Lambert W Random Variables: A New Family of Generalized Skewed Distributions

• Activity Number: 131
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Georg Matthias Goerg*+
• Companies: Carnegie Mellon University
• Keywords: skewness ; transformation of variables ; Lambert W ; family of skewed distributions ; stylized facts

Abstract

I introduce a new class of generalized distributions, which allows a very flexible approach to model skewed data. Originating from a system-theory and an input/output point of view, a parametric non-linear transformation converts a random variable X into a so called "Lambert W" random variable Y. Its skewness depends on the skewness of X and a skew parameter delta. In particular, for symmetric X the output Y is skewed. Maximum likelihood and method of moments estimators are presented, and simulations show that in the symmetric case additional estimation of the skew parameter does not affect the quality of other parameter estimates. Applications in finance and health show the relevance of this class of distributions, which is particularly useful for slightly skewed data. A practical by-result of the Lambert W framework: data can be unskewed. R package: LambertW; arxiv: 0912.4554