IDEAS home Printed from https://ideas.repec.org/a/bla/revinw/v57y2011i3p561-582.html
   My bibliography  Save this article

A General Method For Creating Lorenz Curves

Author

Listed:
  • ZUXIANG WANG
  • YEW‐KWANG NG
  • RUSSELL SMYTH

Abstract

There are currently about two dozen Lorenz models available in the literature for fitting grouped income distribution data. A general method to construct parametric Lorenz models of the weighted product form is offered in this paper. First, a general result to describe the conditions for the weighted product model to be a Lorenz curve, created by using several component parametric Lorenz models, is given. We show that the key property for an ideal component model is that the ratio between its second derivative and its first derivative is increasing. Then, a set of Lorenz models, consisting of a basic group of models along with their convex combinations, is proposed, and it is shown that any model in the set possesses this key property. Equipped with this general result and the model set, we can create a range of different weighted product Lorenz models. Finally, test results are presented which demonstrate that there may be many satisfactory models among those created. The proposed method can be generalized by finding other models with this key property.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Zuxiang Wang & Yew‐Kwang Ng & Russell Smyth, 2011. "A General Method For Creating Lorenz Curves," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 57(3), pages 561-582, September.
    • Handle: RePEc:bla:revinw:v:57:y:2011:i:3:p:561-582
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. ZuXiang Wang & Yew-Kwang Ng & Russell Smyth, 2007. "Revisiting The Ordered Family Of Lorenz Curves," Monash Economics Working Papers 19-07, Monash University, Department of Economics.
    2. Kwang Soo Cheong, 2002. "An empirical comparison of alternative functional forms for the Lorenz curve," Applied Economics Letters, Taylor & Francis Journals, vol. 9(3), pages 171-176.
    3. Ogwang, Tomson & Rao, U. L. Gouranga, 2000. "Hybrid models of the Lorenz curve," Economics Letters, Elsevier, vol. 69(1), pages 39-44, October.
    4. Chotikapanich, Duangkamon, 1993. "A comparison of alternative functional forms for the Lorenz curve," Economics Letters, Elsevier, vol. 41(2), pages 129-138.
    5. ZuXiang Wang & Russell Smyth, 2007. "Two New Exponential Families Of Lorenz Curves," Monash Economics Working Papers 20-07, Monash University, Department of Economics.
    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. Gholamreza Hajargasht & William E. Griffiths, 2016. "Inference for Lorenz Curves," Department of Economics - Working Papers Series 2022, The University of Melbourne.
    2. Collins, Alan R. & Hansen, Evan & Hendryx, Michael, 2012. "Wind versus coal: Comparing the local economic impacts of energy resource development in Appalachia," Energy Policy, Elsevier, vol. 50(C), pages 551-561.
    3. John Ogwang & Dennis Obote & Ursula Abwot, 2021. "A Technical Note on New Applications of Lorenz Curves in Business Based on Pareto Principles," International Journal of Applied Economics, Finance and Accounting, Online Academic Press, vol. 9(2), pages 76-81.
    4. Banica Logica & Stefan Liviu Cristian & Jurian Mariana, 2014. "Business Intelligence For Educational Purpose," Balkan Region Conference on Engineering and Business Education, Sciendo, vol. 1(1), pages 333-338, August.
    5. Wang, ZuXiang & Smyth, Russell, 2015. "A hybrid method for creating Lorenz curves," Economics Letters, Elsevier, vol. 133(C), pages 59-63.
    6. Wang, ZuXiang & Smyth, Russell, 2015. "A piecewise method for estimating the Lorenz curve," Economics Letters, Elsevier, vol. 129(C), pages 45-48.
    7. Caliskan, Hakan & Hepbasli, Arif, 2010. "Energy and exergy prices of various energy sources along with their CO2 equivalents," Energy Policy, Elsevier, vol. 38(7), pages 3468-3481, July.
    8. Ruiz-Lozano, Mercedes & Tirado-Valencia, Pilar, 2016. "Do industrial companies respond to the guiding principles of the Integrated Reporting framework? A preliminary study on the first companies joined to the initiative," Revista de Contabilidad - Spanish Accounting Review, Elsevier, vol. 19(2), pages 252-260.
    9. Wang, Yuanjun & You, Shibing, 2016. "An alternative method for modeling the size distribution of top wealth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 443-453.
    10. Edyta Małecka-Ziembińska & Radosław Ziembiński, 2020. "Application of Genetic Algorithm to Optimal Income Taxation," JRFM, MDPI, vol. 13(11), pages 1-24, October.
    11. 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.
    12. Miguel Sordo & Jorge Navarro & José Sarabia, 2014. "Distorted Lorenz curves: models and comparisons," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 761-780, April.
    13. van Sluisveld, Mariësse A.E. & Worrell, Ernst, 2013. "The paradox of packaging optimization – a characterization of packaging source reduction in the Netherlands," Resources, Conservation & Recycling, Elsevier, vol. 73(C), pages 133-142.

