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

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.

11 pages

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• Modeling of Financial Data: Comparison of the Truncated Lévy Flight and the ARCH(1) and GARCH(1,1) processes
• Logarithmic Lambert $\mathrm{W}\times \mathcal{F}$ random variables for the family of chi-squared distributions and their applications