Empirically Successful Transformations from Non-Gaussian to Close-to-Gaussian Distributions: Theoretical Justification

Thongchai Dumrongpokaphan, Pedro Barragan, Vladik Kreinovich

Abstract

A large number of efficient statistical methods have been designed fora frequent case when the distributions are normal (Gaussian). In practice, manyprobability distributions are not normal. In this case, Gaussian-based techniquescannot be directly applied. In many cases, however, we can apply these tech-niques indirectly – by first applying an appropriate transformation to the originalvariables, after which their distribution becomes close to normal. Empirical anal-ysis of different transformations has shown that the most successful are the powertransformations X → X^h and their modifications. In this paper, we provide asymmetry-based explanation for this empirical success.