Bayesian Estimation in the Proportional Hazards Model of Random Censorship under Asymmetric Loss Functions

In this paper, we consider the Bayesian estimation of parameters in the proportional hazards model of random censorship for the Weibull distribution under different asymmetric loss functions. It is well-known for the Weibull distribution that a joint conjugate prior on the parameters does not exist; we use both the informative and noninformative priors on the model parameters. Bayes estimates under LINEX and general entropy loss functions are obtained using the Gibbs sampling scheme. A simulation study is carried out to observe the behavior of the proposed estimators for different sample sizes and for different censoring parameters. It is observed that the Bayes estimators under LINEX and general entropy loss functions can be used effectively with the appropriate choice of respective loss function parameters. One real data set is analyzed for illustrative purposes.