A Simple Extension of the FGM Copula for Negative Association

• Activity Number: 39 - Methods in Financial Risk Assessment
• Type: Contributed
• Date/Time: Sunday, July 30, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Section on Risk Analysis
• Author(s): Kahadawala Cooray*
• Companies: Central Michigan University
• Keywords: coverage probabilities ; goodness-of-?t ; Kendall's distribution function ; maximum likelihood estimation ; measures of association ; p-value

Abstract

In this paper we introduced a single parameter, absolutely continuous and radially symmetric bivariate extension of the Farlie-Gumbel-Morgenstern (FGM) family of copulas. Speci?cally, this extension measures the higher negative dependencies than most FGM extensions available in literature. Closed-form formulas for distribution, quantile, density, conditional distribution, regression, Spearman's rho, Kendall's tau, and Gini's gamma are obtained. In addition, a formula for random variate generations is presented in closed-form to facilitate simulation studies. The new copula is compared with Frank, Gaussian, and Plackett copulas using three different test statistics: Vuong, Kolmogorov-Smirnov, and Cram´er-von Mises. Finally, a bivariate dataset is analyzed to compare and illustrate the ?exibility of the proposed copula for negative dependence.