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Transformations that minimize the Gini index of a random variable and applications

Author

Listed:
  • Michael McAsey

    (Bradley University)

  • Libin Mou

    (Bradley University)

Abstract

Let X be a continuous or discrete random variable with values in [0,M] and consider all functions (here called transformations) q : [ 0 , M ] → [ 0 , ∞ ) $q:[0,M]\to [0,\infty )$ that are increasing and have given bounded rates B ≤ q ( v ) − q ( u ) v − u ≤ A $B \le \frac {q(v)-q(u)}{v-u} \le A$ for u

Suggested Citation

  • Michael McAsey & Libin Mou, 2022. "Transformations that minimize the Gini index of a random variable and applications," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 20(2), pages 483-502, June.
    • Handle: RePEc:spr:joecin:v:20:y:2022:i:2:d:10.1007_s10888-021-09508-4
    DOI: 10.1007/s10888-021-09508-4
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    References listed on IDEAS

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    1. Carbonell-Nicolau, Oriol & Llavador, Humberto, 2018. "Inequality reducing properties of progressive income tax schedules: the case of endogenous income," Theoretical Economics, Econometric Society, vol. 13(1), January.
    2. Oriol Carbonell-Nicolau & Humberto Llavador, 2018. "Further Results on the Inequality Reducing Properties of Income Tax Schedules," Departmental Working Papers 201801, Rutgers University, Department of Economics.
    3. Johan Fellman & Markus Jäntti & Peter J. Lambert, 1999. "Optimal Tax‐Transfer Systems and Redistributive Policy," Scandinavian Journal of Economics, Wiley Blackwell, vol. 101(1), pages 115-126, March.
    4. Fellman, J, 1976. "The Effect of Transformations on Lorenz Curves," Econometrica, Econometric Society, vol. 44(4), pages 823-824, July.
    5. Kakwani, Nanak C, 1977. "Applications of Lorenz Curves in Economic Analysis," Econometrica, Econometric Society, vol. 45(3), pages 719-727, April.
    6. Fellman, Johan & Jantti, Markus & Lambert, Peter J, 1999. " Optimal Tax-Transfer Systems and Redistributive Policy," Scandinavian Journal of Economics, Wiley Blackwell, vol. 101(1), pages 115-126, March.
    7. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    8. Fellman, Johan, 2001. "Mathematical properties of classes of income redistributive policies," European Journal of Political Economy, Elsevier, vol. 17(1), pages 179-192, March.
    9. Jakobsson, Ulf, 1976. "On the measurement of the degree of progression," Journal of Public Economics, Elsevier, vol. 5(1-2), pages 161-168.
    10. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
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