A Method for Simulating Nonnormal Distributions with Specified L-Skew, L-Kurtosis, and L-Correlation. (25th September 2012) - Headrick, Todd C.; Pant, Mohan D.
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.