An L-Moment Based Characterization of the Family of Dagum Distributions
Abstract
This paper introduces a method for simulating univariate and multivariate Dagum
distributions through the method of 𝐿-moments and 𝐿-correlations. 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
𝐿-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.