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On the New Notion of the Set-Expectation for a Random Set of Events

Author

Listed:
  • Vorobyev, Oleg Yu.
  • Vorobyev, Alexey O.

Abstract

The paper introduces new notion for the set-valued mean set of a random set. The means are defined as families of sets that minimize mean distances to the random set. The distances are determined by metrics in spaces of sets or by suitable generalizations. Some examples illustrate the use of the new definitions.

Suggested Citation

  • Vorobyev, Oleg Yu. & Vorobyev, Alexey O., 2003. "On the New Notion of the Set-Expectation for a Random Set of Events," MPRA Paper 17901, University Library of Munich, Germany, revised 27 Apr 2003.
  • Handle: RePEc:pra:mprapa:17901
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    File URL: https://mpra.ub.uni-muenchen.de/17901/1/MPRA_paper_17901.pdf
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    Cited by:

    1. Vorobyev, Oleg, 2009. "Eventology versus contemporary theories of uncertainty," MPRA Paper 13961, University Library of Munich, Germany.

    More about this item

    Keywords

    mean random set; metrics in set space; mean distance; Aumann expectation; Frechet expectation; Hausdorff metric; random finite set; mean set; set-median; set-expectation;

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics

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