This paper introduces a method for simulating univariate and multivariate Dagum distributions through the method of L-moments and L-correlation. A method is developed for characterizing non-normal Dagum distributions with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of contexts such as statistical modeling (e.g., income distribution, personal wealth distributions, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that -moment-based Dagum distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed method also demonstrates that the estimates of L-skew, L-kurtosis, and L-correlation are substantially superior to their conventional product-moment based counterparts of skew, kurtosis, and Pearson correlation in terms of relative bias and relative efficiency–most notably in the context of heavy-tailed distributions.
Pant, Mohan D. and Headrick, Todd C. "An L-Moment Based Characterization of the Family of Dagum Distributions." (Aug 2013).