The FGM Long-Term Bivariate Survival Copula Model: Modeling, Bayesian Estimation, and Case Influence Diagnostics

Abstract

In this article, we propose a bivariate long-term distribution based on the Farlie-Gumbel-Morgenstern copula model. The proposed model allows for the presence of censored data and covariates. For inferential purposes, a Bayesian approach via Markov Chain Monte Carlo (MCMC) were considered. Further, some discussions on the model selection criteria are given. In order to examine outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated on artificial and real data.

Keywords:

• Bayesian approach
• Farlie-Gumbel-Morgenstern copula
• Influence diagnostics
• Kullback-Leibler divergence
• Long-term survival

Mathematics Subject Classification:

• Primary 62Nxx
• Secondary 62N99

Acknowledgments

The researchers of Francisco Louzada and Vicente G. Cancho are supported by the Brazilian organization CNPq.