Generalized bivariate copulas and their properties

Article type: Research Article

Authors: Kim, Jong-Min^{a; *} | Sungur, Engin A.^a | Choi, Taeryon^b | Heo, Tae-Young^c

Affiliations: [a] Statistics Discipline, Division of Science and Mathematics, University of Minnesota, Morris, MN, USA | [b] Department of Statistics, Korea University, Seoul, 136-701, South Korea | [c] Department of Data Information Science, Korea Maritime University, Busan, 606-791, South Korea

Correspondence: [*] Address for correspondence: Jong-Min Kim, E-mail: [email protected]

Abstract: Copulas are useful devices to explain the dependence structure among variables by eliminating the influence of marginals. In this paper, we propose a new class of bivariate copulas to quantify dependency and incorporate it into various iterated copula families. We investigate properties of the new class of bivariate copulas and derive the measure of association, such as Spearman's ρ, Kendall's τ, and the regression function for the new class. We also provide the concept of directional dependence in bivariate regression setting by using copulas.

Keywords: Bivariate copulas, Spearman's ρ, Kendall's τ, Marginal distribution, Regression function, Farlie-Gumbel-Morgenstern copula, Directional dependence

DOI: 10.3233/MAS-2011-0185

Journal: Model Assisted Statistics and Applications, vol. 6, no. 2, pp. 127-136, 2011