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On measuring asymmetry and the reliability of the skewness measure

Author

Listed:
  • Xiaojun, Li
  • Morris, Joel M.

Abstract

The reliability of the skewness measure, [xi] = [mu]3/[sigma]3, is examined. It is shown that the measure [xi] may not correctly indicate the degree of asymmetry of a probability density, f(x), in some cases. An asymmetry measure [eta] = [integral operator]+[infinity]-[infinity]|f([mu]+x) - f([mu] - x)|dx is proposed that quantifies the degree of asymmetry more accurately than [xi]. The application and effectiveness of [eta] are demonstrated with examples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:12:y:1991:i:3:p:267-271
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    Citations

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    Cited by:

    1. 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.
    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. Chen, Yi-Ting & Chou, Ray Y. & Kuan, Chung-Ming, 2000. "Testing time reversibility without moment restrictions," Journal of Econometrics, Elsevier, vol. 95(1), pages 199-218, March.
    4. P. Patil & P. Patil & D. Bagkavos, 2012. "A measure of asymmetry," Statistical Papers, Springer, vol. 53(4), pages 971-985, November.
    5. Christopher Partlett & Prakash Patil, 2017. "Measuring asymmetry and testing symmetry," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 429-460, April.

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