Modeling Income Distributions Using Two-Sided Densities

Johan René van Dorp () and Ekundayo Shittu ()
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Johan René van Dorp: School of Engineering and Applied Science, The George Washington University
Ekundayo Shittu: School of Engineering and Applied Science, The George Washington University

Chapter Chapter 1 in Advances in Quantitative Methods for Economics and Business, 2025, pp 3-31 from Springer

Abstract: 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-t 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.

Keywords: Distribution theory; Conditional value at risk; Income distribution data (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/978-3-031-84782-0_1

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