Measuring skewness: We do not assume much

Abstract

Since skewness plays a vital role in different engineering phenomena, its accurate measurement gains significance. Several measures have been taken to quantify the extent of skewness in distributions over the years, but each measure is subject to some serious limitations. In this regard, the present study aims to propose a new skewness measuring functional based on distribution function evaluated at mean with minimal assumptions and limitations. Four well-recognized properties for an appropriate measure of skewness were verified and demonstrated for the new measure. A comparison was made between the new measure and the conventional moment-based measure using both functionals over the range of distributions available in the literature. Furthermore, the robustness of the proposed measure against unusual data points was explored using influence function. The mathematical findings were verified through meticulous simulation studies; further, they were verified by real data sets derived from diverse fields of inquiries. As observed, compared to the classical moment-based measure, the proposed one passed all the checks with distinction. Given the computational simplicity, applicability in a more general environment, and preservation of c-ordering of distribution, the proposed measure may be regarded as an attractive addition to the family of skewness measures.