Estimation and prediction for Burr type III distribution based on unified progressive hybrid censoring scheme

Abstract

The present communication develops the tools for estimation and prediction of the Burr-III distribution under unified progressive hybrid censoring scheme. The maximum likelihood estimates of model parameters are obtained. It is shown that the maximum likelihood estimates exist uniquely. Expectation maximization and stochastic expectation maximization methods are employed to compute the point estimates of unknown parameters. Based on the asymptotic distribution of the maximum likelihood estimators, approximate confidence intervals are proposed. In addition, the bootstrap confidence intervals are constructed. Furthermore, the Bayes estimates are derived with respect to squared error and LINEX loss functions. To compute the approximate Bayes estimates, Metropolis–Hastings algorithm is adopted. The highest posterior density credible intervals are obtained. Further, maximum a posteriori estimates of the model parameters are computed. The Bayesian predictive point, as well as interval estimates, are proposed. A Monte Carlo simulation study is employed in order to evaluate the performance of the proposed statistical procedures. Finally, two real data sets are considered and analysed to illustrate the methodologies established in this paper.

KEYWORDS:

• Unified progressive hybrid censoring scheme
• EM and SEM
• Bayes estimates
• maximum a posterior estimates
• Metropolis–Hastings algorithm
• Bayesian prediction

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62F10
• 62F15
• 62N01
• 62N02

Acknowledgements

The authors would like to thank the Editor in Chief, an Associate Editor and two anonymous reviewers for their positive remarks and useful comments. The author S. Dutta, thanks the Council of Scientific and Industrial Research (C.S.I.R. Grant No. 09/983(0038)/2019-EMR-I), India, for the financial assistantship received to carry out this research work. Both the authors thank the research facilities received from the Department of Mathematics, National Institute of Technology Rourkela, India.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Council of Scientific and Industrial Research [09/983(0038)/2019-EMR-I].