Summary: Recently the generalized exponential distribution has received considerable attentions. We deal with Bayesian inference of the unknown parameters of the progressively censored generalized exponential distribution. It is assumed that the scale and the shape parameters have independent gamma priors. The Bayes estimates of the unknown parameters cannot be obtained in closed form. Lindley’s approximation and importance sampling techniques have been suggested to compute the approximate Bayes estimates. A Markov chain Monte Carlo method has been used to compute the approximate Bayes estimates and also to construct the highest posterior density credible intervals.
We also provide different criteria to compare two different sampling schemes and hence to find the optimal sampling schemes. It is observed that finding the optimum censoring procedure is a computationally expensive process. We have recommended to use a sub-optimal censoring procedure, which can be obtained very easily. Monte Carlo simulations are performed to compare the performances of the different methods and data analysis has been performed for illustrative purposes.