A Method for Simulating Nonnormal Distributions with Specified L-Skew, L-Kurtosis, and L-Correlation. (25th September 2012)

• Record Type: Journal Article
• Authors: Headrick, Todd C.; Pant, Mohan D.
• Other Names: Fernandez J. R. Academic Editor.; Skubalska-Rafajlowicz E. Academic Editor.; Yeih W. Academic Editor.
• Is Part Of: ISRN applied mathematics. Volume 2012(2012)
• Publication Date: 2012-09-25
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; Electronic journals; 510
• DOI: 10.5402/2012/980827
• Languages: English
• ISSNs: 2090-5564

Abstract

Abstract : This paper introduces two families of distributions referred to as the symmetric κ and asymmetric κ ℒ -κ 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.