A new class of copulas involving geometric distribution: Estimation and applications

Copula is becoming a popular tool for modeling the dependence structure among multiple variables. Commonly used copulas are Gaussian, t and Gumbel copulas. To further generalize these copulas, a new class of copulas, referred to as geometric copulas, is introduced by adding geometric distribution into the existing copulas. The interior-point penalty function algorithm is proposed to obtain maximum likelihood estimation of the parameters of geometric copulas. Simulation studies are carried out to evaluate the efficiency of the proposed method. The proposed estimation method is illustrated with workers' compensation insurance data and exchange rate series data.