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

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