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Dependence structure and test of independence for some well-known bivariate distributions

Author

Listed:
  • M. Zargar

    (Ferdowsi University of Mashhad)

  • H. Jabbari

    (Ferdowsi University of Mashhad)

  • M. Amini

    (Ferdowsi University of Mashhad)

Abstract

In this paper, we study the dependence structure of some bivariate distribution functions based on dependence measures of Kochar and Gupta (Biometrika 74(3):664–666, 1987) and Shetty and Pandit (Stat Methods Appl 12:5–17, 2003) and then compare these measures with Spearman’s rho and Kendall’s tau. Moreover, the empirical power of the class of distribution-free tests introduced by Kochar and Gupta (1987) and Shetty and Pandit (2003) is computed based on exact and asymptotic distribution of U-statistics. Our results are obtained from simulation work in some continuous bivariate distributions for the sample of sizes $$n=6,8,15,20$$ n = 6 , 8 , 15 , 20 and 50. Also, we apply some examples to illustrate the results. Finally, we compare the common estimators of dependence parameter based on empirical MSE.

Suggested Citation

  • M. Zargar & H. Jabbari & M. Amini, 2017. "Dependence structure and test of independence for some well-known bivariate distributions," Computational Statistics, Springer, vol. 32(4), pages 1423-1451, December.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:4:d:10.1007_s00180-016-0696-9
    DOI: 10.1007/s00180-016-0696-9
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    References listed on IDEAS

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    1. I. D. Shetty & Parameshwar V. Pandit, 2003. "Distribution-free tests for independence against positive quadrant dependence: A generalization," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 12(1), pages 5-17, February.
    2. Saralees Nadarajah & Kosto Mitov & Samuel Kotz, 2003. "Local dependence functions for extreme value distributions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(10), pages 1081-1100.
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