Lambert W normal distribution: a viable extension for skew-normal?

Abstract

Several distributions and families of distributions, such as skew-normal and related distributions, are proposed to model skewed data. Lambert W transformation offers a flexible approach to introduce skewness to any random variable. In this paper, we compare the Lambert W normal distribution with the widely known skew-normal distribution and point out the similarities and differences, focusing mainly on risk-related characteristics and data fitting. While mathematically a different construction, one can think of Lambert W normal approach as an extension of the skew-normal to a more skewed situation.