Estimation and prediction for a progressively censored generalized inverted exponential distribution

• Bayesian and classical estimates are derived for the unknown parameters of a generalized inverted exponential distribution based on progressively Type-II censored data.
• Prediction of future failures are discussed using classical and Bayesian approaches.
• A simulation study is conducted to assess the behavior of proposed methods and two real data sets are analyzed for illustrative purposes.

In this paper, we consider generalized inverted exponential distribution which is capable of modeling various shapes of failure rates and aging criteria. The purpose of this paper is two fold. Based on progressive type-II censored data, first we consider the problem of estimation of parameters under classical and Bayesian approaches. In this regard, we obtain maximum likelihood estimates, and Bayes estimates under squared error loss function. We also compute 95% asymptotic confidence interval and highest posterior density interval estimates under the respective approaches. Second, we consider the problem of prediction of future observations using maximum likelihood predictor, best unbiased predictor, conditional median predictor and Bayes predictor. The associated predictive interval estimates for the censored observations are computed as well. Finally, we analyze two real data sets and conduct a Monte Carlo simulation study to compare the performance of the various proposed estimators and predictors.