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Dependence orderings for generalized order statistics

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  • Khaledi, Baha-Eldin
  • Kochar, Subhash

Abstract

Generalized order statistics (gOSs) unify the study of order statistics, record values, k-records, Pfeifer's records and several other cases of ordered random variables. In this paper we consider the problem of comparing the degree of dependence between a pair of gOSs thus extending the recent work of Avérous et al. [2005. J. Multivariate Anal. 94, 159-171]. It is noticed that as in the case of ordinary order statistics, copula of gOSs is independent of the parent distribution. For this comparison we consider the notion of more regression dependence or more stochastic increasing. It follows that under some conditions, for i

Suggested Citation

  • Khaledi, Baha-Eldin & Kochar, Subhash, 2005. "Dependence orderings for generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 357-367, July.
    • Handle: RePEc:eee:stapro:v:73:y:2005:i:4:p:357-367
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    References listed on IDEAS

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    1. Marco Scarsini, 1984. "On measures of concordance," Post-Print hal-00542380, HAL.
    2. Avérous, Jean & Genest, Christian & C. Kochar, Subhash, 2005. "On the dependence structure of order statistics," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 159-171, May.
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    Cited by:

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    2. Balakrishnan, Narayanaswamy & Belzunce, Félix & Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2012. "Increasing directionally convex orderings of random vectors having the same copula, and their use in comparing ordered data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 45-54.
    3. Bezgina, E. & Burkschat, M., 2019. "On total positivity of exchangeable random variables obtained by symmetrization, with applications to failure-dependent lifetimes," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 95-109.
    4. Kochar, Subhash & Xu, Maochao, 2008. "A new dependence ordering with applications," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2172-2184, October.
    5. Fountain, Robert L. & Herman Jr., John R. & Rustvold, D. Leif, 2008. "An application of Kendall distributions and alternative dependence measures: SPX vs. VIX," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 469-472, April.
    6. Navarro, Jorge & Balakrishnan, N., 2010. "Study of some measures of dependence between order statistics and systems," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 52-67, January.
    7. Yashi Wang & Weiwei Zhuang & Taizhong Hu, 2010. "Conditionally stochastic domination of generalized order statistics from two samples," Statistical Papers, Springer, vol. 51(2), pages 369-373, June.
    8. Burkschat, M. & Kamps, U. & Kateri, M., 2010. "Sequential order statistics with an order statistics prior," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1826-1836, September.
    9. Hashemi, Marzieh & Tavangar, Mahdi & Asadi, Majid, 2010. "Some properties of the residual lifetime of progressively Type-II right censored order statistics," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 848-859, May.
    10. Burkschat, M., 2009. "Multivariate dependence of spacings of generalized order statistics," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1093-1106, July.
    11. Pellerey, Franco & Shaked, Moshe & Yasaei Sekeh, Salimeh, 2012. "Comparisons of concordance in additive models," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2059-2067.
    12. Félix Belzunce & Carolina Martínez-Riquelme, 2015. "Some results for the comparison of generalized order statistics in the total time on test and excess wealth orders," Statistical Papers, Springer, vol. 56(4), pages 1175-1190, November.

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