Skewness of Continuous Statistical Distributions

Abstract

Continuous statistical distributions can be broken down into symmetric and asymmetric distributions. Asymmetric distributions deviate from symmetric ones by having different shapes on the left and right side of a suitable point of symmetry. They can be classified into “left”- and “right-skew” by generally applicable skewness measures based on convex ordering of distributions. This classification, however, leads to conflicting results for the (mirrored) Weibull distribution, which subsequently leads to a skewness measure conflict to classify distributions. Based on those conflicts it is concluded that the skewness concept is not suitable for continuous statistical distributions.

Keywords: Skewness, Symmetry, Asymmetry, Statistical Distribution, Convex Ordering

JEL Classification: C10, C16