Pareto versus lognormal: A maximum entropy test

Marco Bee, Massimo Riccaboni, and Stefano Schiavo
Phys. Rev. E 84, 026104 – Published 4 August 2011

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 many physical, natural, and social events (earthquake size, species abundance, income and wealth, as well as file, city, and firm sizes) display this structure. We present a test for the occurrence of power-law tails in statistical distributions based on maximum entropy. This methodology allows one 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 other widely used methods and applied to different levels of aggregation of complex systems. Our results provide support for the theory that distributions with lognormal body and Pareto tail can be generated as mixtures of lognormally distributed units.

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  • Received 11 February 2011

DOI:https://doi.org/10.1103/PhysRevE.84.026104

©2011 American Physical Society

Authors & Affiliations

Marco Bee*

  • Department of Economics, University of Trento, Trento, Italy

Massimo Riccaboni

  • DISA, University of Trento, Trento, Italy and IMT School of Advanced Studies, Lucca, Italy

Stefano Schiavo

  • Department of Economics, University of Trento, Trento, Italy and OFCE-DRIC, Valbonne, France

  • *marco.bee@unitn.it
  • massimo.riccaboni@unitn.it
  • stefano.schiavo@unitn.it

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Issue

Vol. 84, Iss. 2 — August 2011

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