ABSTRACT
The concept of skewness can be thought of informally as a lack of symmetry. However while symmetry is unambiguous, a rigorous definition of skewness is neither obvious nor unique. A skewness ordering compares two distributions to define which is more ‘skew to the right’, or equivalently less ‘skew to the left’. This chapter considers three skewness orderings based on: moment skewness, centile skewness, and van Zwet skewness. The skewness orderings are used to provide alternative definitions of positive skewness, and are applied to compare the skewness of distributions. In order to distinguish a loosely-defined skewness parameter from the explicitly defined skewness, a ‘true’ skewness parameter is defined as a parameter which changes monotonically with one of the moment, centile, or van Zwet skewness orderings.
