Statistical inference for dependence competing risks model under middle censoring

Middle censoring is an important censoring scheme, in which the actual failure data of an observation becomes unobservable if it falls into a random interval. This paper considers the statistical analysis of the dependent competing risks model by using the Marshall-Olkin bivariate Weibull (MOBW) distribution. The maximum likelihood estimations (MLEs), midpoint approximation (MPA) estimations and approximate confidence intervals (ACIs) of the unknown parameters are obtained. In addition, the Bayes approach is also considered based on the Gamma-Dirichlet prior of the scale parameters, with the given shape parameter. The acceptance-rejection sampling method is used to obtain the Bayes estimations and construct credible intervals (CIs). Finally, two numerical examples are used to show the performance of the proposed methods.