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The Gompertz-Pareto Income Distribution

Author

Listed:
  • F. Chami Figueira

    (Federal University of Rio de Janeiro-UFRJ)

  • N. J. Moura Jr

    (Brazilian Institute for Geography ans Statistics-IBGE)

  • Marcelo B. Ribeiro

    (Federal University of Rio de Janeiro-UFRJ)

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.

Suggested Citation

  • F. Chami Figueira & N. J. Moura Jr & Marcelo B. Ribeiro, 2010. "The Gompertz-Pareto Income Distribution," Papers 1010.1994, arXiv.org.
    • Handle: RePEc:arx:papers:1010.1994
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    Cited by:

    1. Soares, Abner D. & Moura Jr., Newton J. & Ribeiro, Marcelo B., 2016. "Tsallis statistics in the income distribution of Brazil," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 158-171.
    2. Aydiner, Ekrem & Cherstvy, Andrey G. & Metzler, Ralf, 2018. "Wealth distribution, Pareto law, and stretched exponential decay of money: Computer simulations analysis of agent-based models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 278-288.
    3. Domma, Filippo & Condino, Francesca & Giordano, Sabrina, 2018. "A new formulation of the Dagum distribution in terms of income inequality and poverty measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 104-126.
    4. Safari, Muhammad Aslam Mohd & Masseran, Nurulkamal & Ibrahim, Kamarulzaman, 2018. "Optimal threshold for Pareto tail modelling in the presence of outliers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 169-180.
    5. Marcelo B. Ribeiro, 2025. "Modeling Income Distribution with the Gause-Witt Population Ecology System," Papers 2506.20881, arXiv.org.
    6. Kerim Eser Afc{s}ar & Mehmet Ozyi~git & Yusuf Yuksel & Umit Ak{i}nc{i}, 2021. "Testing the Goodwin Growth Cycles with Econophysics Approach in 2002-2019 Period in Turkey," Papers 2106.02546, arXiv.org.
    7. Siudem, Grzegorz & Nowak, Przemysław & Gagolewski, Marek, 2022. "Power laws, the Price model, and the Pareto type-2 distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    8. Néda, Zoltán & Gere, István & Biró, Tamás S. & Tóth, Géza & Derzsy, Noemi, 2020. "Scaling in income inequalities and its dynamical origin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    9. Bourguignon, Marcelo & Saulo, Helton & Fernandez, Rodrigo Nobre, 2016. "A new Pareto-type distribution with applications in reliability and income data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 166-175.
    10. Sarabia, José María & Prieto, Faustino & Trueba, Carmen & Jordá, Vanesa, 2013. "About the modified Gaussian family of income distributions with applications to individual incomes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1398-1408.
    11. Elvis Oltean, 2016. "Modelling income, wealth, and expenditure data by use of Econophysics," Papers 1603.08383, arXiv.org.
    12. Zoltan Neda & Istvan Gere & Tamas S. Biro & Geza Toth & Noemi Derzsy, 2019. "Scaling in Income Inequalities and its Dynamical Origin," Papers 1911.02449, arXiv.org, revised Mar 2020.
    13. Safari, Muhammad Aslam Mohd & Masseran, Nurulkamal & Ibrahim, Kamarulzaman & Hussain, Saiful Izzuan, 2021. "Measuring income inequality: A robust semi-parametric approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 562(C).
    14. Moura, N.J. & Ribeiro, Marcelo B., 2013. "Testing the Goodwin growth-cycle macroeconomic dynamics in Brazil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2088-2103.
    15. Maria Letizia Bertotti & Giovanni Modanese, 2011. "From microscopic taxation and redistribution models to macroscopic income distributions," Papers 1109.0606, arXiv.org.
    16. Bertotti, Maria Letizia & Modanese, Giovanni, 2011. "From microscopic taxation and redistribution models to macroscopic income distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3782-3793.

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