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 × F X 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 redu...
| Publicado en: | Scientific World Journal Vol. 2015; pp. 1 - 17 |
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| Autor principal: | |
| Formato: | Journal Article |
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Wiley-Blackwell
8/25/2015
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=ccm&AN=109322035&site=ehost-live header: @attributes: shortDbName: ccm uiTerm: 109322035 longDbName: CINAHL Complete uiTag: AN controlInfo: bkinfo: dissinfo: jinfo: jid: 1537744X 1BX5 jtl: Scientific World Journal issn: 1537744X maglogo: N pubinfo: dt: 8/25/2015 vid: 2015 pid: 480 pub: Wiley-Blackwell place: Malden, Massachusetts artinfo: ui: 109322035 109322035 NLM26380372 10.1155/2015/909231 NLM26380372 PMC4562338 109322035 ppf: 1 ppct: 16 formats: tig: atl: The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey's h Transformation as a Special Case. aug: au: Goerg, Georg M. affil: Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213, USA sug: ab: I present a parametric, bijective transformation to generate heavy tail versions of arbitrary random variables. The tail behavior of this heavy tail Lambert W × F X 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 Lambert W implements most of the introduced methodology and is publicly available on CRAN. pubtype: Academic Journal doctype: Journal Article ougenre: Article language: English refInfo: holdings: @attributes: islocal: N |
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