The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey’s h Transformation as a Special Case

Figure 1

Schematic view of the heavy tail Lambert W ×   framework. Latent input : from (6) transforms (solid arrows) to Lambert W ×   and generates heavy tails (right) Observed heavy-tailed and : use to back-transform to latent “Normal” , use model of your choice (regression, time series models, hypothesis testing, etc.) for inference on , and convert results back to the original “heavy-tailed world” of (right).