IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v88y2016icp158-171.html
   My bibliography  Save this article

Tsallis statistics in the income distribution of Brazil

Author

Listed:
  • Soares, Abner D.
  • Moura Jr., Newton J.
  • Ribeiro, Marcelo B.

Abstract

This paper discusses the empirical evidence of Tsallis statistical functions in the personal income distribution of Brazil. Yearly samples from 1978 to 2014 were linearized by the q-logarithm and straight lines were fitted to the entire range of the income data in all samples, producing a two-parameters-only single function representation of the whole distribution in every year. The results showed that the time evolution of the parameters is periodic and plotting one in terms of the other reveals a cycle mostly clockwise. It was also found that the empirical data oscillate periodically around the fitted straight lines with the amplitude growing as the income values increase. Since the entire income data range can be fitted by a single function, this raises questions on previous results claiming that the income distribution is constituted by a well defined two-classes-base income structure, since such a division in two very distinct income classes might not be an intrinsic property of societies, but a consequence of an a priori fitting-choice procedure that may leave aside possibly important income dynamics at the intermediate levels.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:88:y:2016:i:c:p:158-171
    DOI: 10.1016/j.chaos.2016.02.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077916300571
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2016.02.026?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Borges, Ernesto P, 2004. "Empirical nonextensive laws for the county distribution of total personal income and gross domestic product," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 255-266.
    2. Yamano, Takuya, 2002. "Some properties of q-logarithm and q-exponential functions in Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(3), pages 486-496.
    3. F. Clementi & M. Gallegati & G. Kaniadakis, 2007. "κ-generalized statistics in personal income distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(2), pages 187-193, May.
    4. Ernesto P. Borges, 2002. "Empirical nonextensive laws for the county distribution of total personal income and gross domestic product," Papers cond-mat/0205520, arXiv.org, revised Jan 2004.
    5. N. J. Moura & M. B. Ribeiro, 2009. "Evidence for the Gompertz curve in the income distribution of Brazil 1978–2005," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 67(1), pages 101-120, January.
    6. Wosnitza, Jan Henrik & Leker, Jens, 2014. "Can log-periodic power law structures arise from random fluctuations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 401(C), pages 228-250.
    7. Clementi, F. & Di Matteo, T. & Gallegati, M. & Kaniadakis, G., 2008. "The κ-generalized distribution: A new descriptive model for the size distribution of incomes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3201-3208.
    8. 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.
    9. Anand Banerjee & Victor M. Yakovenko, 2009. "Universal patterns of inequality," Papers 0912.4898, arXiv.org, revised Apr 2010.
    10. F. Clementi & M. Gallegati & G. Kaniadakis, 2009. "A k-generalized statistical mechanics approach to income analysis," Papers 0902.0075, arXiv.org, revised Feb 2009.
    11. F. Clementi & M. Gallegati & G. Kaniadakis, 2012. "A generalized statistical model for the size distribution of wealth," Papers 1209.4787, arXiv.org, revised Dec 2012.
    12. Ferrero, Juan C, 2004. "The statistical distribution of money and the rate of money transference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 575-585.
    13. A. Drăgulescu & V.M. Yakovenko, 2001. "Evidence for the exponential distribution of income in the USA," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(4), pages 585-589, April.
    14. Chami Figueira, F. & Moura, N.J. & Ribeiro, M.B., 2011. "The Gompertz–Pareto income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 689-698.
    15. Vandewalle, N. & Boveroux, Ph. & Minguet, A. & Ausloos, M., 1998. "The crash of October 1987 seen as a phase transition: amplitude and universality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 255(1), pages 201-210.
    16. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
    17. Coelho, Ricardo & Richmond, Peter & Barry, Joseph & Hutzler, Stefan, 2008. "Double power laws in income and wealth distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3847-3851.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Răzvan-Cornel Sfetcu & Vasile Preda, 2024. "Order Properties Concerning Tsallis Residual Entropy," Mathematics, MDPI, vol. 12(3), pages 1-16, January.
