Characterizing Tukey h and hh-Distributions through L-Moments and the L-Correlation. (12th February 2012)

• Record Type: Journal Article
• Authors: Headrick, Todd C.; Pant, Mohan D.
• Other Names: Cho M. Academic Editor.; Karamanos K. Academic Editor.
• Is Part Of: ISRN applied mathematics. Volume 2012(2012)
• Publication Date: 2012-02-12
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; Electronic journals; 510
• DOI: 10.5402/2012/980153
• Languages: English
• ISSNs: 2090-5564

Abstract

Abstract : 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.