Rebuttal of the 'Letter to the Editor' of Annals of Applied Statistics on Lambert W x F Distributions and the IGMM Algorithm

TL;DR

This paper clarifies misconceptions about Lambert W x F distributions and the IGMM algorithm, refutes some empirical claims, and introduces a new variant suitable for distributions with non-finite moments.

Contribution

It provides a clarification of Lambert W x F distributions, addresses misunderstandings, and proposes a new variant applicable to broader classes of distributions.

Findings

Most empirical results from Stehlik and Hermann (2015) cannot be reproduced.

Clarification of the definition and use of Lambert W x F distributions.

Introduction of a new variant for distributions with non-finite mean and variance.

Abstract

I discuss comments and claims made in Stehlik and Hermann (2015) about skewed Lambert W x F random variables and the IGMM algorithm. I clarify misunderstandings about the definition and use of Lambert W x F distributions and show that most of their empirical results cannot be reproduced. I also introduce a variant of location-scale Lambert W x F distributions that are well-defined for random variables X ~ F with non-finite mean and variance.