Computational Statistics

, Volume 32, Issue 4, pp 1423–1451 | Cite as

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

Original Paper


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 \(n=6,8,15,20\) and 50. Also, we apply some examples to illustrate the results. Finally, we compare the common estimators of dependence parameter based on empirical MSE.


Copula functions Celebioǧlu–Cuadras copula Gumbel–Barnett distribution Gumbel’s bivariate distribution Negative quadrant dependence U-statistics 



The authors would like to thank the associate editor and referees for their careful reading and constructive comments that improved presentation of the paper. The research was supported by a grant from Ferdowsi University of Mashhad (No. MS93321JAB).


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© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Statistics, Ordered and Spatial Data Center of ExcellenceFerdowsi University of MashhadMashhadIran

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