IDEAS home Printed from https://ideas.repec.org/a/bla/anzsta/v44y2002i4p439-446.html
   My bibliography  Save this article

The Asymptotic Distribution of the S–Gini Index

Author

Listed:
  • Ričardas Zitikis
  • Joseph L. Gastwirth

Abstract

Several generalizations of the classical Gini index, placing smaller or greater weights on various portions of income distribution, have been proposed by a number of authors. For purposes of statistical inference, the large sample distribution theory of the estimators of those measures of economic inequality is required. The present paper was stimulated by the use of bootstrap by Xu (2000) to estimate the variance of the estimator of the S–Gini index. It shows that the theory of L–statistics (Chernoff, Gastwirth & Johns, 1967; Shorack & Wellner, 1986) makes possible the construction of a consistent estimator for the S–Gini index and proof of its asymptotic normality. The paper also presents an explicit formula for the asymptotic variance. The formula should be helpful in planning the size of samples from which the S–Gini index can be estimated with a prescribed margin of error.

Suggested Citation

  • Ričardas Zitikis & Joseph L. Gastwirth, 2002. "The Asymptotic Distribution of the S–Gini Index," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 44(4), pages 439-446, December.
    • Handle: RePEc:bla:anzsta:v:44:y:2002:i:4:p:439-446
    DOI: 10.1111/1467-842X.00245
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-842X.00245
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-842X.00245?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
    ---><---

    Citations

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


    Cited by:

    1. Andrew Leigh, 2005. "Can Redistributive State Taxes Reduce Inequality?," CEPR Discussion Papers 490, Centre for Economic Policy Research, Research School of Economics, Australian National University.
    2. Khosravi Tanak, A. & Mohtashami Borzadaran, G.R. & Ahmadi, J., 2017. "Maximum Tsallis entropy with generalized Gini and Gini mean difference indices constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 554-560.
    3. N. Nakhaei Rad & G.R. Mohtashami Borzadaran & G.H. Yari, 2016. "Maximum entropy estimation of income share function from generalized Gini index," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(16), pages 2910-2921, December.
    4. Stephen G. Donald & Yu‐Chin Hsu & Garry F. Barrett, 2012. "Incorporating covariates in the measurement of welfare and inequality: methods and applications," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 1-30, February.
    5. Khosravi Tanak, A. & Mohtashami Borzadaran, G.R. & Ahmadi, Jafar, 2018. "New functional forms of Lorenz curves by maximizing Tsallis entropy of income share function under the constraint on generalized Gini index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 511(C), pages 280-288.
    6. Agostino Tarsitano, 2004. "A new class of inequality measures based on a ratio of L-statistics," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 137-160.
    7. Francis Bilson Darku & Frank Konietschke & Bhargab Chattopadhyay, 2020. "Gini Index Estimation within Pre-Specified Error Bound: Application to Indian Household Survey Data," Econometrics, MDPI, vol. 8(2), pages 1-20, June.
    8. Michael Beenstock & Daniel Felsenstein, 2007. "Mobility and Mean Reversion in the Dynamics of Regional Inequality," International Regional Science Review, , vol. 30(4), pages 335-361, October.
    9. Sudheesh K. Kattumannil & N. Sreelakshmi & N. Balakrishnan, 2022. "Non-Parametric Inference for Gini Covariance and its Variants," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 790-807, August.

    More about this item

    Statistics

    Access and download statistics

    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:bla:anzsta:v:44:y:2002:i:4:p:439-446. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=1369-1473 .

    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.