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On relative skewness for multivariate distributions

Author

Listed:
  • Félix Belzunce
  • Julio Mulero
  • José María Ruíz
  • Alfonso Suárez-Llorens

Abstract

In this paper, we provide a new concept of relative skewness among multivariate distributions, extending to the multivariate case a similar concept in the univariate case. In this case, a random variable $$Y$$ Y is said to be more right skewed than a random variable $$X$$ X if there exists an increasing convex transformation which maps $$X$$ X onto $$Y$$ Y . Given two random vectors $$\mathbf X$$ X and $$\mathbf Y$$ Y and an appropriate transformation which maps $$\mathbf X$$ X onto $$\mathbf Y$$ Y , we define a new concept of relative skewness assuming the convexity of this transformation. Properties and applications of this concept are given. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • Félix Belzunce & Julio Mulero & José María Ruíz & Alfonso Suárez-Llorens, 2015. "On relative skewness for multivariate distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(4), pages 813-834, December.
    • Handle: RePEc:spr:testjl:v:24:y:2015:i:4:p:813-834
    DOI: 10.1007/s11749-015-0436-4
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    References listed on IDEAS

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    Cited by:

    1. Jorge M. Arevalillo & Hilario Navarro, 2019. "A stochastic ordering based on the canonical transformation of skew-normal vectors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 475-498, June.
    2. A. Arriaza & A. Crescenzo & M. A. Sordo & A. Suárez-Llorens, 2019. "Shape measures based on the convex transform order," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 99-124, January.

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