Modeling Income Distributions using Two-Sided densities

Conferenciante: Johan Rene van Dorp (School of Engineering and Applied Science. The George Washington University)

Abstract: A framework of two-sided (TS) densities is presented for asymmetric continuous distributions consisting of two branches each with its own generating density. The framework supports the construction of distributions with positive support and a specified mode. A general expression for the Lorentz curve, depicting income inequality, is derived in terms of these generating densities. The TS beta family of distributions is constructed herein as an instance within that framework. Its generating densities are a half-symmetric beta distribution for its left branch and half Student-t distribution for its right branch. A novel procedure solving for its parameters given a lower quantile, an upper quantile, a modal value and a value for the conditional-value-at-risk (CVaR) with a specified confidence is derived. The procedure shall be demonstrated using publicly available US income distribution data from 2022 by ethnicity by fitting TS beta-t parameters to those data sets. The fitted distributions shall be compared to a fitted Burr XII distributions using the maximum-likelihood estimation (MLE) method. In that process a novel income-inequality metric termed dominance-index is introduced. That dominance-index compares income inequality between two income distributions, whereas the classical Gini-index evaluates income-inequality within a single income distribution.