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Characterization of a Marshall-Olkin type class of distributions

Author

Listed:
  • 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])

  • Pietro Muliere

Abstract

A class of bivariate distributions that generalize Marshall-Olkin's one is characterized through a functional equation which involves two associative operations. The obtained distributions concentrate positive mass on the linex=y when the two associative operations coincide; otherwise a positive mass is concentrated on a continuous monotone function.

Suggested Citation

  • Marco Scarsini & Pietro Muliere, 1987. "Characterization of a Marshall-Olkin type class of distributions," Post-Print hal-00542248, HAL.
    • Handle: RePEc:hal:journl:hal-00542248
    DOI: 10.1007/BF02491480
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    Citations

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    Cited by:

    1. Sloot Henrik, 2020. "The deFinetti representation of generalised Marshall–Olkin sequences," Dependence Modeling, De Gruyter, vol. 8(1), pages 107-118, January.
    2. Alfred Müller & Marco Scarsini, 2001. "Stochastic Comparison of Random Vectors with a Common Copula," Mathematics of Operations Research, INFORMS, vol. 26(4), pages 723-740, November.
    3. Matthias Scherer & Henrik Sloot, 2019. "Exogenous shock models: analytical characterization and probabilistic construction," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(8), pages 931-959, November.
    4. Umberto Cherubini & Sabrina Mulinacci, 2021. "Hierarchical Archimedean Dependence in Common Shock Models," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 143-163, March.
    5. Jianhua Lin & Xiaohu Li, 2014. "Multivariate Generalized Marshall–Olkin Distributions and Copulas," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 53-78, March.
    6. Haijun Li, 2008. "Tail Dependence Comparison of Survival Marshall–Olkin Copulas," Methodology and Computing in Applied Probability, Springer, vol. 10(1), pages 39-54, March.
    7. Sabrina Mulinacci, 2018. "Archimedean-based Marshall-Olkin Distributions and Related Dependence Structures," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 205-236, March.
    8. Sloot Henrik, 2020. "The deFinetti representation of generalised Marshall–Olkin sequences," Dependence Modeling, De Gruyter, vol. 8(1), pages 107-118, January.

    More about this item

    Keywords

    Probability law; Bivariate distribution;

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