| Summary: | In this paper we compare different structures of dependence for the risks that compete in a trivariate competing risk model, using the C-Vines and D-Vines copula techniques, through statistical simulation. The vines can obtain multivariate flexibility and are able to capture all the possible range of dependencies between the competing risks, which are of great interest in financial markets, social, genetic among others problems. Then, we estimated survival function for the minimum time, both for the independent case, through the Kaplan Meier estimator and for the dependent case, in which we will use the risk combination method, which is an extension of the copula graphic estimator. The C-DVines copulas work with a cascade of bivariate copulas, which can be selected independently and allow a wide range of possibilities for characterizing the dependence of competing risks, we study particular cases where two of the three risks have equal dependence and the remaining risk is independent to the previous ones. We also study the case where two risks are equally dependent and the other is highly dependent. In addition, a particular case where the three risks have different dependence is analyzed. In all the cases studied, the risk combination method is a good alternative to estimate the marginal distribution functions and the survival function when there is a dependence between the risks of a dependent competing risks model.
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