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

Figure 4

Pdf (left) and cdf (right) of a heavy tail (a) “noncentral, nonscaled,” (b) “scale,” and (c and d) “location-scale” Lambert W ×   random variable for various degrees of heavy tails (color, dashed lines).

(a) Lambert W ×   with

(b) Lambert W ×   with

(c) Lambert W ×   with

(d) Lambert W ×   with