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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| Format: | Article |
| Language: | English |
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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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| author | Georg M. Goerg |
| author_facet | Georg M. Goerg |
| author_sort | Georg M. Goerg |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c50d7b5a7de54ba09e3a3fc8cfe3b808 |
| institution | DOAJ |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-c50d7b5a7de54ba09e3a3fc8cfe3b8082025-08-20T03:23:04ZengWileyThe Scientific World Journal2356-61401537-744X2015-01-01201510.1155/2015/909231909231The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey’s h Transformation as a Special CaseGeorg M. Goerg0Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213, USAI 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.http://dx.doi.org/10.1155/2015/909231 |
| spellingShingle | Georg M. Goerg The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey’s h Transformation as a Special Case The Scientific World Journal |
| title | The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey’s h Transformation as a Special Case |
| title_full | The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey’s h Transformation as a Special Case |
| title_fullStr | The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey’s h Transformation as a Special Case |
| title_full_unstemmed | The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey’s h Transformation as a Special Case |
| title_short | The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey’s h Transformation as a Special Case |
| title_sort | lambert way to gaussianize heavy tailed data with the inverse of tukey s h transformation as a special case |
| url | http://dx.doi.org/10.1155/2015/909231 |
| work_keys_str_mv | AT georgmgoerg thelambertwaytogaussianizeheavytaileddatawiththeinverseoftukeyshtransformationasaspecialcase AT georgmgoerg lambertwaytogaussianizeheavytaileddatawiththeinverseoftukeyshtransformationasaspecialcase |