Parameter Estimation for a Burr XII Distribution under Progressive Censoring

SYNOPTIC ABSTRACT

This article deals with the problem of estimating unknown parameters of a Burr Type XII distribution with the data that are progressive Type-II censored. The maximum likelihood estimators are derived using an EM algorithm. Approximate confidence intervals based on the observed Fisher information matrix and bootstrap intervals of the unknown parameters are obtained. Bayes estimators are derived under different loss functions by making use of the Tierney and Kadane method and importance sampling procedure. Samples obtained from the importance sampling procedure are further used to construct the highest posterior density intervals of unknown parameters. A simulation study is conducted to study the performance of proposed estimators. Finally, a real life data and a simulated data are analyzed for illustration.

KEY WORDS AND PHRASES:

• Bayes estimators
• bootstrapping
• EM algorithm
• Fisher information matrix
• importance sampling
• loss function
• Tierney and Kadane method

Acknowledgments

The authors are thankful to the editor and two referees for their valuable suggestions that significantly improved the content and the presentation of the article.

Funding

The author Yogesh Mani Tripathi gratefully acknowledges the partial financial support provided for this research work by the Department of Science and Technology, India under grant SR/S4/MS : 785/12.