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

Abstract

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 $\phi(t)$ ($t\in [0,1]$), where $\phi$ 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 $\phi$ 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.

Keywords

• Bernstein polynomial
• Copula
• Kendall
• FGM copula

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