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Variability orders and mean differences

Author

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  • Marco Scarsini

    (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique, Dipartimento di Scienze Economiche e Aziendali - LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma])

  • Bruno Bassan
  • Michel Denuit

Abstract

Several well-known stochastic orderings are defined in terms of iterated integrals of distribution or survival functions. In this note we will provide necessary conditions for some variability orderings of the above type. These conditions will be based on the comparison of mean differences, which will be written by using the iterated integrals of survival and distribution functions. An interesting by-product of this idea is a curious formula for the variance. A bivariate version of the above results will be provided, as well.

Suggested Citation

  • Marco Scarsini & Bruno Bassan & Michel Denuit, 1999. "Variability orders and mean differences," Post-Print hal-00540242, HAL.
    • Handle: RePEc:hal:journl:hal-00540242
    DOI: 10.1016/S0167-7152(99)00050-4
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    References listed on IDEAS

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    1. Ekern, Steinar, 1980. "Increasing Nth degree risk," Economics Letters, Elsevier, vol. 6(4), pages 329-333.
    2. Fishburn, Peter C., 1976. "Continua of stochastic dominance relations for bounded probability distributions," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 295-311, December.
    3. Peter C. Fishburn, 1980. "Stochastic Dominance and Moments of Distributions," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 94-100, February.
    4. Kochar, Subhash C. & Carrière, K. C., 1997. "Connections among various variability orderings," Statistics & Probability Letters, Elsevier, vol. 35(4), pages 327-333, November.
    5. Fishburn, Peter C., 1980. "Continua of stochastic dominance relations for unbounded probability distributions," Journal of Mathematical Economics, Elsevier, vol. 7(3), pages 271-285, December.
    6. Denuit, Michel & Lefevre, Claude & Mesfioui, M'hamed, 1999. "A class of bivariate stochastic orderings, with applications in actuarial sciences," Insurance: Mathematics and Economics, Elsevier, vol. 24(1-2), pages 31-50, March.
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    Cited by:

    1. Capaldo, Marco & Di Crescenzo, Antonio & Pellerey, Franco, 2024. "Generalized Gini’s mean difference through distortions and copulas, and related minimizing problems," Statistics & Probability Letters, Elsevier, vol. 206(C).
    2. Jones, M.C., 2019. "Inverting Khintchine’s relationship and generating length biased data," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    3. Klimczak, Monika & Rychlik, Tomasz, 2004. "Maximum variance of Kth records," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 421-430, October.
    4. Taizhong Hu & Asok K. Nanda & Huiliang Xie & Zegang Zhu, 2004. "Properties of some stochastic orders: A unified study," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(2), pages 193-216, March.
    5. Patricia Ortega-Jiménez & Miguel A. Sordo & Alfonso Suárez-Llorens, 2021. "Stochastic Comparisons of Some Distances between Random Variables," Mathematics, MDPI, vol. 9(9), pages 1-14, April.

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