Aspects of Dependence in Generalized Farlie-Gumbel-Morgenstern Distributions |
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Authors: | M Amini H Jabbari G R Mohtashami Borzadaran |
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Institution: | 1. Department of Statistics, Ordered and Spatial Data Center of Excellence , Ferdowsi University of Mashhad , Mashhad , Iran m-amini@um.ac.ir;3. Department of Statistics, Ordered and Spatial Data Center of Excellence , Ferdowsi University of Mashhad , Mashhad , Iran |
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Abstract: | In this article, we obtained a dependence measure for generalized Farlie-Gumbel-Morgenstern (FGM) family in view of Kochar and Gupta (1987
Kochar , S. G. ,
Gupta , R. P. ( 1987 ). Competitors of Kendall-tau test for testing independence against PQD . Biometrika 74 ( 3 ): 664 – 669 .Crossref], Web of Science ®] , Google Scholar]) and then compared this measure with Spearman's rho and Kendall's tau in FGM family. Moreover, we evaluated the empirical power of the class of distribution-free tests proposed by Kochar and Gupta (1987
Kochar , S. G. ,
Gupta , R. P. ( 1987 ). Competitors of Kendall-tau test for testing independence against PQD . Biometrika 74 ( 3 ): 664 – 669 .Crossref], Web of Science ®] , Google Scholar], 1990
Kochar , S. G. ,
Gupta , R. P. ( 1990 ). Distribution-free tests based on sub-sample extrema for testing against positive dependence . Australian Journal of Statistics 32 : 45 – 51 .Crossref] , Google Scholar]) based on exact distribution of a U-statistics. This is derived via a simulation study for sample of sizes n = 6, 8, 10, 12, 16, and 20. Also, we compared our simulation results with those achieved by Amini et al. (2010
Amini , M. ,
Jabbari , H. ,
Mohtashami Borzadaran , G. R. ,
Azadbakhsh , M. ( 2010 ). Power comparison of independence test for the Farlie-Gumbel-Moregenstern family . Communications of the Korean Statistical Society 17 ( 4 ): 493 – 505 .Crossref] , Google Scholar]) and Güven and Kotz (2008
Güven , B. ,
Kotz , S. ( 2008 ). Test of independence for generalized Farlie-Gumbel-Morgenstern distributions . Journal of Computational and Applied Mathematics 212 : 102 – 111 .Crossref], Web of Science ®] , Google Scholar]). |
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Keywords: | Copula functions Farlie-Gumbel-Morgenstern family Negative and positive quadrant dependence U-statistics |
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