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Measuring statistical evenness: A panoramic overview

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  • Eliazar, Iddo I.
  • Sokolov, Igor M.

Abstract

Motivated by the question “how equal is the distribution of wealth within a given human population?” economics devised an impressive toolbox of quantitative measures of societal egalitarianism including the Lorenz curve and the following indices: Gini, Pietra, Hoover, Amato, Hirschman, Theil and Atkinson. These quantitative measures–considered in the broader context of general data-sets with positive values–are, in effect, general gauges of statistical evenness. While the application of Gini’s index grew beyond economics and reached diverse fields of science, the aforementioned “evenness toolbox” has largely remained within the confines of the social sciences. The aim of this Paper is to expose this “evenness toolbox” to the physics community by presenting a comprehensive evenness-based approach to a fundamental problem in science—the measurement of statistical heterogeneity.

Suggested Citation

  • Eliazar, Iddo I. & Sokolov, Igor M., 2012. "Measuring statistical evenness: A panoramic overview," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1323-1353.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:1323-1353
    DOI: 10.1016/j.physa.2011.09.007
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    References listed on IDEAS

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    Cited by:

    1. I. Josa & A. Aguado, 2020. "Measuring Unidimensional Inequality: Practical Framework for the Choice of an Appropriate Measure," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 149(2), pages 541-570, June.
    2. Fontanari, Andrea & Cirillo, Pasquale & Oosterlee, Cornelis W., 2018. "From Concentration Profiles to Concentration Maps. New tools for the study of loss distributions," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 13-29.
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    4. Chun-Xiao Nie & Fu-Tie Song, 2021. "Entropy of Graphs in Financial Markets," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1149-1166, April.
    5. Iddo Eliazar & Giovanni M. Giorgi, 2020. "From Gini to Bonferroni to Tsallis: an inequality-indices trek," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 119-153, August.
    6. Sarabia, José María & Jordá, Vanesa, 2014. "Explicit expressions of the Pietra index for the generalized function for the size distribution of income," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 582-595.
    7. Kolluru Mythili & Semenenko Tetiana, 2021. "Income Inequalities in EU Countries: Gini Indicator Analysis," Economics, Sciendo, vol. 9(1), pages 125-142, June.
    8. Andrea Fontanari & Nassim Nicholas Taleb & Pasquale Cirillo, 2017. "Gini estimation under infinite variance," Papers 1707.01370, arXiv.org, revised Dec 2017.
    9. Abraham Nunes & Thomas Trappenberg & Martin Alda, 2020. "Measuring heterogeneity in normative models as the effective number of deviation patterns," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-16, November.
    10. Thitithep Sitthiyot & Kanyarat Holasut, 2020. "A simple method for measuring inequality," Palgrave Communications, Palgrave Macmillan, vol. 6(1), pages 1-9, December.
    11. Thitithep Sitthiyot & Kanyarat Holasut, 2021. "A simple method for estimating the Lorenz curve," Palgrave Communications, Palgrave Macmillan, vol. 8(1), pages 1-9, December.
    12. Aisling J. Daly & Jan M. Baetens & Bernard De Baets, 2018. "Ecological Diversity: Measuring the Unmeasurable," Mathematics, MDPI, vol. 6(7), pages 1-28, July.
    13. Amparo Ba'illo & Javier C'arcamo & Carlos Mora-Corral, 2021. "Extremal points of Lorenz curves and applications to inequality analysis," Papers 2103.03286, arXiv.org.
    14. Nie, Chun-Xiao & Song, Fu-Tie & Li, Sai-Ping, 2016. "Rényi indices of financial minimum spanning trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 883-889.
    15. Fontanari, Andrea & Taleb, Nassim Nicholas & Cirillo, Pasquale, 2018. "Gini estimation under infinite variance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 256-269.
    16. Salois, Matthew J., 2013. "Regional changes in the distribution of foreign aid: An entropy approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(13), pages 2893-2902.
    17. Dashti Moghaddam, M. & Mills, Jeffrey & Serota, R.A., 2020. "From a stochastic model of economic exchange to measures of inequality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).

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