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Conditional orderings and positive dependence

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  • Colangelo, Antonio
  • Hu, Taizhong
  • Shaked, Moshe
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    Abstract

    Every univariate random variable is smaller, with respect to the ordinary stochastic order and with respect to the hazard rate order, than a right censored version of it. In this paper we attempt to generalize these facts to the multivariate setting. It turns out that in general such comparisons do not hold in the multivariate case, but they do under some assumptions of positive dependence. First we obtain results that compare the underlying random vectors with respect to the usual multivariate stochastic order. A larger slew of results, that yield comparisons of the underlying random vectors with respect to various multivariate hazard rate orders, is given next. Some comparisons with respect to the orthant orders are also discussed.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 99 (2008)
    Issue (Month): 3 (March)
    Pages: 358-371

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    Handle: RePEc:eee:jmvana:v:99:y:2008:i:3:p:358-371

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    Related research

    Keywords: Usual stochastic order Hazard rate order Association Right corner set increasing (RCSI) Right tail increasing (RTI) Positive quadrant dependence (PQD);

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Lindqvist, Bo Henry, 1988. "Association of probability measures on partially ordered spaces," Journal of Multivariate Analysis, Elsevier, vol. 26(2), pages 111-132, August.
    2. Hu, Taizhong & Khaledi, Baha-Eldin & Shaked, Moshe, 2003. "Multivariate hazard rate orders," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 173-189, January.
    3. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2006. "Some positive dependence stochastic orders," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 46-78, January.
    4. Karlin, Samuel & Rinott, Yosef, 1980. "Classes of orderings of measures and related correlation inequalities. I. Multivariate totally positive distributions," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 467-498, December.
    5. 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.
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    Cited by:
    1. Cai, Jun & Wei, Wei, 2012. "Optimal reinsurance with positively dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 57-63.
    2. Franco, Manuel & Vivo, Juana-MarĂ­a, 2010. "A multivariate extension of Sarhan and Balakrishnan's bivariate distribution and its ageing and dependence properties," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 491-499, March.

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