Some properties of the Kendall distribution in bivariate Archimedean copula models under censoring

Suppose that (T1,T2) can be modelled by an Archimedean copula model and it is subject to dependent or independent right censoring. In this paper, we present some distributional results for the random variable V=S(T1,T2) under different censoring patterns (singly or doubly censored). The results are expected to be useful in setting up both the model fitting and checking procedures for Archimedean copula models for censored bivariate data. As an application of the theoretical results we obtained, a simple moment estimator of the dependence parameter in Archimedean copula models is proposed. Simulation studies have shown that the proposed estimator parameter works well and the estimator is used in analyzing a medical data set.