The double prior selection for the parameter of power function distribution under type-II censoring

In this paper a comparison of double priors assumed for the parameter of power distribution is ‘made sometimes we may have different prior information’s available instead of single prior for the parameter of the power distribution. It may be beneficial to include such different types of information’s in the Bayes estimation of the parameter. We have considered three double prior distributions viz. Gamma and Uniform priors, Gamma and Jeffrey’s priors, Gamma and priors and only Gamma prior. The results are compared with results based on single Gamma prior. We have derived Bayes estimator for the parameter and reliability of the distribution under squared error loss function based on type-II censored sample. The predictive distribution for future failure time and for the remaining failure times after the first r failures observed have been derived. For each case corresponding equal tail credible intervals are also obtained. A simulation study is done to exemplify the results obtained.