Testing Copula Functions as a Method to Derive Bivariate Weibull Distributions

This paper presents copula functions as a method to derive bivariate distributions. Copula functions allow for the construction of previously unknown bivariate distributions based on known marginals. This paper uses Weibull marginals to construct six bivariate Weibull distributions suitable for survival analysis. The paper tests the performance of these distributions with a simulation experiment. The results from the experiment show that all bivariate distributions perform as well or better than the marginal distribution. Furthermore, some bivariate distributions perform better than others. However, performance is not the only element to consider in the selection of a distribution. The structure of dependence between marginals and estimation complexity are also key criteria for the selection of the right copula