IDEAS home Printed from https://ideas.repec.org/a/spr/metron/v77y2019i1d10.1007_s40300-019-00149-2.html
   My bibliography  Save this article

The Gini mean difference and variance

Author

Listed:
  • Roberta La Haye

    (Mount Royal University)

  • Petr Zizler

    (Mount Royal University)

Abstract

A quick, alternate proof is given for a previously known inequality relating the standard deviation and the Gini mean difference. The inequality is sharpened and generalized to higher, even moments. Further inequalities are derived that involve the standard deviation, higher Ginis and order statistics.

Suggested Citation

  • Roberta La Haye & Petr Zizler, 2019. "The Gini mean difference and variance," METRON, Springer;Sapienza Università di Roma, vol. 77(1), pages 43-52, April.
    • Handle: RePEc:spr:metron:v:77:y:2019:i:1:d:10.1007_s40300-019-00149-2
    DOI: 10.1007/s40300-019-00149-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40300-019-00149-2
    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/s40300-019-00149-2?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. Walter Piesch, 2005. "A look at the structure of some extended Ginis," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 263-296.
    2. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pierpaolo Angelini, 2024. "Invariance of the Mathematical Expectation of a Random Quantity and Its Consequences," Risks, MDPI, vol. 12(1), pages 1-17, January.
    2. Gabriela M. Rodrigues & Edwin M. M. Ortega & Gauss M. Cordeiro & Roberto Vila, 2023. "Quantile Regression with a New Exponentiated Odd Log-Logistic Weibull Distribution," Mathematics, MDPI, vol. 11(6), pages 1-20, March.
    3. Fabrizio Maturo & Pierpaolo Angelini, 2023. "Aggregate Bound Choices about Random and Nonrandom Goods Studied via a Nonlinear Analysis," Mathematics, MDPI, vol. 11(11), pages 1-30, May.
    4. Jan Jekl & Jiří Jánský, 2022. "Security Challenges and Economic-Geographical Metrics for Analyzing Safety to Achieve Sustainable Protection," Sustainability, MDPI, vol. 14(22), pages 1-19, November.
    5. Valérie Bérenger & Jacques Silber, 2022. "On the Measurement of Happiness and of its Inequality," Journal of Happiness Studies, Springer, vol. 23(3), pages 861-902, March.
    6. Frank Cowell & Emmanuel Flachaire, 2021. "Inequality Measurement: Methods and Data," Post-Print hal-03589066, HAL.

    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. 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.
    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. 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.
    4. Charles Condevaux & Stéphane Mussard & Téa Ouraga & Guillaume Zambrano, 2020. "Generalized Gini linear and quadratic discriminant analyses," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 219-236, August.
    5. Barry Arnold, 2015. "On Zenga and Bonferroni curves," METRON, Springer;Sapienza Università di Roma, vol. 73(1), pages 25-30, April.
    6. Vanesa Jorda & Jos Mar a Sarabia & Markus J ntti, 2020. "Estimation of Income Inequality from Grouped Data," LIS Working papers 804, LIS Cross-National Data Center in Luxembourg.
    7. 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.
    8. Sarabia, José María, 2008. "A general definition of the Leimkuhler curve," Journal of Informetrics, Elsevier, vol. 2(2), pages 156-163.
    9. Fabio Clementi & Mauro Gallegati & Giorgio Kaniadakis, 2010. "A model of personal income distribution with application to Italian data," Empirical Economics, Springer, vol. 39(2), pages 559-591, October.
    10. Carmen Puerta & Ana Urrutia, 2012. "Lower and upper tail concern and the rank dependent social evaluation functions," Economics Bulletin, AccessEcon, vol. 32(4), pages 3250-3259.
    11. Ravallion, Martin & Chen, Shaohua, 2003. "Measuring pro-poor growth," Economics Letters, Elsevier, vol. 78(1), pages 93-99, January.
    12. Yu Zhang & Jiayu Wu & Chunyao Zhou & Qingyu Zhang, 2019. "Installation Planning in Regional Thermal Power Industry for Emissions Reduction Based on an Emissions Inventory," IJERPH, MDPI, vol. 16(6), pages 1-13, March.
    13. Masato Okamoto, 2014. "Interpolating the Lorenz Curve: Methods to Preserve Shape and Remain Consistent with the Concentration Curves for Components," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 60(2), pages 349-384, June.
    14. Zhu, Yongjun & Yan, Erjia, 2017. "Examining academic ranking and inequality in library and information science through faculty hiring networks," Journal of Informetrics, Elsevier, vol. 11(2), pages 641-654.
    15. Belzunce, Félix & Pinar, José F. & Ruiz, José M. & Sordo, Miguel A., 2013. "Comparison of concentration for several families of income distributions," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1036-1045.
    16. Yuanying Guan & Zhanyi Jiao & Ruodu Wang, 2022. "A reverse ES (CVaR) optimization formula," Papers 2203.02599, arXiv.org, revised May 2023.
    17. Csörgö, Miklós & Zitikis, Ricardas, 1997. "On the rate of strong consistency of Lorenz curves," Statistics & Probability Letters, Elsevier, vol. 34(2), pages 113-121, June.
    18. Yoel Finkel & Yevgeny Artsev & Shlomo Yitzhaki, 2006. "Inequality measurement and the time structure of household income in Israel," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 4(2), pages 153-179, August.
    19. Ndéné Ka & Stéphane Mussard, 2016. "ℓ 1 regressions: Gini estimators for fixed effects panel data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(8), pages 1436-1446, June.
    20. Eisenberg, Bennett, 2015. "The multivariate Gini ratio," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 292-298.

    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:77:y:2019:i:1:d:10.1007_s40300-019-00149-2. 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.