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The Gini mean difference and variance

Author

Listed:
  • Roberta La Haye

    (Mount Royal University)

  • Petr Zizler

    (Mount Royal University)

Abstract

A quick, alternate proof is given for a previously known inequality relating the standard deviation and the Gini mean difference. The inequality is sharpened and generalized to higher, even moments. Further inequalities are derived that involve the standard deviation, higher Ginis and order statistics.

Suggested Citation

  • Roberta La Haye & Petr Zizler, 2019. "The Gini mean difference and variance," METRON, Springer;Sapienza Università di Roma, vol. 77(1), pages 43-52, April.
    • Handle: RePEc:spr:metron:v:77:y:2019:i:1:d:10.1007_s40300-019-00149-2
    DOI: 10.1007/s40300-019-00149-2
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    References listed on IDEAS

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    1. 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.
    2. Walter Piesch, 2005. "A look at the structure of some extended Ginis," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 263-296.
    3. 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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    Cited by:

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