IDEAS home Printed from https://ideas.repec.org/a/spr/metron/v73y2015i1p25-30.html
   My bibliography  Save this article

On Zenga and Bonferroni curves

Author

Listed:
  • Barry Arnold

Abstract

Three alternative inequality curves are considered as competitors of the classical Lorenz curve as descriptors of income inequality. The Bonferroni curve and the Zenga-07 curve appear to be essentially equivalent to the Lorenz curve. They each determine the parent distribution up to scale factor, and they each yield an inequality partial order that is equivalent to the Lorenz order. The Zenga-84 curve is more problematic. It is scale invariant, but it is possible that different distributions can have the same Zenga-84 curve. Thus it fails to identify the parent distribution up to a scale factor. Copyright Sapienza Università di Roma 2015

Suggested Citation

  • Barry Arnold, 2015. "On Zenga and Bonferroni curves," METRON, Springer;Sapienza Università di Roma, vol. 73(1), pages 25-30, April.
    • Handle: RePEc:spr:metron:v:73:y:2015:i:1:p:25-30
    DOI: 10.1007/s40300-014-0050-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s40300-014-0050-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s40300-014-0050-3?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. Gaetano Pietra, 2014. "On the relationships between variability indices (Note I)," METRON, Springer;Sapienza Università di Roma, vol. 72(1), pages 5-16, April.
    2. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
    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. Francesca Battisti & Francesco Porro, 2023. "A multi-decomposition of Zenga-84 inequality index: an application to the disparity in CO $$_2$$ 2 emissions in European countries," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 957-981, September.
    2. Francesco Porro & Michele Zenga, 2020. "Decomposition by subpopulations of the Zenga-84 inequality curve and the related index $$\zeta $$ζ: an application to 2014 Bank of Italy survey," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 187-207, March.
    3. Zahra Behdani & Gholam Reza Mohtashami Borzadaran & Bahram Sadeghpour Gildeh, 2020. "Some properties of double truncated distributions and their application in view of income inequality," Computational Statistics, Springer, vol. 35(1), pages 359-378, March.

    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. 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.
    2. Vanesa Jorda & José María Sarabia & Markus Jäntti, 2020. "Estimation of Income Inequality from Grouped Data," LIS Working papers 804, LIS Cross-National Data Center in Luxembourg.
    3. 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.
    4. Sarabia, José María, 2008. "A general definition of the Leimkuhler curve," Journal of Informetrics, Elsevier, vol. 2(2), pages 156-163.
    5. 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.
    6. Magali Jaoul-Grammare & Brice Magdalou, 2013. "Opportunities in Higher Education: An Application to France," Annals of Economics and Statistics, GENES, issue 111-112, pages 295-325.
    7. Masters-Waage, Theodore C. & Nai, Jared & Reb, Jochen & Sim, Samantha & Narayanan, Jayanth & Tan, Noriko, 2021. "Going far together by being here now: Mindfulness increases cooperation in negotiations," Organizational Behavior and Human Decision Processes, Elsevier, vol. 167(C), pages 189-205.
    8. 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.
    9. Stephen Bazen & Patrick Moyes, 2012. "Elitism and stochastic dominance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(1), pages 207-251, June.
    10. Ravallion, Martin & Chen, Shaohua, 2003. "Measuring pro-poor growth," Economics Letters, Elsevier, vol. 78(1), pages 93-99, January.
    11. 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.
    12. Domonkos, Tomas & Fisera, Boris & Siranova, Maria, 2023. "Income inequality as long-term conditioning factor of monetary transmission to bank rates," Economic Modelling, Elsevier, vol. 128(C).
    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. Fontanari Andrea & Cirillo Pasquale & Oosterlee Cornelis W., 2020. "Lorenz-generated bivariate Archimedean copulas," Dependence Modeling, De Gruyter, vol. 8(1), pages 186-209, January.
    19. Alfred Ultsch & Jörn Lötsch, 2015. "Computed ABC Analysis for Rational Selection of Most Informative Variables in Multivariate Data," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-15, June.
    20. Michel Lubrano & Zhou Xun, 2023. "The Bayesian approach to poverty measurement," Post-Print hal-04347292, HAL.

    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:73:y:2015:i:1:p:25-30. 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.