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Pareto versus lognormal: a maximum entropy test

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Author Info

  • 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.

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Bibliographic Info

Paper provided by Department of Economics, University of Trento, Italia in its series Department of Economics Working Papers with number 1102.

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Date of creation: 2011
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Handle: RePEc:trn:utwpde:1102

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

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  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. 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.
  3. Giorgio Fazio & Marco Modica, 2012. "Pareto or log-normal? A recursive-truncation approach to the distribution of (all) cities," Working Papers 2012_10, Business School - Economics, University of Glasgow.

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