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Gini’s Mean difference: a superior measure of variability for non-normal distributions

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  • Shlomo Yitzhaki

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  • 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.
  • Handle: RePEc:mtn:ancoec:030208
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    File URL: ftp://metron.sta.uniroma1.it/RePEc/articoli/2003-2-285-316.pdf
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    References listed on IDEAS

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    1. Yitzhaki, Shlomo & Slemrod, Joel, 1991. "Welfare Dominance: An Application to Commodity Taxation," American Economic Review, American Economic Association, vol. 81(3), pages 480-496, June.
    2. 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.
    3. Anthony F. Shorrocks, 1983. "The Impact of Income Components on the Distribution of Family Incomes," The Quarterly Journal of Economics, Oxford University Press, vol. 98(2), pages 311-326.
    4. Russell Davidson & Jean-Yves Duclos, 1997. "Statistical Inference for the Measurement of the Incidence of Taxes and Transfers," Econometrica, Econometric Society, vol. 65(6), pages 1453-1466, November.
    5. Bishop, John A & Formby, John P & Thistle, Paul D, 1992. "Convergence of the South and Non-South Income Distributions, 1969-1979," American Economic Review, American Economic Association, vol. 82(1), pages 262-272, March.
    6. Dale W. Jorgenson & Daniel T. Slesnick, 1984. "Aggregate Consumer Behaviour and the Measurement of Inequality," Review of Economic Studies, Oxford University Press, vol. 51(3), pages 369-392.
    7. Suits, Daniel B, 1977. "Measurement of Tax Progressivity," American Economic Review, American Economic Association, vol. 67(4), pages 747-752, September.
    8. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
    9. Milanovic, Branko & Yitzhaki, Shlomo, 2002. "Decomposing World Income Distribution: Does the World Have a Middle Class?," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 48(2), pages 155-178, June.
    10. McKenzie, G W & Pearce, I F, 1982. "Welfare Measurement-A Synthesis," American Economic Review, American Economic Association, vol. 72(4), pages 669-682, September.
    11. Haim Levy, 1992. "Stochastic Dominance and Expected Utility: Survey and Analysis," Management Science, INFORMS, vol. 38(4), pages 555-593, April.
    12. Yitzhaki, Shlomo, 1983. "On an Extension of the Gini Inequality Index," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 617-628, October.
    13. Yitzhaki, Shlomo & Lerman, Robert I, 1991. "Income Stratification and Income Inequality," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 37(3), pages 313-329, September.
    14. Yitzhaki, Shlomo, 1990. "On the Sensitivity of a Regression Coefficient to Monotonic Transformations," Econometric Theory, Cambridge University Press, vol. 6(02), pages 165-169, June.
    15. Kakwani, Nanak C, 1977. "Applications of Lorenz Curves in Economic Analysis," Econometrica, Econometric Society, vol. 45(3), pages 719-727, April.
    16. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Oxford University Press, vol. 36(3), pages 335-346.
    17. Rockinger, M. & Jondeau, E., 2001. "Conditional Dependency of Financial Series: An Application of Copulas," Working papers 82, Banque de France.
    18. Haim Shalit & Shlomo Yitzhaki, 2005. "The Mean-Gini Efficient Portfolio Frontier," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 28(1), pages 59-75.
    19. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    20. Silber, Jacques, 1989. "Factor Components, Population Subgroups and the Computation of the Gini Index of Inequality," The Review of Economics and Statistics, MIT Press, vol. 71(1), pages 107-115, February.
    21. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    22. Grether, David M., 1974. "Correlations with ordinal data," Journal of Econometrics, Elsevier, vol. 2(3), pages 241-246, September.
    23. Levy, H & Markowtiz, H M, 1979. "Approximating Expected Utility by a Function of Mean and Variance," American Economic Review, American Economic Association, vol. 69(3), pages 308-317, June.
    24. Dagum, Camilo, 1987. "Measuring the Economic Affluence between Populations of Income Receivers," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(1), pages 5-12, January.
    25. 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.
    26. Yitzhaki, Shlomo, 1994. "Economic distance and overlapping of distributions," Journal of Econometrics, Elsevier, vol. 61(1), pages 147-159, March.
    27. E. Schechtman & S. Yitzhaki, 2003. "A Family of Correlation Coefficients Based on the Extended Gini Index," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 1(2), pages 129-146, August.
    28. Schechtman, E. & Yitzhaki, S., 1999. "On the proper bounds of the Gini correlation," Economics Letters, Elsevier, vol. 63(2), pages 133-138, May.
    29. Yitzhaki, Shlomo, 1996. "On Using Linear Regressions in Welfare Economics," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 478-486, October.
    30. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
    31. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," Review of Economic Studies, Oxford University Press, vol. 50(4), pages 723-735.
    32. Yaari, Menahem E., 1988. "A controversial proposal concerning inequality measurement," Journal of Economic Theory, Elsevier, vol. 44(2), pages 381-397, April.
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    Citations

