IDEAS home Printed from https://ideas.repec.org/a/spr/metron/v82y2024i3d10.1007_s40300-024-00271-w.html
   My bibliography  Save this article

Beautiful Gini

Author

Listed:
  • Iddo Eliazar

    (Tel Aviv University)

Abstract

You may very well be familiar with the Gini Coefficient, also known as the Gini index: a quantitative gauge with which socioeconomic inequality is measured, e.g. income disparity and wealth disparity. However, you may not know that the Gini Coefficient is an exquisite mathematical object. Enter this review paper—whose aim is to showcase (some of) the mathematical beauty and riches of the Gini Coefficient. The paper does so, in a completely self-contained manner, by illuminating the Gini Coefficient from various perspectives: Euclidean geometry vs. grid geometry; maxima and minima of random variables; statistical distribution functions; the residual lifetime and the total lifetime of renewal processes; increasing and decreasing failure rates; socioeconomic divergence from perfect equality; and weighted differences of statistical distribution functions. Together, these different perspectives offer a deep and comprehensive understanding of the Gini Coefficient. In turn, a profound understanding of the Gini Coefficient may lead to novel ‘Gini applications’ in science and engineering—such as recently established in the multidisciplinary field of restart research.

Suggested Citation

  • Iddo Eliazar, 2024. "Beautiful Gini," METRON, Springer;Sapienza Università di Roma, vol. 82(3), pages 293-313, December.
    • Handle: RePEc:spr:metron:v:82:y:2024:i:3:d:10.1007_s40300-024-00271-w
    DOI: 10.1007/s40300-024-00271-w
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40300-024-00271-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s40300-024-00271-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Giovanni Maria Giorgi & Chiara Gigliarano, 2017. "The Gini Concentration Index: A Review Of The Inference Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 31(4), pages 1130-1148, September.
    2. William F. Sharpe, 1971. "Mean-Absolute-Deviation Characteristic Lines for Securities and Portfolios," Management Science, INFORMS, vol. 18(2), pages 1-13, October.
    3. Cowell, Frank, 2011. "Measuring Inequality," OUP Catalogue, Oxford University Press, edition 3, number 9780199594047.
    4. Yuval Arbel & Chaim Fialkoff & Amichai Kerner & Miryam Kerner, 2022. "Do population density, socio-economic ranking and Gini Index of cities influence infection rates from coronavirus? Israel as a case study," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 68(1), pages 181-206, February.
    5. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
    6. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, April.
    7. Shlomo Yitzhaki, 2003. "Gini’s Mean difference: a superior measure of variability for non-normal distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 285-316.
    8. Giovanni M. Giorgi & Stefania Gubbiotti, 2017. "Celebrating the Memory of Corrado Gini: a Personality Out of the Ordinary," International Statistical Review, International Statistical Institute, vol. 85(2), pages 325-339, August.
    9. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Francesca Greselin & Ričardas Zitikis, 2018. "From the Classical Gini Index of Income Inequality to a New Zenga-Type Relative Measure of Risk: A Modeller’s Perspective," Econometrics, MDPI, vol. 6(1), pages 1-20, January.
    3. Wojtek Michalowski & Włodzimierz Ogryczak, 2001. "Extending the MAD portfolio optimization model to incorporate downside risk aversion," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 185-200, April.
    4. Ziqing Dong & Yves Tillé & Giovanni M. Giorgi & Alessio Guandalini, 2021. "Linearization and variance estimation of the Bonferroni inequality index," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 1008-1029, July.
    5. Fabio Clementi & Mauro Gallegati & Lisa Gianmoena & Simone Landini & Joseph E. Stiglitz, 2019. "Mis-measurement of inequality: a critical reflection and new insights," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(4), pages 891-921, December.
    6. Mariateresa Ciommi & Chiara Gigliarano & Giovanni Maria Giorgi, 2019. "Bonferroni And De Vergottini Are Back: New Subgroup Decompositions And Bipolarization Measures," Working Papers 439, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    7. Enora Belz, 2019. "Estimating Inequality Measures from Quantile Data," Economics Working Paper Archive (University of Rennes & University of Caen) 2019-09, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    8. Sehgal, Ruchika & Sharma, Amita & Mansini, Renata, 2023. "Worst-case analysis of Omega-VaR ratio optimization model," Omega, Elsevier, vol. 114(C).
    9. Eliazar, Iddo, 2021. "Five degrees of randomness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
    10. Greselin, Francesca & Zitikis, Ricardas, 2015. "Measuring economic inequality and risk: a unifying approach based on personal gambles, societal preferences and references," MPRA Paper 65892, University Library of Munich, Germany.
    11. Giovanni Maria Giorgi, 2019. "The Gini concentration ratio: Back to the future," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 73(2), pages 5-14, April-Jun.
    12. Alessio Guandalini, 2022. "Things you should know about the Gini index," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - The Italian Journal of Economic, Demographic and Statistical Studies, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 76(4), pages 4-12, October-D.
    13. Yang Liu & Joseph L. Gastwirth, 2020. "On the capacity of the Gini index to represent income distributions," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 61-69, April.
    14. Anders Bredahl Kock & David Preinerstorfer & Bezirgen Veliyev, 2022. "Functional Sequential Treatment Allocation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(539), pages 1311-1323, September.
    15. Shlomo Yitzhaki & Peter Lambert, 2013. "The relationship between the absolute deviation from a quantile and Gini’s mean difference," METRON, Springer;Sapienza Università di Roma, vol. 71(2), pages 97-104, September.
    16. Shlomo Yitzhaki & Edna Schechtman, 2004. "The Gini Instrumental Variable, or the “double instrumental variable” estimator," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 287-313.
    17. Eliazar, Iddo, 2024. "From Zipf to Price and beyond," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 647(C).
    18. Canh Phuc Nguyen & Binh Quang Nguyen & Duyen Thuy Le Tran, 2023. "Economic complexity and income inequality: New evidence of a nonlinear effect," Social Science Quarterly, Southwestern Social Science Association, vol. 104(4), pages 829-868, July.
    19. Enora Belz, 2019. "Estimating Inequality Measures from Quantile Data," Working Papers halshs-02320110, HAL.
    20. Mansini, Renata & Ogryczak, Wlodzimierz & Speranza, M. Grazia, 2014. "Twenty years of linear programming based portfolio optimization," European Journal of Operational Research, Elsevier, vol. 234(2), pages 518-535.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metron:v:82:y:2024:i:3:d:10.1007_s40300-024-00271-w. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.