Estimation for the parameters of competing risks model with middle censored exponential data

In this paper, we consider some problems of estimation based on middle censored competing risks data. It is assumed that the lifetime distribution of the latent failure times are independent and exponential-distributed with the different parameters and also censoring mechanism is independent and non-informative.The maximum likelihood estimators of the unknown parameters are obtained. Based on gamma priors, the Lindely’s approximation and Gibbs sampling methods are applied to obtain the Bayesian estimates of the unknown parameters under squared error loss function. Finally, a simulation study is given by Monte-Carlo simulations to evaluate the performances of the different methods