IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-02901877.html
   My bibliography  Save this paper

A nice estimation of Gini index and power Pen's parade

Author

Listed:
  • Jules Sadefo-Kamdem

    (LAMETA - Laboratoire Montpelliérain d'Économie Théorique et Appliquée - UM1 - Université Montpellier 1 - UPVM - Université Paul-Valéry - Montpellier 3 - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

Abstract

Under the assumption that an economic variable y such as income, is a power function of its rank among n individuals, we provide the coefficient of variation and the Gini index as functions of the power degree of the Pen's parade. In fact, knowing the power degree of the Pen's parade function, we obtain the coefficient of variation and a sharp analytical simple way to compute Gini index in terms of the power degree. Reciprocally, knowing, the coefficient of variation of a said variable, we can also provide the power degree of the corresponding Pen's parade, hence deducting its shape. Several examples are given to illustrate our methods. Special attention is given to countries' Gini indices of the World development indicators report 2009 (WDI 2009).

Suggested Citation

  • Jules Sadefo-Kamdem, 2012. "A nice estimation of Gini index and power Pen's parade," Post-Print hal-02901877, HAL.
    • Handle: RePEc:hal:journl:hal-02901877
    DOI: 10.1016/j.econmod.2012.03.015
    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. World Bank, 2009. "World Development Indicators 2009," World Bank Publications - Books, The World Bank Group, number 4367, December.
    2. Stéphane Mussard & J. Sadefo Kamdem & Françoise Seyte & Michel Terraza, 2011. "Quadratic Pen'S Parade And The Computation Of The Gini Index," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 57(3), pages 583-587, September.
    3. Gastwirth, Joseph L, 1972. "The Estimation of the Lorenz Curve and Gini Index," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 306-316, August.
    4. Shalit, Haim & Yitzhaki, Shlomo, 1984. "Mean-Gini, Portfolio Theory, and the Pricing of Risky Assets," Journal of Finance, American Finance Association, vol. 39(5), pages 1449-1468, December.
    5. Tomson Ogwang, 2011. "QUADRATIC PEN's PARADES: SOME NEW RESULTS AND AN APPLICATION," Working Papers 1101, Brock University, Department of Economics, revised Dec 2011.
    6. Milanovic, Branko, 1997. "A simple way to calculate the Gini coefficient, and some implications," Economics Letters, Elsevier, vol. 56(1), pages 45-49, September.
    7. Lerman, Robert I. & Yitzhaki, Shlomo, 1984. "A note on the calculation and interpretation of the Gini index," Economics Letters, Elsevier, vol. 15(3-4), pages 363-368.
    8. Yitzhaki, Shlomo, 1982. "Stochastic Dominance, Mean Variance, and Gini's Mean Difference," American Economic Review, American Economic Association, vol. 72(1), pages 178-185, March.
    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. Shao-Hsun Keng & Peter F. Orazem, 2019. "Performance pay, the marriage market and rising income inequality in Taiwan," Review of Economics of the Household, Springer, vol. 17(3), pages 969-992, September.

    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. David Shaffer & Andrea DeMaskey, 2005. "Currency Hedging Using the Mean-Gini Framework," Review of Quantitative Finance and Accounting, Springer, vol. 25(2), pages 125-137, September.
    2. Schechtman, Edna & Yitzhaki, Shlomo, 1985. "A Measure of Association Based on Gini's Mean Difference," Working Papers 232621, Hebrew University of Jerusalem, Center for Agricultural Economic Research.
    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.
    4. Yves Tillé, 2016. "The legacy of Corrado Gini in survey sampling and inequality theory," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 167-176, August.
    5. Fontanari, Andrea & Cirillo, Pasquale & Oosterlee, Cornelis W., 2018. "From Concentration Profiles to Concentration Maps. New tools for the study of loss distributions," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 13-29.
    6. Wetzstein, Michael E. & Szmedra, Philip I. & McClendon, Ronald W. & Edwards, David M., 1988. "Efficiency Criteria And Risk Aversion: An Empirical Evaluation," Southern Journal of Agricultural Economics, Southern Agricultural Economics Association, vol. 20(1), pages 1-8, July.
    7. Miguel A. Lejeune & John Turner, 2019. "Planning Online Advertising Using Gini Indices," Operations Research, INFORMS, vol. 67(5), pages 1222-1245, September.
    8. Shalit, Haim & Yitzhaki, Shlomo, 1985. "Evaluating the Mean-Gini Approach to Portfolio Selection," Working Papers 232632, Hebrew University of Jerusalem, Center for Agricultural Economic Research.
    9. Blavatskyy, Pavlo, 2016. "Probability weighting and L-moments," European Journal of Operational Research, Elsevier, vol. 255(1), pages 103-109.
    10. Zhenlong Jiang & Ran Ji & Kuo-Chu Chang, 2020. "A Machine Learning Integrated Portfolio Rebalance Framework with Risk-Aversion Adjustment," JRFM, MDPI, vol. 13(7), pages 1-20, July.
    11. Maria-Teresa Bosch-Badia & Joan Montllor-Serrats & Maria-Antonia Tarrazon-Rodon, 2017. "Analysing assets’ performance inside a portfolio: From crossed beta to the net risk premium ratio," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1270251-127, January.
    12. Shao-Hsun Keng & Peter F. Orazem, 2019. "Performance pay, the marriage market and rising income inequality in Taiwan," Review of Economics of the Household, Springer, vol. 17(3), pages 969-992, September.
    13. Ran Ji & Miguel A. Lejeune & Srinivas Y. Prasad, 2017. "Properties, formulations, and algorithms for portfolio optimization using Mean-Gini criteria," Annals of Operations Research, Springer, vol. 248(1), pages 305-343, January.
    14. Peter Martey Addo & Dominique Guegan & Bertrand Hassani, 2018. "Credit Risk Analysis using Machine and Deep Learning models," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01719983, HAL.
    15. Peter Martey Addo & Dominique Guegan & Bertrand Hassani, 2018. "Credit Risk Analysis using Machine and Deep Learning models," Post-Print halshs-01719983, HAL.
    16. Peiheng Yu & Izzy Yi Jian & Esther H. K. Yung & Edwin H. W. Chan & Man Sing Wong & Yiyun Chen, 2023. "Spatial Vertical Equity in Public General Hospitals: Towards a Sustainable Healthcare System," Land, MDPI, vol. 12(8), pages 1-15, July.
    17. Lifeng Wang & Jinwu Gao & Hamed Ahmadzade & Zezhou Zou, 2023. "Partial Gini Coefficient for Uncertain Random Variables with Application to Portfolio Selection," Mathematics, MDPI, vol. 11(18), pages 1-18, September.
    18. Simone Pellegrino, 2020. "The Gini Coefficient: Its Origins," Working papers 070, Department of Economics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino.
    19. Stéphane Mussard & J. Sadefo Kamdem & Françoise Seyte & Michel Terraza, 2011. "Quadratic Pen'S Parade And The Computation Of The Gini Index," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 57(3), pages 583-587, September.
    20. Peter Martey Addo & Dominique Guegan & Bertrand Hassani, 2018. "Credit Risk Analysis Using Machine and Deep Learning Models," Risks, MDPI, vol. 6(2), pages 1-20, April.

    More about this item

    Keywords

    Applied econometrics; Development economics; Gini index; Income inequality; Pen's parade; World development indicators;
    All these keywords.

    JEL classification:

    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

    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:hal:journl:hal-02901877. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.