A multi-parameter Generalized Farlie-Gumbel-Morgenstern bivariate copula family via Bernstein polynomial

In this paper, we are proposing a flexible method for constructing a bivariate generalized Farlie-Gumbel-Morgenstern (G-FGM) copula family. The method is mainly developed around the function ϕ(t) (t ∈ [0, 1]), where ϕ is the generator of the G-FGM copula. The proposed construction method has useful advantages. The first of which is the direct relationship between the ϕ function and Kendall’s tau. The second advantage is the possibility of constructing a multi-parameter G-FGM copula which allows us to better harmonize empirical instruction with the model. The construction method is illustrated by three real data examples.