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Pareto versus lognormal: a maximum entropy test

Author

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  • Marco Bee

    ()

  • Massimo Riccaboni

    ()

  • Stefano Schiavo

    ()

Abstract

It is commonly found that distributions that seem to be lognormal over a broad range change to a power-law (Pareto) distribution for the last few percentiles. The distributions of species abundance, income and wealth as well as file, city and firm sizes are examples with this structure. We present a new test for the occurrence of power-law tails in statistical distributions based on maximum entropy. This methodology allows to identify the true data generating processes even in the case when it is neither lognormal nor Pareto. The maximum entropy approach is then compared with alternative methods at different levels of aggregation of economic systems. Our results provide support to the theory that distributions with lognormal body and Pareto tail can be generated as mixtures of lognormally distributed units.

Suggested Citation

  • Marco Bee & Massimo Riccaboni & Stefano Schiavo, 2011. "Pareto versus lognormal: a maximum entropy test," Department of Economics Working Papers 1102, Department of Economics, University of Trento, Italia.
  • Handle: RePEc:trn:utwpde:1102
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    File URL: http://www.unitn.it/files/download/15312/02_11.schiavo_bee_riccamboni.pdf
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    References listed on IDEAS

    as
    1. De Fabritiis, G. & Pammolli, F. & Riccaboni, M., 2003. "On size and growth of business firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 38-44.
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    Cited by:

    1. Jakub Growiec & Fabio Pammolli & Massimo Riccaboni, 2011. "Innovation and Corporate Dynamics: A Theoretical Framework," DISA Working Papers 2011/08, Department of Computer and Management Sciences, University of Trento, Italy, revised 29 Jul 2011.
    2. repec:eee:phsmap:v:481:y:2017:i:c:p:265-275 is not listed on IDEAS
    3. Fazio, Giorgio & Modica, Marco, 2012. "Pareto or log-normal? A recursive-truncation approach to the distribution of (all) cities," SIRE Discussion Papers 2012-54, Scottish Institute for Research in Economics (SIRE).
    4. Giorgio Fazio & Marco Modica, 2015. "Pareto Or Log-Normal? Best Fit And Truncation In The Distribution Of All Cities," Journal of Regional Science, Wiley Blackwell, vol. 55(5), pages 736-756, November.
    5. Bee, Marco & Riccaboni, Massimo & Schiavo, Stefano, 2017. "Where Gibrat meets Zipf: Scale and scope of French firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 265-275.
    6. Bee, Marco & Riccaboni, Massimo & Schiavo, Stefano, 2013. "The size distribution of US cities: Not Pareto, even in the tail," Economics Letters, Elsevier, vol. 120(2), pages 232-237.
    7. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.

    More about this item

    Keywords

    Pareto distribution; power-law; lognormal distribution; maximum entropy; firm size; international trade;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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