Measuring skewness: we don’t assume much

Document Type : Article

Authors

1 Department of Statistics, Faculty of Natural Sciences, Quaid-i-Azam University, Islamabad

2 Quaid-i-Azam University

3 Department of Mathematical and Physical Sciences, Newcastle University 2308, Australia

4 Department of Mathematics, Statistics and Physics, Qatar University, Doha

Abstract

Skewness plays a vital role in different engineering phenomena so it is desired to measure this characteristic accurately. Several measures to quantify the extent of skewness in distributions have been developed over the course of history but each measure has some serious limitations. Therefore, in this article, we 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 are verified and demonstrated for the new measure. Comparisons with the conventional moment-based measure are carried out by employing both functionals over range of distributions available in literature. Furthermore, the robustness of the proposed measure against unusual data points is explored through the application of influence function. The Mathematical findings are verified through meticulous simulation studies and further verified by real data sets coming from diverse fields of inquiries. It is witnessed that the suggested measure passes all the checks with distinction while comparing to the classical moment-based measure. Based on computational simplicity, applicability in more general environment and preservation of c-ordering of distribution, it may be considered as an attractive addition to the family of skewness measures.

Keywords