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Dispersion measures and dispersive orderings

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  • Ramos, Héctor M.
  • Sordo, Miguel A.
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    Abstract

    In this paper, the comparison of random variables according to the functionals of a general class of dispersion measures is characterized in terms of the dilation order. The Gini's mean difference is a particular member of this general class. In addition, a new and weaker order, called the second-order absolute Lorenz ordering, is introduced, and we judge random variables according to certain functionals of this class when the dilation order is not available.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 61 (2003)
    Issue (Month): 2 (January)
    Pages: 123-131

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    Handle: RePEc:eee:stapro:v:61:y:2003:i:2:p:123-131

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    Related research

    Keywords: Dispersion measures Dilation ordering Second-order absolute Lorenz ordering Absolute Lorenz curve;

    References

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    1. Yitzhaki, Shlomo, 1982. "Stochastic Dominance, Mean Variance, and Gini's Mean Difference," American Economic Review, American Economic Association, vol. 72(1), pages 178-85, March.
    2. Moyes, Patrick, 1987. "A new concept of Lorenz domination," Economics Letters, Elsevier, vol. 23(2), pages 203-207.
    3. W. Sendler, 1979. "On statistical inference in concentration measurement," Metrika, Springer, vol. 26(1), pages 109-122, December.
    4. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-09, July.
    5. Newbery, David, 1970. "A theorem on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 264-266, September.
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    Cited by:
    1. Sordo, Miguel A., 2008. "Characterizations of classes of risk measures by dispersive orders," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1028-1034, June.
    2. Miguel Sordo & Héctor Ramos, 2007. "Characterization of stochastic orders by L-functionals," Statistical Papers, Springer, vol. 48(2), pages 249-263, April.
    3. López-Díaz, Miguel & Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2012. "On the Lp-metric between a probability distribution and its distortion," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 257-264.
    4. Sordo, Miguel A., 2009. "Comparing tail variabilities of risks by means of the excess wealth order," Insurance: Mathematics and Economics, Elsevier, vol. 45(3), pages 466-469, December.

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