A method for simulating non-normal distributions with specified L-skew, L-kurtosis, and L-correlation
Abstract
This paper introduces two families of distributions referred to as the symmetric κ and asymmetric
κL-κR 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.