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

Authors : Selim Orhun SUSAM

Pages : 618-631

Doi:10.15672/hujms.993698

View : 16 | Download : 5

Publication Date : 2022-04-01

Article Type : Research Paper

Abstract :In this paper, we are proposing a flexible method for constructing a bivariate generalized Farlie-Gumbel-Morgenstern insert ignore into journalissuearticles values(G-FGM); copula family. The method is mainly developed around the function $\phiinsert ignore into journalissuearticles values(t);$ insert ignore into journalissuearticles values($t\in [0,1]$);, 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