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Some Positive Dependence Orderings involving Tail Dependence

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  • Colangelo Antonio

    (Department of Economics, University of Insubria, Italy)

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    Abstract

    In this paper we discuss the properties of the orderings of positive dependence introduced by Hollander et al. (1990) as generalizing the bivariate positive dependence concepts of left-tail decreasing (LTD) and right-tail increasing (RTI) studied by Esary and Proschan (1972). We show which of the postulates proposed by Kimeldorf and Sampson (1987) for a reasonable positive dependence ordering are satisfied and how the orders can be studied by restricting them to copulas, and we give some examples. We also investigate the relationship of these orders with some other orderings which have appeared in the literature and generalize the same notions of positive dependence

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    File URL: http://eco.uninsubria.it/dipeco/Quaderni/files/QF2006_1.pdf
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    Bibliographic Info

    Paper provided by Department of Economics, University of Insubria in its series Economics and Quantitative Methods with number qf0601.

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    Length: 17 pages
    Date of creation: Jan 2006
    Date of revision:
    Handle: RePEc:ins:quaeco:qf0601

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    Related research

    Keywords: Copula; Fréchet class; positive dependence stochastic ordering; right-tail decreasing (RTI); left-tail decreasing (LTD);

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    1. Z. Fang & H. Joe, 1992. "Further developments on some dependence orderings for continuous bivariate distributions," Annals of the Institute of Statistical Mathematics, Springer, vol. 44(3), pages 501-517, September.
    2. Ali, Mir M. & Mikhail, N. N. & Haq, M. Safiul, 1978. "A class of bivariate distributions including the bivariate logistic," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 405-412, September.
    3. 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.
    4. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2006. "Some positive dependence stochastic orders," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 46-78, January.
    5. Takemi Yanagimoto & Masashi Okamoto, 1969. "Partial orderings of permutations and monotonicity of a rank correlation statistic," Annals of the Institute of Statistical Mathematics, Springer, vol. 21(1), pages 489-506, December.
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