On relative skewness for multivariate distributions

Félix Belzunce (), Julio Mulero (), José María Ruíz () and Alfonso Suárez-Llorens ()

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2015, vol. 24, issue 4, 813-834

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

Keywords: Relative skewness; Standard construction; Multivariate quantile transform; Multivariate convex order; Copula; 60E05; 60E15; 60E10; 62H05 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11749-015-0436-4

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