Characterizing Tukey h and hh-Distributions through L-Moments and the L-Correlation

This paper introduces 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 nonnormal distributions with controlled degrees of L-skew, L-kurtosis, and L-correlations. Th...

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Bibliographic Details
Published in:ISRN applied mathematics 2012-12, Vol.2012 (2012), p.1-20
Main Authors: Headrick, Todd C., Pant, Mohan D.
Format: Article
Language:English
Online Access:Get full text
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Summary:This paper introduces 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 nonnormal 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 correlation in terms of both relative bias and efficiency when heavy-tailed distributions are of concern.
ISSN:2090-5564
2090-5572
DOI:10.5402/2012/980153