Hazard rate estimation of a mixture model with censored lifetimes

Abstract

This paper is intended to compare the hazard rate from the Bayesian approach with the hazard rate from the maximum likelihood estimate (MLE) method. The MLE of a parameter is appropriate as long as there are sufficient data. For various reasons, however, sufficient data may not be available, which may make the result of the MLE method unreliable. In order to resolve the problem, it is necessary to rely on judgment about unknown parameters. This is done by adopting the Bayesian approach. The hazard rate of a mixture model can be inferred from a method called Bayesian estimation. For eliciting a prior distribution which can be used in deriving a Bayesian estimate, a computerized-simulation method is introduced. Finally, a numerical example is given to illustrate the potential benefits of the Bayesian approach.