Bivariate Modified Weibull Distribution Derived From Farlie-Gumbel-Morgenstern Copula: a Simulation Study

Abstract

In recent years, the use of copulas has grown rapidly, especially in survivalanalysis. In this paper, we introduce a bivariate modied Weibull distribu-tion derived from the Farlie{Gumbel{Morgenstern (FGM), a copula functioncommonly used to model very weak linear dependences. Considering thepresence of non censored data and censored data, an extensive simulationstudy was developed to check the performance of the maximum likelihoodmethod in estimating the parameters of the proposed model. Maximum like-lihood and Bayesian approaches for the estimation of the model parametersare presented. In the Bayesian analysis, the posterior distributions of the pa-rameters are estimated using Markov chain Monte Carlo (MCMC) method-ology. An example, considering a real data set, is introduced to illustrate theproposed methodology.