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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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    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, September.
    2. Oshanin, G. & Holovatch, Yu. & Schehr, G., 2011. "Proportionate vs disproportionate distribution of wealth of two individuals in a tempered Paretian ensemble," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4340-4346.
    3. G. Oshanin & Yu. Holovatch & G. Schehr, 2011. "Proportionate vs disproportionate distribution of wealth of two individuals in a tempered Paretian ensemble," Papers 1106.4710, arXiv.org.
    4. G. Oshanin & Yu. Holovatch & G. Schehr, 2011. "Proportionate vs disproportionate distribution of wealth of two individuals in a tempered Paretian ensemble," Post-Print hal-00611323, HAL.
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    Cited by:

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    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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    6. José Manuel Gavilan-Ruiz & África Ruiz-Gándara & Francisco Javier Ortega-Irizo & Luis Gonzalez-Abril, 2024. "Some Notes on the Gini Index and New Inequality Measures: The nth Gini Index," Stats, MDPI, vol. 7(4), pages 1-12, November.
    7. 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.
    8. 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.
    9. 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.
    10. Kolluru Mythili & Semenenko Tetiana, 2021. "Income Inequalities in EU Countries: Gini Indicator Analysis," Economics, Sciendo, vol. 9(1), pages 125-142, June.
    11. Andrea Fontanari & Nassim Nicholas Taleb & Pasquale Cirillo, 2017. "Gini estimation under infinite variance," Papers 1707.01370, arXiv.org, revised Dec 2017.
    12. 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.
    13. Thitithep Sitthiyot & Kanyarat Holasut, 2020. "A simple method for measuring inequality," Palgrave Communications, Palgrave Macmillan, vol. 6(1), pages 1-9, December.
    14. Thitithep Sitthiyot & Kanyarat Holasut, 2021. "A simple method for estimating the Lorenz curve," Palgrave Communications, Palgrave Macmillan, vol. 8(1), pages 1-9, December.
    15. 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.
    16. Aisling J. Daly & Jan M. Baetens & Bernard De Baets, 2018. "Ecological Diversity: Measuring the Unmeasurable," Mathematics, MDPI, vol. 6(7), pages 1-28, July.
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