Multivariate coefficients of variation: a comparative analysis

The coefficient of variation, which quantifies the variability of a distribution relative to its mean, does not admit a unique extension to the multidimensional setting. The same holds for the multidimensional Gini index, which measures inequality in terms of mean differences among observations. In this paper, we establish a connection between these two indices and propose a new Multivariate Coefficient of Variation (MCV) derived from a multidimensional Gini index. We show that the proposed measure retains the fundamental properties of the univariate coefficient of variation, while also clarifying its relationship with the Voinov–Nikulin’s coefficient. We compare our proposal with existing MCVs discussed in the literature and demonstrate that our proposed MCV is a correction of the Voinov–Nikulin’s MCV, which addresses the vanishing effect that arises as the dimensionality of the indicators under study increases.