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On the theory of high convexity stochastic orders

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  • Denuit, Michel
  • Lefèvre, Claude
  • Shaked, Moshe

Abstract

The purpose of this note is two-fold. First we derive a simple condition under which two s-convex ordered random variables must be stochastically equal, and we indicate the potential usefulness of this result in statistics. Then we highlight the relationship between the canonical moments and the extremal distributions in the s-convex sense, and we indicate how the canonical moments can be computed using the moments of these extremal distributions.

Suggested Citation

  • Denuit, Michel & Lefèvre, Claude & Shaked, Moshe, 2000. "On the theory of high convexity stochastic orders," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 287-293, April.
    • Handle: RePEc:eee:stapro:v:47:y:2000:i:3:p:287-293
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    References listed on IDEAS

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    1. Marco Scarsini, 1998. "Multivariate convex orderings, dependence, and stochastic equality," Post-Print hal-00541775, HAL.
    2. Li, Haijun & Zhu, Haolong, 1994. "Stochastic equivalence of ordered random variables with applications in reliability theory," Statistics & Probability Letters, Elsevier, vol. 20(5), pages 383-393, August.
    3. J. Huang & G. Lin, 1999. "Equality in Distribution in a Convex Ordering Family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(2), pages 345-349, June.
    4. Denuit, Michel & Vylder, Etienne De & Lefevre, Claude, 1999. "Extremal generators and extremal distributions for the continuous s-convex stochastic orderings," Insurance: Mathematics and Economics, Elsevier, vol. 24(3), pages 201-217, May.
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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.

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