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Measuring asymmetry and testing symmetry

Author

Listed:
  • Christopher Partlett

    () (University of Birmingham)

  • Prakash Patil

    (Mississippi State University)

Abstract

Abstract In this paper, we show that some of the most commonly used tests of symmetry do not have power which is reflective of the size of asymmetry. This is because the primary rationale for the test statistics that are proposed in the literature to test for symmetry is to detect the departure from symmetry, rather than the quantification of the asymmetry. As a result, tests of symmetry based upon these statistics do not necessarily generate power that is representative of the departure from the null hypothesis of symmetry. Recent research has produced new measures of asymmetry, which have been shown to do an admirable job of quantifying the amount of asymmetry. We propose several new tests based upon one such measure. We derive the asymptotic distribution of the test statistics and analyse the performance of these proposed tests through the use of a simulation study.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:aistmt:v:69:y:2017:i:2:d:10.1007_s10463-015-0547-4
    DOI: 10.1007/s10463-015-0547-4
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    References listed on IDEAS

    as
    1. Boshnakov, Georgi N., 2007. "Some measures for asymmetry of distributions," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1111-1116, June.
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    3. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2006. "A Constructive Representation of Univariate Skewed Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 823-829, June.
    4. Hall, Peter & Marron, J. S., 1987. "Estimation of integrated squared density derivatives," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 109-115, November.
    5. 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.
    6. Evarist Giné & David M. Mason, 2008. "Uniform in Bandwidth Estimation of Integral Functionals of the Density Function," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 739-761, December.
    7. P. Patil & P. Patil & D. Bagkavos, 2012. "A measure of asymmetry," Statistical Papers, Springer, vol. 53(4), pages 971-985, November.
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