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Are your data really Pareto distributed?

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  • Pasquale Cirillo

Abstract

Pareto distributions, and power laws in general, have demonstrated to be very useful models to describe very different phenomena, from physics to finance. In recent years, the econophysical literature has proposed a large amount of papers and models justifying the presence of power laws in economic data. Most of the times, this Paretianity is inferred from the observation of some plots, such as the Zipf plot and the mean excess plot. If the Zipf plot looks almost linear, then everything is ok and the parameters of the Pareto distribution are estimated. Often with OLS. Unfortunately, as we show in this paper, these heuristic graphical tools are not reliable. To be more exact, we show that only a combination of plots can give some degree of confidence about the real presence of Paretianity in the data. We start by reviewing some of the most important plots, discussing their points of strength and weakness, and then we propose some additional tools that can be used to refine the analysis.

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  • Pasquale Cirillo, 2013. "Are your data really Pareto distributed?," Papers 1306.0100, arXiv.org.
  • Handle: RePEc:arx:papers:1306.0100
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    References listed on IDEAS

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    1. Xavier Gabaix & Rustam Ibragimov, 2011. "Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 24-39, January.
    2. Ghosh, Souvik & Resnick, Sidney, 2010. "A discussion on mean excess plots," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1492-1517, August.
    3. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    4. Gabaix, Xavier & Ibragimov, Rustam, 2011. "Rank − 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 24-39.
    5. Cirillo, Pasquale & Hüsler, Jürg, 2009. "On the upper tail of Italian firms’ size distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1546-1554.
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    Cited by:

    1. repec:eee:phsmap:v:509:y:2018:i:c:p:169-180 is not listed on IDEAS
    2. Ramos, Arturo, 2015. "Are the log-growth rates of city sizes normally distributed? Empirical evidence for the US," MPRA Paper 65584, University Library of Munich, Germany.
    3. Stegehuis, Clara & Litvak, Nelly & Waltman, Ludo, 2015. "Predicting the long-term citation impact of recent publications," Journal of Informetrics, Elsevier, vol. 9(3), pages 642-657.
    4. repec:eee:phsmap:v:502:y:2018:i:c:p:256-269 is not listed on IDEAS
    5. A. B. Atkinson, 2017. "Pareto and the Upper Tail of the Income Distribution in the UK: 1799 to the Present," Economica, London School of Economics and Political Science, vol. 84(334), pages 129-156, April.
    6. Stephen P. Jenkins, 2017. "Pareto Models, Top Incomes and Recent Trends in UK Income Inequality," Economica, London School of Economics and Political Science, vol. 84(334), pages 261-289, April.
    7. Krause, Melanie & Bluhm, Richard, 2016. "Top Lights - Bright Spots and their Contribution to Economic Development," Annual Conference 2016 (Augsburg): Demographic Change 145773, Verein für Socialpolitik / German Economic Association.
    8. repec:eee:insuma:v:78:y:2018:i:c:p:13-29 is not listed on IDEAS
    9. repec:eee:phsmap:v:512:y:2018:i:c:p:1-13 is not listed on IDEAS
    10. Bluhm, Richard & Krause, Melanie, 2018. "Top Lights: Bright cities and their contribution to economic development," MERIT Working Papers 041, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    11. Bessi, Alessandro, 2017. "On the statistical properties of viral misinformation in online social media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 459-470.
    12. Cirillo, Pasquale & Taleb, Nassim Nicholas, 2016. "On the statistical properties and tail risk of violent conflicts," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 29-45.
    13. Ramos, Arturo & Sanz-Gracia, Fernando, 2015. "US city size distribution revisited: Theory and empirical evidence," MPRA Paper 64051, University Library of Munich, Germany.
    14. repec:spr:empeco:v:53:y:2017:i:3:d:10.1007_s00181-016-1147-8 is not listed on IDEAS
    15. Serinaldi, Francesco & Kilsby, Chris G., 2016. "Irreversibility and complex network behavior of stream flow fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 585-600.
    16. Ravaska Terhi, 2018. "Top incomes and income dynamics from a gender perspective : Evidence from Finland 1995-2012," Working Papers 1822, University of Tampere, School of Management, Economics.

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