The Gompertz-Pareto Income Distribution

TL;DR

This paper introduces the Gompertz-Pareto distribution as a simple, three-parameter model for personal income distribution, effectively capturing the entire income spectrum from the lower to the upper classes.

Contribution

It presents a novel combined distribution model for income data, with equations for key economic indicators, validated through empirical analysis of Brazilian income data from 1981 to 2007.

Findings

GPD accurately fits income data across different years.

Only three parameters are needed for complete characterization.

The model provides coherent analytical expressions for income inequality measures.

Abstract

This work analyzes the Gompertz-Pareto distribution (GPD) of personal income, formed by the combination of the Gompertz curve, representing the overwhelming majority of the economically less favorable part of the population of a country, and the Pareto power law, which describes its tiny richest part. Equations for the Lorenz curve, Gini coefficient and the percentage share of the Gompertzian part relative to the total income are all written in this distribution. We show that only three parameters, determined by linear data fitting, are required for its complete characterization. Consistency checks are carried out using income data of Brazil from 1981 to 2007 and they lead to the conclusion that the GPD is consistent and provides a coherent and simple analytical tool to describe personal income distribution data.