Abstract
This article deals with the problem of estimating parameters of the Gompertz distribution (GD) based on progressive first-failure censored data using Bayesian and non-Bayesian approaches. The two-sample prediction problem is considered to derive Bayesian prediction bounds for both future order statistics and future record values based on progressive first failure censored informative samples from GD. The sampling schemes such as, first-failure censoring, progressive type II censoring, type II censoring and complete sample can be obtained as special cases of the progressive first-failure censored scheme. Markov chain Monte Carlo (MCMC) method with Gibbs sampling procedure is used to compute the Bayes estimates and also to construct the corresponding credible intervals of the parameters. A simulation study has been conducted in order to compare the proposed Bayes estimators with the maximum likelihood estimators MLE. Finally, some numerical computations with real data set are presented for illustrating all the proposed inferential procedures.