A Robust Measure of Skewness

Abstract

The asymmetry of a univariate continuous distribution is commonly measured by the classical skewness coefficient. Because this estimator is based on the first three moments of the dataset, it is strongly affected by the presence of one or more outliers. This article investigates the medcouple, a robust alternative to the classical skewness coefficient. We show that it has a 25% breakdown value and a bounded influence function. We present a fast algorithm for its computation, and investigate its finite-sample behavior through simulated and real datasets.