A Bivariate Survival Model Based On Copula And Estimation Under Random Right-censoring

In this paper, we introduce a bivariate survival model using Clayton Copula with Weibull distributions as marginals and discuss its limit distribution, background in medical research and sampling method. We derive further different properties of this distribution, including probability density function, distribution function, moments, hazard rate function, dependency properties and dependency measures. The maximum likelihood estimators of the unknown parameters are obtained under random right censoring, so are the corresponding asymptotic confidence intervals. Then we compare the behavior of the estimators under different sample sizes, different censoring rates and different parameter values by simulations. Finally a data set from the Diabetic Retinopathy Study Group has been analyzed for illustrative purpose and the results are compared with those obtained from other models.