Estimation and Prediction for the Poisson-Exponential Distribution Based on Type-II Censored Data

SYNOPTIC ABSTRACT

This article addresses the problems of estimation and prediction when the lifetime data following Poisson-Exponential distribution are observed under type-II censoring. We obtain maximum likelihood estimates and associated interval estimates under a classical approach, and Bayes estimates using various loss functions and associated highest posterior density interval estimates. Maximum likelihood estimates are obtained using the Newton-Raphson method and Expectation Maximization (EM) algorithm, and Bayes estimates are computed using importance sampling and Lindley approximation. We also compute shrinkage preliminary test estimates based on maximum likelihood and Bayes estimates. Further, we provide inference on the censored observations by making use of best unbiased and condition median predictors under a classical approach, and predictive estimates under the Bayesian paradigm using importance sampling. The associated predictive interval estimates are also obtained using different methods. Finally, we conduct a simulation study to compare the performance of all the proposed methods of estimation and prediction, and analyze a real data set for illustration purpose.

KEY WORDS AND PHRASES:

• Bayesian estimation
• Poisson-exponential distribution
• EM algorithm
• shrinkage estimation
• Lindley approximation
• prediction
• Type-II censoring

Acknowledgement

The authors would like to thank the Editor, associate Editor, and anonymous reviewers for the constructive and valuable suggestions which led to the improvement in an earlier version of this article.

Disclosure Statement

No potential conflict of interest was reported by the authors.