Estimation and prediction based on type-I hybrid censored data from the Poisson-Exponential distribution

Abstract

This paper considers the problems of estimation and prediction when lifetime data following Poisson-exponential distribution are observed under type-I hybrid censoring. For both the problems, we compute point and associated interval estimates under classical and Bayesian approaches. For point estimates in the problem of estimation, we compute maximum likelihood estimates using Newton–Raphson, Expectation-Maximization and Stochastic Expectation-Maximization algorithms under classical approach, and under Bayesian approach we compute Bayes estimates with the help of Lindley and importance sampling technique under informative and non-informative priors using symmetric and asymmetric loss functions. The associated interval estimates are obtained using the Fisher information matrix and Chen and Shao method respectively under classical and Bayesian approaches. Further, the predictive point estimates and associated predictive interval estimates are computed by making use of best unbiased and conditional median predictors under classical approach, and Bayesian predictive and associated Bayesian predictive interval estimates in the problem of prediction. We analysis real data set, and conduct Monte Carlo simulation study for the comparison of various proposed methods of estimation and prediction. Finally, a conclusion is given.

Keywords:

• Bayesian estimation
• Poisson-exponential distribution
• EM algorithm
• SEM algorithm
• Shrinkage estimation
• Lindely approximation
• Prediction

Acknowledgments

Authors would like to thank the Editor, associate Editor and anonymous reviewers for their constructive and valuable suggestions which led much improvement in the earlier version of this manuscript.