    2. Duarte Queirós, Sílvio M. & Anteneodo, Celia, 2016. "Complexity in quantitative finance and economics," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 1-2.
    3. Martins, Adriel M.F. & Fernandes, Leonardo H.S. & Nascimento, Abraão D.C., 2023. "Scientific progress in information theory quantifiers," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. Paulo L. dos Santos & Jangho Yang, 2019. "The persistent and informative distribution of returns on capital," Economics and Business Letters, Oviedo University Press, vol. 8(3), pages 156-165.
    5. da Silva, Sérgio Luiz Eduardo Ferreira, 2021. "Newton’s cooling law in generalised statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    6. 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).
    7. Răzvan-Cornel Sfetcu & Sorina-Cezarina Sfetcu & Vasile Preda, 2021. "Ordering Awad–Varma Entropy and Applications to Some Stochastic Models," Mathematics, MDPI, vol. 9(3), pages 1-15, January.
    8. Paulo L. dos Santos, 2017. "The Principle of Social Scaling," Complexity, Hindawi, vol. 2017, pages 1-9, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chami Figueira, F. & Moura, N.J. & Ribeiro, M.B., 2011. "The Gompertz–Pareto income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 689-698.
    2. 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.
    3. Elvis Oltean, 2016. "Modelling income, wealth, and expenditure data by use of Econophysics," Papers 1603.08383, arXiv.org.
    4. Costas Efthimiou & Adam Wearne, 2016. "Household Income Distribution in the USA," Papers 1602.06234, arXiv.org.
    5. Sarabia, José María & Jordá, Vanesa, 2014. "Explicit expressions of the Pietra index for the generalized function for the size distribution of income," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 582-595.
    6. 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).
    7. Aktaev, Nurken E. & Bannova, K.A., 2022. "Mathematical modeling of probability distribution of money by means of potential formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).
    8. Fabio CLEMENTI & Mauro GALLEGATI, 2017. "NEW ECONOMIC WINDOWS ON INCOME AND WEALTH: THE k-GENERALIZED FAMILY OF DISTRIBUTIONS," Journal of Social and Economic Statistics, Bucharest University of Economic Studies, vol. 6(1), pages 1-15, JULY.
    9. 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.
    10. Istvan Gere & Szabolcs Kelemen & Geza Toth & Tamas Biro & Zoltan Neda, 2021. "Wealth distribution in modern societies: collected data and a master equation approach," Papers 2104.04134, arXiv.org.
    11. Markus P. A. Schneider, 2018. "Revisiting the thermal and superthermal two-class distribution of incomes: A critical perspective," Papers 1804.06341, arXiv.org.
    12. 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.
    13. Soriano-Hernández, P. & del Castillo-Mussot, M. & Campirán-Chávez, I. & Montemayor-Aldrete, J.A., 2017. "Wealth of the world’s richest publicly traded companies per industry and per employee: Gamma, Log-normal and Pareto power-law as universal distributions?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 733-749.
    14. Gere, István & Kelemen, Szabolcs & Tóth, Géza & Biró, Tamás S. & Néda, Zoltán, 2021. "Wealth distribution in modern societies: Collected data and a master equation approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    15. Anwar Shaikh, 2017. "Income Distribution, Econophysics and Piketty," Review of Political Economy, Taylor & Francis Journals, vol. 29(1), pages 18-29, January.
    16. Anwar Shaikh, 2018. "Some Universal Patterns in Income Distribution: An Econophysics Approach," Working Papers 1808, New School for Social Research, Department of Economics.
    17. José María Sarabia & Vanesa Jordá & Lorena Remuzgo, 2017. "The Theil Indices in Parametric Families of Income Distributions—A Short Review," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 63(4), pages 867-880, December.
    18. Scott Lawrence & Qin Liu & Victor M. Yakovenko, 2013. "Global inequality in energy consumption from 1980 to 2010," Papers 1312.6443, arXiv.org, revised Mar 2014.
    19. Calderín-Ojeda, Enrique & Azpitarte, Francisco & Gómez-Déniz, Emilio, 2016. "Modelling income data using two extensions of the exponential distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 756-766.
    20. Shaikh, Anwar & Jacobo, Juan Esteban, 2020. "Economic Arbitrage and the Econophysics of Income Inequality," Review of Behavioral Economics, now publishers, vol. 7(4), pages 299–315-2, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:88:y:2016:i:c:p:158-171. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.