    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. Wang, Yuanjun & You, Shibing, 2016. "An alternative method for modeling the size distribution of top wealth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 443-453.
    2. Johan Fellman, 2021. "Empirical Analyses of Income: Finland (2009) and Australia (1967-1968)," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 10(1), pages 1-3.
    3. WANG, Zuxiang & SMYTH, Russell & NG, Yew-Kwang, 2009. "A new ordered family of Lorenz curves with an application to measuring income inequality and poverty in rural China," China Economic Review, Elsevier, vol. 20(2), pages 218-235, June.
    4. Louis Mesnard, 2022. "About some difficulties with the functional forms of Lorenz curves," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 20(4), pages 939-950, December.
    5. Thitithep Sitthiyot & Kanyarat Holasut, 2021. "A simple method for estimating the Lorenz curve," Palgrave Communications, Palgrave Macmillan, vol. 8(1), pages 1-9, December.
    6. ZuXiang Wang & Russell Smyth, 2007. "Two New Exponential Families Of Lorenz Curves," Monash Economics Working Papers 20-07, Monash University, Department of Economics.
    7. Wang, ZuXiang & Smyth, Russell, 2015. "A hybrid method for creating Lorenz curves," Economics Letters, Elsevier, vol. 133(C), pages 59-63.
    8. ZuXiang Wang & Yew-Kwang Ng & Russell Smyth, 2007. "Revisiting The Ordered Family Of Lorenz Curves," Monash Economics Working Papers 19-07, Monash University, Department of Economics.
    9. Satya Paul & Sriram Shankar, 2020. "An alternative single parameter functional form for Lorenz curve," Empirical Economics, Springer, vol. 59(3), pages 1393-1402, September.
    10. Andrew C. Chang & Phillip Li & Shawn M. Martin, 2018. "Comparing cross‐country estimates of Lorenz curves using a Dirichlet distribution across estimators and datasets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(3), pages 473-478, April.
    11. Sarabia, José María & Gómez-Déniz, Emilio & Sarabia, María & Prieto, Faustino, 2010. "A general method for generating parametric Lorenz and Leimkuhler curves," Journal of Informetrics, Elsevier, vol. 4(4), pages 524-539.
    12. Miguel Sordo & Jorge Navarro & José Sarabia, 2014. "Distorted Lorenz curves: models and comparisons," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 761-780, April.
    13. Wang, ZuXiang & Smyth, Russell, 2015. "A piecewise method for estimating the Lorenz curve," Economics Letters, Elsevier, vol. 129(C), pages 45-48.
    14. Chotikapanich, Duangkamon & Griffiths, William E, 2002. "Estimating Lorenz Curves Using a Dirichlet Distribution," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 290-295, April.
    15. Maria Winkler-Dworak, 2003. "Food Security, Fertility Differentials and Land Degradation in Sub-Saharan Africa: A Dynamic Framework," VID Working Papers 0301, Vienna Institute of Demography (VID) of the Austrian Academy of Sciences in Vienna.
    16. Ogwang, Tomson & Rao, U. L. Gouranga, 2000. "Hybrid models of the Lorenz curve," Economics Letters, Elsevier, vol. 69(1), pages 39-44, October.
    17. 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.
    18. Rohde, Nicholas, 2009. "An alternative functional form for estimating the Lorenz curve," Economics Letters, Elsevier, vol. 105(1), pages 61-63, October.
    19. Helene, Otaviano, 2010. "Fitting Lorenz curves," Economics Letters, Elsevier, vol. 108(2), pages 153-155, August.
    20. Michel Lubrano & Zhou Xun, 2021. "The Bayesian approach to poverty measurement," Working Papers halshs-03234072, HAL.

    More about this item

    JEL classification:

    • D3 - Microeconomics - - Distribution
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

    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:revinw:v:57:y:2011:i:3:p:561-582. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/iariwea.html .

    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.