A simulation study of parameters for the censored shifted Gompertz mixture distribution: A Bayesian approach

Abstract

The Bayesian estimation of unknown parameters of shifted Gompertz mixture model under type-I censorship, assuming both the informative and noninformative priors is investigated using different loss functions to obtain the Bayes estimates. It is seen that the closed-form expressions for the Bayes estimators cannot be obtained under shape and scale parameters. Some properties of the model with some graphs of the mixture density are discussed. These properties include Bayes estimators, posterior risks and reliability function under simulation scheme. The prior belief of the mixture model is represented by the uniform, and gamma prior. Bayes estimates are obtained considering two cases: (a) when the shape parameter is known and (b) when all parameters are unknown. A detailed simulation study is carried out to investigate the performance of the proposed set of estimators of the mixture model parameters. Posterior risks of the Bayes estimators are evaluated and compared to explore the effect of prior belief and loss functions.

Keywords:

• Censored data
• Shifted Gompertz mixture distribution
• Loss functions
• Bayes estimators
• Posterior risk
• Reliability function
• Hazard function