Characterizing Tukey \(h\) and \(hh\)-distributions through \(L\)-moments and the \(L\)-correlation
type: Item
instance of: scholarly article
title: Characterizing Tukey \(h\) and \(hh\)-distributions through \(L\)-moments and the \(L\)-correlation
zbMATH Open document ID: 1264.62007
DOI: 10.5402/2012/980153
author: Todd C. Headrick
author: Mohan D. Pant
published in: ISRN Applied Mathematics
publication date: 2013-06-11T00:00:00Z
review text: Summary: We introduce the Tukey family of symmetric \(h\) and asymmetric \(hh\)-distributions in the contexts of univariate \(L\)-moments and the \(L\)-correlation. Included is the development of a procedure for specifying non-normal distributions with controlled degrees of \(L\)-skew, \(L\)-kurtosis, and \(L\)-correlations. The procedure can be applied in a variety of settings such as modeling events (e.g., risk analysis, extreme events) and Monte Carlo or simulation studies. Further, it is demonstrated that estimates of \(L\)-skew, \(L\)-kurtosis, and \(L\)-correlation are substantially superior to conventional product-moment estimates of skew, kurtosis, and Pearson correlations in terms of both relative bias and efficiency when heavy-tailed distributions are of concern.
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 62H20
Mathematics Subject Classification ID: 65C60
Mathematics Subject Classification ID: 62G32
zbMATH DE Number: 6172995
zbMATH Keywords: Tukey family
zbMATH Keywords: non-normal distributions
Wikidata QID: Q58905624
describes a project that uses: Mathematica
describes a project that uses: Spotfire
describes a project that uses: LMOMENTS
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.5402/2012/980153
OpenAlex ID: W2074101642
cites work: Q3535086
cites work: Robust nonorthogonal analyses revisited: An update based on trimmed means
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cites work: On some expressions for variance, covariance, skewness and L-moments
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description: scientific article; zbMATH DE number 6172995