Statistical Inference for Lognormal Distribution with Type-I Progressive Hybrid Censored Data

SYNOPTIC ABSTRACT

This article deals with problems of estimation and prediction under classical and Bayesian approaches when lifetime data following a lognormal distribution are observed under type-I progressive hybrid censoring. We first obtain maximum likelihood estimates, Bayes estimates, and corresponding interval estimates of unknown lognormal parameters. We then develop predictors to predict censored observations and construct prediction intervals. Further, we analyze two real data sets and conduct a simulation study to compare the performance of proposed methods of estimation and prediction. Finally, optimal censoring schemes are constructed under cost constraints and a conclusion is presented.

KEY WORDS AND PHRASES:

• EM algorithm
• MH algorithm
• prediction
• HPD interval
• equal-tail interval
• optimal censoring

Acknowledgements

The authors are thankful to two anonymous reviewers for their constructive suggestions that led to substantial improvements in the earlier version of this manuscript. Authors also extend their sincere thanks to the Editor and the Associate Editor for some very useful suggestions.