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

Table 3

Summary statistics for observed (heavy-tailed) and back-transformed (Gaussianized) data . stands for <and for <.

	(Section 6.1)			= S&P 500 (Section 6.2)
Min	−161.59	−3.16	0	−7.11	−2.42
Max	952.95	3.81	33.18	4.99	2.23
Mean	2.30	0.03	14.98	0.05	0.05
Median	0.04	0.04	14.96	0.04	0.04
Standard Deviation	46.980	1.06	1.20	0.95	0.71
Skewness	17.43	0.12	3.90	−0.30	−0.04
Kurtosis	343.34	3.21	161.75	7.70	2.93
Shapiro-Wilk		0.71			0.24
Anderson-Darling		0.51			0.18