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Multidimensional Stochastic Ordering and Associated Random Variables

Author

Listed:
  • François Baccelli

    (INRIA, Valbonne, France)

  • Armand M. Makowski

    (University of Maryland, College Park, Maryland)

Abstract

This paper presents several relationships between the concept of associated random variables (RVs) and notions of stochastic ordering. The question that provides the impetus for this work is whether the association of the ℝ-valued RVs { X 1 , …, X n } implies a possible stochastic ordering between the ℝ n -valued RV X ≔ ( X 1 , …, X n ) and its independent version X̄ ≔ ( X̄ 1 , …, X̄ n ). This leads to results on how multidimensional probability distributions are determined by conditions on their one-dimensional marginal distributions in the event of comparison under the stochastic orderings ≤ st , ≤ c1 , ≤ cv , ≤ D and ≤ K . Such results have direct implications for the comparison of bounds for Fork-Join queues and for the structure of monotone functions of several variables.

Suggested Citation

  • François Baccelli & Armand M. Makowski, 1989. "Multidimensional Stochastic Ordering and Associated Random Variables," Operations Research, INFORMS, vol. 37(3), pages 478-487, June.
    • Handle: RePEc:inm:oropre:v:37:y:1989:i:3:p:478-487
    DOI: 10.1287/opre.37.3.478
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    Citations

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    Cited by:

    1. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2006. "Some positive dependence stochastic orders," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 46-78, January.
    2. Savas Dayanik & Jing-Sheng Song & Susan H. Xu, 2003. "The Effectiveness of Several Performance Bounds for Capacitated Production, Partial-Order-Service, Assemble-to-Order Systems," Manufacturing & Service Operations Management, INFORMS, vol. 5(3), pages 230-251, December.
    3. Satya P. DAS & Chetan CHATE, 2001. "Endogenous Distribution, Politics, and Growth," LIDAM Discussion Papers IRES 2001019, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    4. Susan H. Xu & Haijun Li, 2000. "Majorization of Weighted Trees: A New Tool to Study Correlated Stochastic Systems," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 298-323, May.
    5. Prakasa Rao, B.L.S. & Singh, Harshinder, 2010. "Sufficient conditions for stochastic equality of two distributions under some partial orders," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 513-518, March.
    6. Arboretti, Rosa & Bonnini, Stefano & Corain, Livio & Salmaso, Luigi, 2014. "A permutation approach for ranking of multivariate populations," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 39-57.
    7. Susan H. Xu, 1999. "Structural Analysis of a Queueing System with Multiclasses of Correlated Arrivals and Blocking," Operations Research, INFORMS, vol. 47(2), pages 264-276, April.
    8. Li, Haijun & Xu, Susan H., 2001. "Stochastic Bounds and Dependence Properties of Survival Times in a Multicomponent Shock Model," Journal of Multivariate Analysis, Elsevier, vol. 76(1), pages 63-89, January.
    9. 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.
    10. Patrick B. Langthaler & Riccardo Ceccato & Luigi Salmaso & Rosa Arboretti & Arne C. Bathke, 2023. "Permutation testing for thick data when the number of variables is much greater than the sample size: recent developments and some recommendations," Computational Statistics, Springer, vol. 38(1), pages 101-132, March.

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