A Method for Simulating Nonnormal Distributions with Specified L-Skew, L-Kurtosis, and L-Correlation

Authors

Todd C. Headrick, Southern Illinois University CarbondaleFollow
Mohan Dev Pant, Southern Illinois University CarbondaleFollow

Comments

Published in ISRN Applied Mathematics, Vol 2012, at

doi:10.5402/2012/980827

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 productmoment estimates of skew, kurtosis, and Pearson correlation in terms of both relative bias and efficiency when moderate-to-heavy-tailed distributions are of concern.

Recommended Citation

Headrick, Todd C. and Pant, Mohan D. "A Method for Simulating Nonnormal Distributions with Specified L-Skew, L-Kurtosis, and L-Correlation." (Jan 2012).