on IDEAS

    as
    1. V. J. García & M. Martel & F.J. Vázquez-Polo, 2015. "Complementary information for skewness measures," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(4), pages 442-459, November.
    2. Abadir, Karim M., 2005. "The Mean-Median-Mode Inequality: Counterexamples," Econometric Theory, Cambridge University Press, vol. 21(2), pages 477-482, April.
    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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Symmetry; Measure of Skewness; Monte Carlo Study; Midrange; Critical Values.;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

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