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On relative skewness for multivariate distributions

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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 \(Y\) is said to be more right skewed than a random variable \(X\) if there exists an increasing convex transformation which maps \(X\) onto \(Y\). Given two random vectors \(\mathbf X\) and \(\mathbf Y\) and an appropriate transformation which maps \(\mathbf X\) onto \(\mathbf Y\), we define a new concept of relative skewness assuming the convexity of this transformation. Properties and applications of this concept are given.

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Acknowledgments

The authors acknowledge the comments by the two anonymous referees and the Editor of Test which have improved significantly the presentation of this paper. Félix Belzunce, Julio Mulero and José M. Ruiz acknowledge support received from the Ministerio de Economía y Competitividad (Spain) under grant MTM2012-34023-FEDER.

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Authors and Affiliations

  1. Dpto. Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100, Espinardo, Murcia, Spain

    Félix Belzunce & José María Ruíz

  2. Dpto. Estadística e Investigación Operativa, Facultad de Ciencias, Universidad de Alicante, Apartado de correos 99, 03080, Alicante, Spain

    Julio Mulero

  3. Dpto. Estadística e Investigación Operativa, Facultad de Ciencias Económicas y Empresariales, Universidad de Cádiz, C/ Duque de Nájera, 8, 11002, Cádiz, Spain

    Alfonso Suárez-Llorens

Authors
  1. Félix Belzunce
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  2. Julio Mulero
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  3. José María Ruíz
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  4. Alfonso Suárez-Llorens
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Correspondence to Alfonso Suárez-Llorens.

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Belzunce, F., Mulero, J., Ruíz, J. et al. On relative skewness for multivariate distributions. TEST 24, 813–834 (2015). https://doi.org/10.1007/s11749-015-0436-4

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