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On Order-Preserving Properties of Probability Metrics

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  • Claude Lefèvre
  • Sergey Utev

Abstract

Stochastic orders and probability metrics are two areas that have received considerable attention in recent literature. A question of interest on its own and for certain applications is the preservation of metrics with respect to orders. This property does not seem to have been examined explicitly so far. Our purpose in this paper is to provide some useful remarks and results related to several orders and metrics which are standard in probability.

Suggested Citation

  • Claude Lefèvre & Sergey Utev, 1998. "On Order-Preserving Properties of Probability Metrics," Journal of Theoretical Probability, Springer, vol. 11(4), pages 907-920, October.
    • Handle: RePEc:spr:jotpro:v:11:y:1998:i:4:d:10.1023_a:1022608613982
    DOI: 10.1023/A:1022608613982
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    References listed on IDEAS

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    1. De Pril, Nelson & Dhaene, Jan, 1992. "Error Bounds for Compound Poisson Approximations of the Individual Risk Model," ASTIN Bulletin, Cambridge University Press, vol. 22(2), pages 135-148, November.
    2. Lefèvre, Claude & Utev, Sergei, 1997. "Mixed Poisson approximation in the collective epidemic model," Stochastic Processes and their Applications, Elsevier, vol. 69(2), pages 217-246, September.
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