On progressively censored inverted exponentiated Rayleigh distribution

ABSTRACT

In this paper, we discuss a progressively censored inverted exponentiated Rayleigh distribution. Estimation of unknown parameters is considered under progressive censoring using maximum likelihood and Bayesian approaches. Bayes estimators of unknown parameters are derived with respect to different symmetric and asymmetric loss functions using gamma prior distributions. An importance sampling procedure is taken into consideration for deriving these estimates. Further highest posterior density intervals for unknown parameters are constructed and for comparison purposes bootstrap intervals are also obtained. Prediction of future observations is studied in one- and two-sample situations from classical and Bayesian viewpoint. We further establish optimum censoring schemes using Bayesian approach. Finally, we conduct a simulation study to compare the performance of proposed methods and analyse two real data sets for illustration purposes.

KEYWORDS:

• Progressive censoring
• Bayes estimate
• maximum likelihood estimate
• predictive estimate
• prediction interval
• optimum censoring

MSC:

• 62 F10
• 62 N01
• 62 N02

Acknowledgments

The authors are grateful to a referee for encouraging suggestions that significantly improved content and presentation of the paper. They also thank the Editor and an Associate Editor for useful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Yogesh Mani Tripathi gratefully acknowledges the partial financial support for this research work under a grant EMR/2016/001401 Science and Engineering Research Board – SERB, India.