An Influence Function Approach to Describing the Skewness of a Distribution

Abstract

Abstract Skewness, like kurtosis, is a qualitative property of a distribution. A comparison of several measures of skewness of univariate distributions is carried out. Hampel's influence function is used to clarify the differences and similarities among these measures. A general concept of skewness as a location- and scale-free deformation of the probability mass of a symmetric distribution emerges. Positive skewness can be thought of as resulting from movement of mass at the right of the median from the center to the right tail of the distribution together with movement of mass at the left of the median from the left tail to the center of the distribution.