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A general theory of some positive dependence notions

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  • Shaked, Moshe

Abstract

A general theory of concepts of positive dependence, which are weaker than association but stronger than orthant dependence, is developed. A random vector X is associated if and only if P(X [set membership, variant] A [down curve] B) >= P(X [set membership, variant] A) P(X [set membership, variant] B) for all open upper sets A and B. By requiring the above inequality to hold only for some open upper sets A and B various notions of positive dependence which are weaker than association are obtained. First a general theory is given and then the results are specialized to some concepts of a particular interest. Various properties and interrelationships are derived and some applications are discussed.

Suggested Citation

  • Shaked, Moshe, 1982. "A general theory of some positive dependence notions," Journal of Multivariate Analysis, Elsevier, vol. 12(2), pages 199-218, June.
    • Handle: RePEc:eee:jmvana:v:12:y:1982:i:2:p:199-218
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    Citations

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    Cited by:

    1. Finkelstein, M. S., 2003. "On one class of bivariate distributions," Statistics & Probability Letters, Elsevier, vol. 65(1), pages 1-6, October.
    2. Marcello Basili & Paulo Casaca & Alain Chateauneuf & Maurizio Franzini, 2017. "Multidimensional Pigou–Dalton transfers and social evaluation functions," Theory and Decision, Springer, vol. 83(4), pages 573-590, December.
    3. Enrique de Amo & María del Rosario Rodríguez-Griñolo & Manuel Úbeda-Flores, 2024. "Directional Dependence Orders of Random Vectors," Mathematics, MDPI, vol. 12(3), pages 1-14, January.
    4. 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.
    5. Zhang, Xiaoyu & Xu, Maochao & Su, Jianxi & Zhao, Peng, 2023. "Structural models for fog computing based internet of things architectures with insurance and risk management applications," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1273-1291.
    6. Baek, Jong-Il, 1997. "A weakly dependence structure of multivariate processes," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 355-363, June.
    7. Roy, Dilip & Mukherjee, S. P., 1998. "Multivariate Extensions of Univariate Life Distributions," Journal of Multivariate Analysis, Elsevier, vol. 67(1), pages 72-79, October.
    8. Huang, Wen-Tao & Xu, Bing, 2002. "Some maximal inequalities and complete convergences of negatively associated random sequences," Statistics & Probability Letters, Elsevier, vol. 57(2), pages 183-191, April.
    9. Holzer, Jorge & Olson, Lars J., 2021. "Precautionary buffers and stochastic dependence in environmental policy," Journal of Environmental Economics and Management, Elsevier, vol. 106(C).
    10. Sanders, Lisanne & Melenberg, Bertrand, 2016. "Estimating the joint survival probabilities of married individuals," Insurance: Mathematics and Economics, Elsevier, vol. 67(C), pages 88-106.
    11. Sanders, E.A.T., 2011. "Annuity market imperfections," Other publications TiSEM 227f9684-ccba-4646-99bc-3, Tilburg University, School of Economics and Management.
    12. Dilip Roy, 2004. "Bivariate models from univariate life distributions: A characterization cum modeling approach," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(5), pages 741-754, August.

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