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

M. Zargar, H. Jabbari () and M. Amini
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M. Zargar: Ferdowsi University of Mashhad
H. Jabbari: Ferdowsi University of Mashhad
M. Amini: Ferdowsi University of Mashhad

Computational Statistics, 2017, vol. 32, issue 4, No 11, 1423-1451

Abstract: 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.

Keywords: Copula functions; Celebioǧlu–Cuadras copula; Gumbel–Barnett distribution; Gumbel’s bivariate distribution; Negative quadrant dependence; U-statistics (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s00180-016-0696-9

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