Affiliations: [a] Departamento de Medicina Social - FMRP, Universidade de Sao Paulo, Ribeiro Preto, SP, Brazil | [b] Escuela de Estadstica, Universidad del Valle, Santiago de Cali, Colombia
Corresponding author: Jos Rafael Tovar Cuevas, Escuela de Estadstica, Universidad del Valle, Santiago de Cali, Colombia. Tel.: +57 2 3212138; E-mail:[email protected]
Abstract: In this paper, we introduce bivariate lifetime models derived from copula functions considering two copula functions, the Farlie Gumbel Morgenstern (FGM) commonly used to model very weak linear dependences and the Gumbel-Barnett copula which models very weak non necessarily linear dependences. Considering the presence of cure fractions for both lifetimes, censored data and covariates, we use standard MCMC (Markov Chain Monte Carlo) methods to get a Bayesian analysis for the proposed models. This new modelling approach gives a great flexibility of fit for bivariate data, since we could assume any existing parametric marginal lifetime distribution for the bivariate lifetimes as standard Weibull, log-normal, gamma, generalized gamma, generalized Weibull or generalized F distributions. An example, considering a medical data set is introduced to illustrate the proposed methodology.