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Maximization of statistical heterogeneity: From Shannon’s entropy to Gini’s index

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  • Eliazar, Iddo
  • Sokolov, Igor M.
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    Abstract

    Different fields of Science apply different quantitative gauges to measure statistical heterogeneity. Statistical Physics and Information Theory commonly use Shannon’s entropy which measures the randomness of probability laws, whereas Economics and the Social Sciences commonly use Gini’s index which measures the evenness of probability laws. Motivated by the principle of maximal entropy, we explore the maximization of statistical heterogeneity–for probability laws with a given mean–in the four following scenarios: (i) Shannon entropy maximization subject to a given dispersion level; (ii) Gini index maximization subject to a given dispersion level; (iii) Shannon entropy maximization subject to a given Gini index; (iv) Gini index maximization subject to a given Shannon entropy. Analysis of these four scenarios results in four different classes of heterogeneity-maximizing probability laws–yielding an in-depth description of both the marked differences and the interplay between the Physical “randomness-based” and the Economic “evenness-based” approaches to the maximization of statistical heterogeneity.

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    Bibliographic Info

    Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

    Volume (Year): 389 (2010)
    Issue (Month): 16 ()
    Pages: 3023-3038

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    Handle: RePEc:eee:phsmap:v:389:y:2010:i:16:p:3023-3038

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    Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

    Related research

    Keywords: Statistical heterogeneity; Dispersion; Entropy; Egalitarianism; Shannon’s entropy; Gini’s index; Subbotin’s distribution; The logistic distribution;

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    1. Alfarano, Simone & Milakovic, Mishael, 2008. "Does classical competition explain the statistical features of firm growth?," Economics Letters, Elsevier, vol. 101(3), pages 272-274, December.
    2. S. Illeris & G. Akehurst, 2002. "Introduction," The Service Industries Journal, Taylor & Francis Journals, vol. 22(1), pages 1-3, January.
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