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Increasing directionally convex orderings of random vectors having the same copula, and their use in comparing ordered data

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  • Balakrishnan, Narayanaswamy
  • Belzunce, Félix
  • Sordo, Miguel A.
  • Suárez-Llorens, Alfonso
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    Abstract

    In this paper, we establish some results for the increasing convex comparisons of generalized order statistics. First, we prove that if the minimum of two sets of generalized order statistics are ordered in the increasing convex order, then the remaining generalized order statistics are also ordered in the increasing convex order. This result is extended to the increasing directionally convex comparisons of random vectors of generalized order statistics. For establishing this general result, we first prove a new result in that two random vectors with a common conditionally increasing copula are ordered in the increasing directionally convex order if the marginals are ordered in the increasing convex order. This latter result is, of course, of interest in its own right.

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    Bibliographic Info

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

    Volume (Year): 105 (2012)
    Issue (Month): 1 ()
    Pages: 45-54

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    Handle: RePEc:eee:jmvana:v:105:y:2012:i:1:p:45-54

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    Related research

    Keywords: Increasing convex order; Increasing directionally convex order; Generalized order statistics; Copulas;

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    1. Muller, Alfred, 1997. "Stop-loss order for portfolios of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 219-223, December.
    2. Kochar, Subhash & Ma, Chunsheng, 1999. "Dispersive ordering of convolutions of exponential random variables," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 321-324, July.
    3. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    4. Belzunce, Félix & Ruiz, José M. & Suárez-Llorens, Alfonso, 2008. "On multivariate dispersion orderings based on the standard construction," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 271-281, February.
    5. Fathi Manesh, Sirous & Khaledi, Baha-Eldin, 2008. "On the likelihood ratio order for convolutions of independent generalized Rayleigh random variables," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3139-3144, December.
    6. Korwar, Ramesh M., 2002. "On Stochastic Orders for Sums of Independent Random Variables," Journal of Multivariate Analysis, Elsevier, vol. 80(2), pages 344-357, February.
    7. Zhao, Peng & Balakrishnan, N., 2009. "Mean residual life order of convolutions of heterogeneous exponential random variables," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1792-1801, September.
    8. Belzunce, Félix & Shaked, Moshe, 2001. "Stochastic comparisons of mixtures of convexly ordered distributions with applications in reliability theory," Statistics & Probability Letters, Elsevier, vol. 53(4), pages 363-372, July.
    9. Miguel Sordo & Héctor Ramos, 2007. "Characterization of stochastic orders by L-functionals," Statistical Papers, Springer, vol. 48(2), pages 249-263, April.
    10. Kochar, Subhash & Xu, Maochao, 2010. "On the right spread order of convolutions of heterogeneous exponential random variables," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 165-176, January.
    11. Khaledi, Baha-Eldin & Kochar, Subhash, 2005. "Dependence orderings for generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 357-367, July.
    12. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
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