Bayesian Estimation of 3-Component Mixture of the Inverse Weibull Distributions

This article focuses on the study of a 3-component mixture of the inverse Weibull distributions under Bayesian perspective. The censored sampling scheme is used because it is popular in reliability theory and survival analysis. To achieve this objective, the Bayes estimates of the parameter of the mixture model along with their posterior risks using informative and non-informative priors are attained. These estimates have been acquired under two cases: (a) when the shape parameter is known and (b) when all parameters are unknown. For the case (a), Bayes estimates are gained under three loss functions while for the case (b) only the squared error loss function is used. To study numerically, the performance of the Bayes estimators under different loss functions, their statistical properties have been simulated for different sample sizes and test termination times.