IDEAS home Printed from https://ideas.repec.org/a/taf/amstat/v70y2016i1p25-32.html
   My bibliography  Save this article

The Advantages of Using Group Means in Estimating the Lorenz Curve and Gini Index From Grouped Data

Author

Listed:
  • Merritt Lyon
  • Li C. Cheung
  • Joseph L. Gastwirth

Abstract

A recent article proposed a histogram-based method for estimating the Lorenz curve and Gini index from grouped data that did not use the group means reported by government agencies. When comparing their method to one based on group means, the authors assume a uniform density in each grouping interval, which leads to an overestimate of the overall average income. After reviewing the additional information in the group means, it will be shown that as the number of groups increases, the bounds on the Gini index obtained from the group means become narrower. This is not necessarily true for the histogram method. Two simple interpolation methods using the group means are described and the accuracy of the estimated Gini index they yield and the histogram-based one are compared to the published Gini index for the 1967--2013 period. The average absolute errors of the estimated Gini index obtained from the two methods using group means are noticeably less than that of the histogram-based method. Supplementary materials for this article are available online.[Received August 2014. Revised September 2015.]

Suggested Citation

  • Merritt Lyon & Li C. Cheung & Joseph L. Gastwirth, 2016. "The Advantages of Using Group Means in Estimating the Lorenz Curve and Gini Index From Grouped Data," The American Statistician, Taylor & Francis Journals, vol. 70(1), pages 25-32, February.
    • Handle: RePEc:taf:amstat:v:70:y:2016:i:1:p:25-32
    DOI: 10.1080/00031305.2015.1105152
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/00031305.2015.1105152
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/00031305.2015.1105152?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.

    Citations

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


    Cited by:

    1. Kangmennaang, Joseph & Elliott, Susan J., 2018. "Towards an integrated framework for understanding the links between inequalities and wellbeing of places in low and middle income countries," Social Science & Medicine, Elsevier, vol. 213(C), pages 45-53.
    2. Yue Liu & Yuwei Su & Xiaoyu Li, 2022. "Analyzing the Spatial Equity of Walking-Based Chronic Disease Pharmacies: A Case Study in Wuhan, China," IJERPH, MDPI, vol. 20(1), pages 1-14, December.
    3. Tatjana Miljkovic & Ying-Ju Chen, 2021. "A new computational approach for estimation of the Gini index based on grouped data," Computational Statistics, Springer, vol. 36(3), pages 2289-2311, September.
    4. Dilanka S. Dedduwakumara & Luke A. Prendergast & Robert G. Staudte, 2021. "Some confidence intervals and insights for the proportion below the relative poverty line," SN Business & Economics, Springer, vol. 1(10), pages 1-22, October.
    5. Youri Davydov & Francesca Greselin, 2020. "Comparisons Between Poorest and Richest to Measure Inequality," Sociological Methods & Research, , vol. 49(2), pages 526-561, May.
    6. Songpu Shang & Songhao Shang, 2021. "Estimating Gini Coefficient from Grouped Data Based on Shape-Preserving Cubic Hermite Interpolation of Lorenz Curve," Mathematics, MDPI, vol. 9(20), pages 1-11, October.

    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:taf:amstat:v:70:y:2016:i:1:p:25-32. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UTAS20 .

    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.