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

Abstract EN

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 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.