A method for simulating nonnormal distributions with specified \(L\)-skew, \(L\)-kurtosis, and \(L\)-correlation
type: Item
instance of: scholarly article
title: A method for simulating nonnormal distributions with specified \(L\)-skew, \(L\)-kurtosis, and \(L\)-correlation
zbMATH Open document ID: 1264.60016
DOI: 10.5402/2012/980827
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 two families of distributions referred to as the symmetric \(\kappa\) and asymmetric \(\kappa_{\mathcal L}-\kappa_{\mathcal R}\) distributions. The families are based on transformations of standard logistic pseudo-random deviates. The primary focus of the theoretical development is in the contexts of \(L\)-moments and the \(L\)-correlation. Also included is the development of a method for specifying distributions with controlled degrees of \(L\)-skew, \(L\)-kurtosis, and \(L\)-correlation. The method can be applied in a variety of settings such as Monte Carlo studies, simulation, or modeling events. It is also demonstrated that estimates of \(L\)-skew, \(L\)-kurtosis, and \(L\)-correlation are superior to conventional product-moment estimates of skew, kurtosis, and Pearson correlation in terms of both relative bias and efficiency when moderate-to-heavy-tailed distributions are of concern.
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 62E15
zbMATH DE Number: 6172996
zbMATH Keywords: standard logistic pseudo-random deviates
zbMATH Keywords: \(L\)-moments
zbMATH Keywords: \(L\)-correlation
zbMATH Keywords: \(L\)-skew
zbMATH Keywords: \(L\)-kurtosis
Wikidata QID: Q58905628
describes a project that uses: Mathematica
describes a project that uses: LMOMENTS
describes a project that uses: Spotfire
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.5402/2012/980827
OpenAlex ID: W2134313208
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description: scientific article; zbMATH DE number 6172996