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A concept of negative dependence using stochastic ordering

Author

Listed:
  • Block, Henry W.
  • Savits, Thomas H.
  • Shaked, Moshe

Abstract

A concept of negative dependence called negative dependence by stochastic ordering is introduced. This concept satisfies various closure properties. It is shown that three models for negetive dependence satisfy it and that it implies the basic negative orthant inequalities. This concept is also satisfied by the multinomial, multivariate hypergeometric. Dirichlet and Dirichlet compound multinomial distributions. Furthermore, the joint distribution of ranks of a sample and the multivariate normal with nonpositive pairwise correlations also satisfy this condition. The positive dependence analog of this condition is also studied.

Suggested Citation

  • Block, Henry W. & Savits, Thomas H. & Shaked, Moshe, 1985. "A concept of negative dependence using stochastic ordering," Statistics & Probability Letters, Elsevier, vol. 3(2), pages 81-86, April.
    • Handle: RePEc:eee:stapro:v:3:y:1985:i:2:p:81-86
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    Citations

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    Cited by:

    1. Yuyu Chen & Seva Shneer, 2024. "Risk aggregation and stochastic dominance for a class of heavy-tailed distributions," Papers 2408.15033, arXiv.org, revised Dec 2024.
    2. Cai, Jun & Wei, Wei, 2012. "On the invariant properties of notions of positive dependence and copulas under increasing transformations," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 43-49.
    3. Chenguang (Allen) Wu & Achal Bassamboo & Ohad Perry, 2019. "Service System with Dependent Service and Patience Times," Management Science, INFORMS, vol. 65(3), pages 1151-1172, March.
    4. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2005. "Some notions of multivariate positive dependence," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 13-26, August.
    5. Bäuerle, Nicole & Glauner, Alexander, 2018. "Optimal risk allocation in reinsurance networks," Insurance: Mathematics and Economics, Elsevier, vol. 82(C), pages 37-47.
    6. Liyuan Lin & Ruodu Wang & Ruixun Zhang & Chaoyi Zhao, 2024. "The checkerboard copula and dependence concepts," Papers 2404.15023, arXiv.org, revised Feb 2025.
    7. Sordo, Miguel A. & Suárez-Llorens, Alfonso & Bello, Alfonso J., 2015. "Comparison of conditional distributions in portfolios of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 62-69.
    8. Jean-Gabriel Lauzier & Liyuan Lin & Ruodu Wang, 2023. "Pairwise counter-monotonicity," Papers 2302.11701, arXiv.org, revised May 2023.
    9. Yuyu Chen & Paul Embrechts & Ruodu Wang, 2024. "Risk exchange under infinite-mean Pareto models," Papers 2403.20171, arXiv.org.
    10. Saumard, Adrien & Wellner, Jon A., 2018. "Efron’s monotonicity property for measures on R2," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 212-224.
    11. Lauzier, Jean-Gabriel & Lin, Liyuan & Wang, Ruodu, 2023. "Pairwise counter-monotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 279-287.
    12. Cai, Jun & Wei, Wei, 2012. "Optimal reinsurance with positively dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 57-63.
    13. Franco Pellerey & Jorge Navarro, 2022. "Stochastic monotonicity of dependent variables given their sum," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 543-561, June.
    14. 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.
    15. repec:bpj:demode:v:6:y:2018:i:1:p:156-177:n:10 is not listed on IDEAS
    16. Qi-Man Shao, 2000. "A Comparison Theorem on Moment Inequalities Between Negatively Associated and Independent Random Variables," Journal of Theoretical Probability, Springer, vol. 13(2), pages 343-356, April.
    17. Nicole Bauerle & Alexander Glauner, 2017. "Optimal Risk Allocation in Reinsurance Networks," Papers 1711.10210, arXiv.org.
    18. Ortega-Jiménez, P. & Sordo, M.A. & Suárez-Llorens, A., 2021. "Stochastic orders and multivariate measures of risk contagion," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 199-207.
    19. Patricia Ortega-Jiménez & Miguel A. Sordo & Alfonso Suárez-Llorens, 2021. "Stochastic Comparisons of Some Distances between Random Variables," Mathematics, MDPI, vol. 9(9), pages 1-14, April.
    20. Daduna, Hans & Szekli, Ryszard, 1996. "A queueing theoretical proof of increasing property of Polya frequency functions," Statistics & Probability Letters, Elsevier, vol. 26(3), pages 233-242, February.
    21. Diwakar Gupta & Yigal Gerchak, 2002. "Quantifying Operational Synergies in a Merger/Acquisition," Management Science, INFORMS, vol. 48(4), pages 517-533, April.
    22. Taras Bodnar & Thorsten Dickhaus, 2017. "On the Simes inequality in elliptical models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 215-230, February.
    23. Chen Li & Xiaohu Li, 2018. "Preservation of increasing convex/concave order under the formation of parallel/series system of dependent components," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(4), pages 445-464, May.
    24. Block, Henry W. & Savits, Thomas H. & Wang, Jie & Sarkar, Sanat K., 2013. "The multivariate-t distribution and the Simes inequality," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 227-232.

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