On relative skewness for multivariate distributions

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 X and Y and an appropriate transformation which maps X onto Y, we define a new concept of relative skewness assuming the convexity of this transformation. Properties and applications of this concept are given.