A robust measure of skewness using cumulative statistic calculation

TL;DR

This paper introduces a new skewness measure based on cumulative statistics that is more robust to outliers than traditional methods, improving the accuracy of distribution asymmetry analysis.

Contribution

A novel skewness metric using cumulative statistics within the Lorenz curve framework that is less sensitive to outliers than the standard third moment coefficient.

Findings

The new measure behaves similarly to traditional skewness for normal distributions.

It remains robust in the presence of outliers, unlike the standard skewness measure.

The proposed method satisfies key requirements for skewness measurement.

Abstract

An important aspect of the shape of a distribution is the level of asymmetry. Strong asymmetries play a role in many ecosystems and are found in the size and reproductive success of individuals. But the standard third moment coefficient of skewness has the drawback that it is very sensitive to outliers, which can lead to incorrect interpretations. A new metric is introduced that is based on calculating the cumulative statistics of the Lorenz curve framework, but it evaluates the asymmetry of the underlying distribution. The standard requirements for skewness measures which the proposed measure satisfies are briefly described and it is compared to the moment-based measure using the lognormal distribution with and without outliers. The results demonstrate that the proposed measure behaves similarly for 'normal' distributions, but is robust(not overly sensitive) if there are outliers.