Simulating non‐normal distributions with specifiedL‐moments andL‐correlations

Abstract

This paper derives a procedure for simulating continuous non‐normal distributions with specifiedL‐moments andL‐correlations in the context of power method polynomials of order three. It is demonstrated that the proposed procedure has computational advantages over the traditional product‐moment procedure in terms of solving for intermediate correlations. Simulation results also demonstrate that the proposedL‐moment‐based procedure is an attractive alternative to the traditional procedure when distributions with more severe departures from normality are considered. Specifically, estimates ofL‐skew andL‐kurtosis are superior to the conventional estimates of skew and kurtosis in terms of both relative bias and relative standard error. Further, theL‐correlation also demonstrated to be less biased and more stable than the Pearson correlation. It is also shown how the proposedL‐moment‐based procedure can be extended to the larger class of power method distributions associated with polynomials of order five.