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A Comparison of Some New Measures of Skewness

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Developments in Robust Statistics

Summary

Asymmetry of a univariate continuous distribution is commonly described as skewness. The well-known classical skewness coefficient is based on the first three moments of the data set, and hence it is strongly affected by the presence of one or more outliers. In this paper we propose several new measures of skewness which are more robust against outlying values. Their properties are compared using both real and simulated data.

* Postdoctoral Fellow of the Fund for Scientific Research - Flanders (Belgium)

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References

  • A.L. Bowley. Elements of statistics. Charles Scribner’s Sons, New York, 1920.

    Google Scholar 

  • D.V. Hinkley. On power transformations to symmetry. Biometrika, 62:101–111, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  • D.C. Hoaglin, F. Mosteller, and J.W. Tukey. Exploring data tables, trends, and shapes. Wiley, New York, 1985.

    Google Scholar 

  • J.L. Hodges and E.L. Lehmann. Estimates of location based on rank tests. Ann. Math. Statist., 34:598–611, 1963.

    Article  MathSciNet  MATH  Google Scholar 

  • J.J.A. Moors, R.Th.A. Wagemakers, V.M.J. Coenen, R.M.J. Heuts, and M.J.B.T. Janssens. Characterizing systems of distributions by quantile measures. Statistica Neerlandica, 50: 417–430, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  • P.J. Rousseeuw and C. Croux. Alternatives to the median absolute deviation. J. Am. Statist. Assoc., 88:1273–1283, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  • P.J. Rousseeuw and M. Hubert. Regression-free and robust estimation of scale for bivariate data. Computational Statistics and Data Analysis, 21:67–85, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  • P.J. Rousseeuw and A.M. Leroy. Robust regression and outlier detection. Wiley, New York, 1987.

    Book  MATH  Google Scholar 

  • P.K. Sen. Estimates of the regression coefficient based on Kendall’s Tau. J. Am. Statist. Assoc., 63:1379–1389, 1968.

    Article  MATH  Google Scholar 

  • A.F. Siegel. Robust regression using repeated medians. Biometrika, 69:242–244, 1982.

    Article  MATH  Google Scholar 

  • H. Theil. A rank-invariant method of linear and polynomial regression analysis (Parts 1–3). Ned. Akad. Wetensch. Proc.,Ser. A, 53:386–392, 521–525, 1397–1412, 1950.

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Antwerp (UIA), Belgium

    G. Brys & A. Struyf

  2. Department of Mathematics, Catholic University of Leuven, Belgium

    M. Hubert

Authors
  1. G. Brys
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  2. M. Hubert
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  3. A. Struyf
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Editor information

Editors and Affiliations

  1. Institute of Statistics, Vienna University of Technology, Wiedner Hauptstraße 8-10, Vienna, 1040, Austria

    Rudolf Dutter  & Peter Filzmoser  & 

  2. Statistics Department, University of Dortmund, Dortmund, 44221, Germany

    Ursula Gather

  3. Department of Mathematics and Computer Science, University of Antwerp, Universiteitsplein 1, Antwerp, 2610, Belgium

    Peter J. Rousseeuw

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© 2003 Springer-Verlag Berlin Heidelberg

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Brys, G., Hubert, M., Struyf, A. (2003). A Comparison of Some New Measures of Skewness. In: Dutter, R., Filzmoser, P., Gather, U., Rousseeuw, P.J. (eds) Developments in Robust Statistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57338-5_8

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  • DOI: https://doi.org/10.1007/978-3-642-57338-5_8

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-642-63241-9

  • Online ISBN: 978-3-642-57338-5

  • eBook Packages: Springer Book Archive

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