IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v61y1997i1p86-101.html
   My bibliography  Save this article

Supermodular Stochastic Orders and Positive Dependence of Random Vectors

Author

Listed:
  • Shaked, Moshe
  • Shanthikumar, J. George

Abstract

The supermodular and the symmetric supermodular stochastic orders have been cursorily studied in previous literature. In this paper we study these orders more thoroughly. First we obtain some basic properties of these orders. We then apply these results in order to obtain comparisons of random vectors with common values, but with different levels of multiplicity. Specifically, we show that if the vectors of the levels of multiplicity are ordered in the majorization order, then the associated random vectors are ordered in the symmetric supermodular stochastic order. In the non-symmetric case we obtain bounds (in the supermodular stochastic order sense) on such random vectors. Finally, we apply the results to problems of optimal assembly of reliability systems, of optimal allocation of minimal repair efforts, and of optimal allocation of reliability items.

Suggested Citation

  • Shaked, Moshe & Shanthikumar, J. George, 1997. "Supermodular Stochastic Orders and Positive Dependence of Random Vectors," Journal of Multivariate Analysis, Elsevier, vol. 61(1), pages 86-101, April.
    • Handle: RePEc:eee:jmvana:v:61:y:1997:i:1:p:86-101
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(97)91656-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
    2. Shaked, M. & Shanthikumar, J. G. & Tong, Y. L., 1995. "Parametric Schur Convexity and Arrangement Monotonicity Properties of Partial Sums," Journal of Multivariate Analysis, Elsevier, vol. 53(2), pages 293-310, May.
    3. Block, Henry W. & Sampson, Allan R., 1988. "Conditionally ordered distributions," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 91-104, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Müller, Alfred & Scarsini, Marco, 2000. "Some Remarks on the Supermodular Order," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 107-119, April.
    2. Mehdi Amiri & Narayanaswamy Balakrishnan & Abbas Eftekharian, 2022. "Hessian orderings of multivariate normal variance-mean mixture distributions and their applications in evaluating dependent multivariate risk portfolios," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(3), pages 679-707, September.
    3. Samanthi, Ranadeera Gamage Madhuka & Wei, Wei & Brazauskas, Vytaras, 2016. "Ordering Gini indexes of multivariate elliptical risks," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 84-91.
    4. Koen Decancq, 2020. "Measuring cumulative deprivation and affluence based on the diagonal dependence diagram," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 103-117, August.
    5. Ho-Yin Mak & Zuo-Jun Max Shen, 2014. "Pooling and Dependence of Demand and Yield in Multiple-Location Inventory Systems," Manufacturing & Service Operations Management, INFORMS, vol. 16(2), pages 263-269, May.
    6. Di Bernardino Elena & Rullière Didier, 2016. "On an asymmetric extension of multivariate Archimedean copulas based on quadratic form," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-20, December.
    7. Koen Decancq, 2014. "Copula-based measurement of dependence between dimensions of well-being," Oxford Economic Papers, Oxford University Press, vol. 66(3), pages 681-701.
    8. Grothe, Oliver & Schnieders, Julius & Segers, Johan, 2013. "Measuring Association and Dependence Between Random Vectors," LIDAM Discussion Papers ISBA 2013026, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Ansari, Jonathan & Rüschendorf, Ludger, 2021. "Ordering results for elliptical distributions with applications to risk bounds," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    10. Deng, Wenli & Wang, Jinglong & Zhang, Riquan, 2022. "Measures of concordance and testing of independence in multivariate structure," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    11. Roger Nelsen & Manuel Úbeda-Flores, 2012. "Directional dependence in multivariate distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 677-685, June.
    12. Ma, Chunsheng, 2000. "ISO* Property of Two-Parameter Compound Poisson Distributions with Applications," Journal of Multivariate Analysis, Elsevier, vol. 75(2), pages 279-294, November.
    13. Meyer, Margaret & Strulovici, Bruno, 2012. "Increasing interdependence of multivariate distributions," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1460-1489.
    14. Pérez, Ana & Prieto-Alaiz, Mercedes, 2016. "A note on nonparametric estimation of copula-based multivariate extensions of Spearman’s rho," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 41-50.
    15. Włodzimierz Wysocki, 2015. "Kendall's tau and Spearman's rho for n -dimensional Archimedean copulas and their asymptotic properties," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(4), pages 442-459, December.
    16. Cooray Kahadawala, 2018. "Strictly Archimedean copulas with complete association for multivariate dependence based on the Clayton family," Dependence Modeling, De Gruyter, vol. 6(1), pages 1-18, February.
    17. Liebscher, Eckhard, 2021. "Kendall regression coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    18. Fuchs, Sebastian & Tschimpke, Marco, 2024. "A novel positive dependence property and its impact on a popular class of concordance measures," Journal of Multivariate Analysis, Elsevier, vol. 200(C).
    19. Ferreira Helena & Ferreira Marta, 2020. "Multivariate medial correlation with applications," Dependence Modeling, De Gruyter, vol. 8(1), pages 361-372, January.
    20. Antonia Arsova & Deniz Dilan Karaman Örsal, 2016. "An intersection test for the cointegrating rank in dependent panel data," Working Paper Series in Economics 357, University of Lüneburg, Institute of Economics.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:61:y:1997:i:1:p:86-101. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.