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Some positive dependence stochastic orders


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  • Colangelo, Antonio
  • Scarsini, Marco
  • Shaked, Moshe


In this paper we study some stochastic orders of positive dependence that arise when the underlying random vectors are ordered with respect to some multivariate hazard rate stochastic orders, and have the same univariate marginal distributions. We show how the orders can be studied by restricting them to copulæ, we give a number of examples, and we study some positive dependence concepts that arise from the new positive dependence orders. We also discuss the relationship of the new orders to other positive dependence orders that have appeared in the literature.

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Bibliographic Info

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

Volume (Year): 97 (2006)
Issue (Month): 1 (January)
Pages: 46-78

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Handle: RePEc:eee:jmvana:v:97:y:2006:i:1:p:46-78

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Keywords: Copula Frechet classes and bounds Marshall-Olkin distributions Farlie-Gumbel-Morgenstern distributions Archimedean copula Left tail decreasing (LTD) Right tail increasing (RTI) Multivariate total positivity Likelihood ratio order Lower orthant decreasing ratio (lodr) order Upper orthant increasing ratio (uoir) order;


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Cited by:
  1. Torrado, Nuria & Lillo, Rosa E. & Wiper, Michael P., 2010. "On the conjecture of Kochar and Korwar," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1274-1283, May.
  2. Alessandra Michelangeli & Eugenio Peluso & Alain Trannoy, 2011. "Detecting a change in wealth concentration without the knowledge of the wealth distribution," Journal of Economic Inequality, Springer, vol. 9(3), pages 373-391, September.
  3. Dolati, Ali & Genest, Christian & Kochar, Subhash C., 2008. "On the dependence between the extreme order statistics in the proportional hazards model," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 777-786, May.
  4. Lucia, Umberto, 2013. "Thermodynamic paths and stochastic order in open systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 3912-3919.
  5. Malinovsky, Yaakov & Rinott, Yosef, 2009. "On stochastic orders of absolute value of order statistics in symmetric distributions," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2086-2091, October.
  6. Xu, Minghui & Lu, Ye, 2013. "The effect of supply uncertainty in price-setting newsvendor models," European Journal of Operational Research, Elsevier, vol. 227(3), pages 423-433.
  7. Koen DECANCQ, 2009. "Copula-based measurement of dependence between dimensions of well-being," Center for Economic Studies - Discussion papers ces09.24, Katholieke Universiteit Leuven, Centrum voor Economische Studiën.
  8. Colangelo Antonio, 2005. "Multivariate hazard orderings of discrete random vectors," Economics and Quantitative Methods qf05010, Department of Economics, University of Insubria.
  9. Yu, Dennis Z. & Tang, Sammi Y. & Niederhoff, Julie, 2011. "On the benefits of operational flexibility in a distribution network with transshipment," Omega, Elsevier, vol. 39(3), pages 350-361, June.
  10. Cha, Ji Hwan & Finkelstein, Maxim, 2011. "Burn-in and the performance quality measures in heterogeneous populations," European Journal of Operational Research, Elsevier, vol. 210(2), pages 273-280, April.
  11. Chakravarty, Satya R. & Zoli, Claudio, 2012. "Stochastic dominance relations for integer variables," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1331-1341.
  12. 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.
  13. Colangelo Antonio, 2006. "Some Positive Dependence Orderings involving Tail Dependence," Economics and Quantitative Methods qf0601, Department of Economics, University of Insubria.
  14. Gijbels, Irène & Sznajder, Dominik, 2013. "Testing tail monotonicity by constrained copula estimation," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 338-351.
  15. Sordo, Miguel A., 2008. "Characterizations of classes of risk measures by dispersive orders," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1028-1034, June.
  16. Ramesh Gupta, 2011. "Bivariate odds ratio and association measures," Statistical Papers, Springer, vol. 52(1), pages 125-138, February.


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