Probabilistic Models to Analyze and Gaussianize Heavy-Tailed, Skewed Data

Lambert W x F distributions are a generalized framework to analyze skewed, heavy-tailed data. It is based on an input/output system, where the output random variable (RV) Y is a non-linearly transformed version of an input RV X ~ F with similar properties as X, but slightly skewed (heavy-tailed). The transformed RV Y has a Lambert W x F distribution. This package contains functions to model and analyze skewed, heavy-tailed data the Lambert Way: simulate random samples, estimate parameters, compute quantiles, and plot/ print results nicely. The most useful function is 'Gaussianize', which works similarly to 'scale', but actually makes the data Gaussian. A do-it-yourself toolkit allows users to define their own Lambert W x 'MyFavoriteDistribution' and use it in their analysis right away.

LambertW R package

This is the github repo for the LambertW R package hosted on CRAN. For any changes after the official version, see the commit history and here.

Installation & usage

To install LambertW run

install.packages("LambertW")
citation("LambertW")

See ?LambertW for examples on how to use the LambertW package.

There is also an R vignette on CRAN with a brief tutorial on the main functionalities.

Python implementation

See https://github.com/gmgeorg/pylambertw for the Python equivalent of the LambertW package.

Tutorials & posts

See cross-validated / stackoverflow for a variety of LambertW posts on how to normalize/Gaussianize data and model skewed/heavy-tailed distributions.

References

Georg M. Goerg (2011): Lambert W random variables - a new family of generalized skewed distributions with applications to risk estimation. Annals of Applied Statistics 3(5). 2197-2230.

Georg M. Goerg (2014): The Lambert Way to Gaussianize heavy-tailed data with the inverse of Tukey's h transformation as a special case. The Scientific World Journal.