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    Cited by:

    1. M. Grazia Pittau & Shlomo Yitzhaki & Roberto Zelli, 2015. "The “Make-up” of a Regression Coefficient: Gender Gaps in the European Labor Market," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 61(3), pages 401-421, September.
    2. repec:spr:metrik:v:80:y:2017:i:6:d:10.1007_s00184-017-0620-5 is not listed on IDEAS
    3. Casey J. Dawkins, 2007. "Space And The Measurement Of Income Segregation," Journal of Regional Science, Wiley Blackwell, vol. 47(2), pages 255-272.
    4. Edna Schechtman & Shlomo Yitzhaki & Taina Pudalov, 2011. "Gini’s multiple regressions: two approaches and their interaction," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 67-99.
    5. Yoel Finkel & Yevgeny Artsev & Shlomo Yitzhaki, 2006. "Inequality measurement and the time structure of household income in Israel," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 4(2), pages 153-179, August.
    6. Stéphane Mussard & Fattouma Souissi-Benrejab, 2015. "Gini-PLS Regressions," Working Papers 15-03, LAMETA, Universitiy of Montpellier, revised Feb 2015.
      • Stephane Mussard & Fattouma Souissi-Benrejab, 2015. "Gini-PLS Regressions," Cahiers de recherche 17-02, Departement d'Economique de l'École de gestion à l'Université de Sherbrooke, revised Jan 2017.
    7. Shelef, Amit, 2016. "A Gini-based unit root test," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 763-772.
    8. Carina Gerstenberger & Daniel Vogel, 2015. "On the efficiency of Gini’s mean difference," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(4), pages 569-596, November.
    9. N. Nair & P. Sankaran & B. Vineshkumar, 2012. "Characterization of distributions by properties of truncated Gini index and mean difference," METRON, Springer;Sapienza Università di Roma, vol. 70(2), pages 173-191, August.
    10. Erreygers, Guido, 2009. "Can a single indicator measure both attainment and shortfall inequality?," Journal of Health Economics, Elsevier, vol. 28(4), pages 885-893, July.
    11. repec:spr:soinre:v:133:y:2017:i:1:d:10.1007_s11205-016-1354-x is not listed on IDEAS
    12. Ndéné Ka & Stéphane Mussard, 2016. "ℓ 1 regressions: Gini estimators for fixed effects panel data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(8), pages 1436-1446, June.
    13. Greselin, Francesca & Zitikis, Ricardas, 2015. "Measuring economic inequality and risk: a unifying approach based on personal gambles, societal preferences and references," MPRA Paper 65892, University Library of Munich, Germany.
    14. Stefania Capecchi & Maria Iannario, 2016. "Gini heterogeneity index for detecting uncertainty in ordinal data surveys," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 223-232, August.
    15. repec:gam:jecnmx:v:6:y:2018:i:1:p:4-:d:128699 is not listed on IDEAS
    16. Shlomo Yitzhaki & Peter Lambert, 2014. "Is higher variance necessarily bad for investment?," Review of Quantitative Finance and Accounting, Springer, vol. 43(4), pages 855-860, November.
    17. Klein, Ingo & Mangold, Benedikt, 2015. "Cumulative Paired ," FAU Discussion Papers in Economics 07/2015, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    18. Shlomo Yitzhaki & Peter Lambert, 2013. "The relationship between the absolute deviation from a quantile and Gini’s mean difference," METRON, Springer;Sapienza Università di Roma, vol. 71(2), pages 97-104, September.
    19. M. Grazia Pittau & Shlomo Yitzhaki & Roberto Zelli, 2011. "The make-up of a regression coefficient: An application to gender," DSS Empirical Economics and Econometrics Working Papers Series 2011/3, Centre for Empirical Economics and Econometrics, Department of Statistics, "Sapienza" University of Rome.
    20. Shlomo Yitzhaki & Edna Schechtman, 2004. "The Gini Instrumental Variable, or the “double instrumental variable” estimator," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 287-313.
    21. Ndene Ka & Stephane Mussard, 2015. "l1 Regressions: Gini Estimators for Fixed Effects Panel Data," Cahiers de recherche 15-02, Departement d'Economique de l'École de gestion à l'Université de Sherbrooke.
    22. Elsayed Amir, 2012. "On uses of mean absolute deviation: decomposition, skewness and correlation coefficients," METRON, Springer;Sapienza Università di Roma, vol. 70(2), pages 145-164, August.

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