Bayesian estimation of 3-component mixture of Gumbel type-II distributions under non-informative and informative priors

This paper deals with 3-component mixture of the Gumbel type-II distributions when the scale parameter is known under Bayesian view point. The type-I right censored sampling scheme is considered due to its extensive use in reliability theory and survival analysis, taking different non-informative and informative priors. Bayes estimates of the parameters of the mixture model along with their posterior risks are derived under different loss functions. In case where no or little prior information is available, elicitation of hyperparameters is given. In order to numerically study the execution of the Bayes estimators under different loss functions, their statistical properties have been simulated for different sample sizes and test termination times. The comparisons among the estimators have been made in terms of the corresponding posterior risks. A real life data example is also given to illustrate the study.