On the Construction of Preliminary Test Estimator Based on Record Values for the Burr XII Model

Abstract

In this paper some different sorts of estimators are proposed based on record breaking observations in the Burr type XII model. We define Bayes as well as empirical Bayes preliminary test estimators in the same fashion as in the ordinary preliminary test estimator using relevant combinations of uniformly minimum variance unbiased (UMVU) and Bayes estimators. Exact and asymptotic bias and mean square error (MSE) expressions for the proposed estimators are derived under two different conditions of knowing the shape parameters. We compare the MSEs and obtain the confidence interval for the parameter of interest in which the preliminary test type estimators outperform the UMVU, Bayes and empirical Bayes estimators. An application of the ordinary preliminary test estimator is also considered. We conclude this approach by a useful discussion for practical purposes and a summary.

Keywords:

• Bayes estimator
• Burr type XII distribution
• Empirical Bayes estimator
• Preliminary test estimator
• Record values

Mathematics Subject Classification:

• Primary 62F10
• Secondary 62C12.

Acknowledgments

The authors would like to thank the anonymous referees for their constructive comments that led to put many details on the paper and substantially improved the presentation.