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Complementary information for skewness measures

Author

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  • V. J. García
  • M. Martel
  • F.J. Vázquez-Polo

Abstract

type="main" xml:id="stan12067-abs-0001"> This paper introduces some new elements to measure the skewness of a probability distribution, suggesting that a given distribution can have both positive and negative skewness, depending on the centred sub-interval of the support set being observed. A skewness function for positive reals is defined, from which a bivariate index of positive–negative skewness is obtained. Certain interesting properties of this new index are studied, and they are also obtained for some common discrete distributions. We show the advantages of their use as a complement to the information derived by traditional measures of skewness.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:stanee:v:69:y:2015:i:4:p:442-459
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    References listed on IDEAS

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    1. W. R. van Zwet, 1979. "Mean, median, mode II," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 33(1), pages 1-5, March.
    2. Abadir, Karim M., 2005. "The Mean-Median-Mode Inequality: Counterexamples," Econometric Theory, Cambridge University Press, vol. 21(2), pages 477-482, April.
    3. Ramesh Gupta & Rameshwar Gupta, 2004. "Generalized skew normal model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 501-524, December.
    4. Martel-Escobar, M. & Hernández-Bastida, A. & Vázquez-Polo, F.J., 2012. "On the independence between risk profiles in the compound collective risk actuarial model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(8), pages 1419-1431.
    5. R. Ven & N. Weber, 1993. "Bounds for the median of the negative binomial distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 185-189, December.
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    Cited by:

    1. ALTINAY, Galip, 2016. "A Simple Class of Measures of Skewness," MPRA Paper 72353, University Library of Munich, Germany.

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