Skewness and Asymmetry: Measures and Orderings

Recent interest in skewness has tended to separate two aspects of the concept. Two distributions may be compared with respect to skewness, or a distribution may be self-compared, that is, the distributions of the random variables of X and - X may be compared. This paper uses the unification of these two aspects to attemp to complete a skewness structure of orderings that identifies the roles of various skewness and scale measures and enables classification of the skewness properties of any distribution. The structure is also used to propose measures of asymmetry. Some skewness properties of the Weibull and Johnson systems are examined.