A new distance based measure of asymmetry

Abstract

In a univariate setting there is a near unanimous agreement on the notion of skewness. Nevertheless, many more skewness measures, or also called asymmetry measures (or indices) exist, each with their benefits. Extending the concept of skewness or asymmetry to a multivariate setting is a much harder problem. Attempts have been made, but the unanimity of the univariate setting is no longer present. Most asymmetry indices are scalar or vector based measures, but this can lead to a loss of information concerning asymmetry. To this end, we propose a novel functional asymmetry index which is based on the natural idea of reflective symmetry around the mode. The proposed index is also extended to the multivariate setting and a summarizing scalar (or vector based index in multivariate setting) is derived from it.(c) 2022 Elsevier Inc. All rights reserved.