An L-Moment Based Characterization of the Family of Dagum Distributions

Mohan D. Pant and Todd C. Headrick

Journal of Statistical and Econometric Methods, 2013, vol. 2, issue 3, 3

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.

Date: 2013
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