IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v461y2016icp756-766.html
   My bibliography  Save this article

Modelling income data using two extensions of the exponential distribution

Author

Listed:
  • Calderín-Ojeda, Enrique
  • Azpitarte, Francisco
  • Gómez-Déniz, Emilio

Abstract

In this paper we propose two extensions of the Exponential model to describe income distributions. The Exponential ArcTan (EAT) and the composite EAT–Lognormal models discussed in this paper preserve key properties of the Exponential model including its capacity to model distributions with zero incomes. This is an important feature as the presence of zeros conditions the modelling of income distributions as it rules out the possibility of using many parametric models commonly used in the literature. Many researchers opt for excluding the zeros from the analysis, however, this may not be a sensible approach especially when the number of zeros is large or if one is interested in accurately describing the lower part of the distribution. We apply the EAT and the EAT–Lognormal models to study the distribution of incomes in Australia for the period 2001–2012. We find that these models in general outperform the Gamma and Exponential models while preserving the capacity of the latter to model zeros.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:461:y:2016:i:c:p:756-766
    DOI: 10.1016/j.physa.2016.06.047
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437116303156
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2016.06.047?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 search for a different version of it.

    References listed on IDEAS

    as
    1. F. Clementi & M. Gallegati & G. Kaniadakis, 2009. "A k-generalized statistical mechanics approach to income analysis," Papers 0902.0075, arXiv.org, revised Feb 2009.
    2. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
    3. Benito Frosini, 2012. "Approximation and decomposition of Gini, Pietra–Ricci and Theil inequality measures," Empirical Economics, Springer, vol. 43(1), pages 175-197, August.
    4. Mark Wooden & Nicole Watson, 2007. "The HILDA Survey and its Contribution to Economic and Social Research (So Far)," The Economic Record, The Economic Society of Australia, vol. 83(261), pages 208-231, June.
    5. 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.
    6. Banerjee, Anand & Yakovenko, Victor M. & Di Matteo, T., 2006. "A study of the personal income distribution in Australia," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 54-59.
    7. 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.
    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. Neveka M. Olmos & Emilio Gómez-Déniz & Osvaldo Venegas & Héctor W. Gómez, 2024. "A Composite Half-Normal-Pareto Distribution with Applications to Income and Expenditure Data," Mathematics, MDPI, vol. 12(11), pages 1-17, May.
    2. Tomaschitz, Roman, 2020. "Multiply broken power-law densities as survival functions: An alternative to Pareto and lognormal fits," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).

    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. 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. 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.
    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. Kaldasch, Joachim, 2012. "Evolutionary model of the personal income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5628-5642.
    6. 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).
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Adams Vallejos & Ignacio Ormazabal & Felix A. Borotto & Hernan F. Astudillo, 2018. "A new $\kappa$-deformed parametric model for the size distribution of wealth," Papers 1805.06929, arXiv.org.
    12. Newby, Michael & Behr, Adam & Feizabadi, Mitra Shojania, 2011. "Investigating the distribution of personal income obtained from the recent U.S. data," Economic Modelling, Elsevier, vol. 28(3), pages 1170-1173, May.
    13. 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).
    14. Díaz, Juan D. & Gutiérrez Cubillos, Pablo & Tapia Griñen, Pablo, 2021. "The exponential Pareto model with hidden income processes: Evidence from Chile," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    15. Sebastian Guala, 2009. "Taxes in a Wealth Distribution Model by Inelastically Scattering of Particles," Interdisciplinary Description of Complex Systems - scientific journal, Croatian Interdisciplinary Society Provider Homepage: http://indecs.eu, vol. 7(1), pages 1-7.
    16. Remuzgo, Lorena & Trueba, Carmen & Sarabia, José María, 2016. "Evolution of the global inequality in greenhouse gases emissions using multidimensional generalized entropy measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 146-157.
    17. E. Gómez-Déniz, 2016. "A family of arctan Lorenz curves," Empirical Economics, Springer, vol. 51(3), pages 1215-1233, November.
    18. Muhammad Hilmi Abdul Majid & Kamarulzaman Ibrahim & Nurulkamal Masseran, 2023. "Three-Part Composite Pareto Modelling for Income Distribution in Malaysia," Mathematics, MDPI, vol. 11(13), pages 1-15, June.
    19. 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.
    20. Vallejos, Adams & Ormazábal, Ignacio & Borotto, Félix A. & Astudillo, Hernán F., 2019. "A new κ-deformed parametric model for the size distribution of wealth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 819-829.

    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:phsmap:v:461:y:2016:i:c:p:756-766. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.