LAMBERT W RANDOM VARIABLES-A NEW FAMILY OF GENERALIZED SKEWED DISTRIBUTIONS WITH APPLICATIONS TO RISK ESTIMATION

• 成果类型: Article
• 署名作者: Goerg, Georg M.
• 署名单位: Carnegie Mellon University
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/11-AOAS457
• 发表日期: 2011
• 页码: 2197-2230
• 关键词: autoregressive conditional heteroscedasticity; returns; MODEL

摘要

Originating from a system theory and an input/output point of view, I introduce a new class of generalized distributions. A parametric nonlinear transformation converts a random variable X into a so-called Lambert W random variable Y, which allows a very flexible approach to model skewed data. Its shape depends on the shape of X and a skewness parameter gamma. In particular, for symmetric X and nonzero gamma the output Y is skewed. Its distribution and density function are particular variants of their input counterparts. Maximum likelihood and method of moments estimators are presented, and simulations show that in the symmetric case additional estimation of gamma does not affect the quality of other parameter estimates. Applications in finance and biomedicine 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. The R package LambertW developed by the author is publicly available (CRAN).