A note on generalized Farlie-Gumbel-Morgenstern copulas. (2nd January 2016)

• Record Type: Journal Article
• Authors: Pathak, A. K.; Vellaisamy, P.
• Is Part Of: Journal of statistical theory and practice. Volume 10:Number 1(2016)
• Page Start: 40
• Page End: 58
• Publication Date: 2016-01-02
• Subjects: FGM copulas -- regression -- measures of association -- dependence concepts; 60E05 -- 62H20 -- 62J05; 519.505
• DOI: 10.1080/15598608.2015.1064838
• Languages: English
• ISSNs: 1559-8608

Abstract

ABSTRACT: In this note, we discuss a generalization of a subclass of the Rodríguez-Lallena and Úbeda-Flores family of copulas, through order statistics. This generalized family includes an important class of the Farlie–Gumbel–Morgenstern (FGM) family of copulas, which are widely used in statistics. We derive the expressions for regression function and cumulative conditional expectation function. The explicit expressions for some measures of dependence like Spearman's rho, Gini's gamma coefficient, and quadrant dependence are discussed. Finally, Spearman's rho is numerically tabulated and compared for some generalized families of FGM copulas.