The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey’s h Transformation as a Special Case
I present a parametric, bijective transformation to generate heavy tail versions of arbitrary random variables. The tail behavior of this heavy tail Lambert W × FX random variable depends on a tail parameter δ≥0: for δ=0, Y≡X, for δ>0 Y has heavier tails than X. For X being Gaussian it reduces t...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2015/909231 |
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| Summary: | I present a parametric, bijective transformation to generate heavy tail versions of arbitrary random variables. The tail behavior of this heavy tail Lambert W × FX random variable depends on a tail parameter δ≥0: for δ=0, Y≡X, for δ>0 Y has heavier tails than X. For X being Gaussian it reduces to Tukey’s h distribution. The Lambert W function provides an explicit inverse transformation, which can thus remove heavy tails from observed data. It also provides closed-form expressions for the cumulative distribution (cdf) and probability density function (pdf). As a special case, these yield analytic expression for Tukey’s h pdf and cdf. Parameters can be estimated by maximum likelihood and applications to S&P 500 log-returns demonstrate the usefulness of the presented methodology. The R package LambertW implements most of the introduced methodology and is publicly
available on CRAN. |
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| ISSN: | 2356-6140 1537-744X |