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

Year 2022, Volume: 51 Issue: 2, 618 - 631, 01.04.2022

Selim Orhun Susam

https://doi.org/10.15672/hujms.993698

Cited By: 10

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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