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

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  • R. Arabi Belaghi
  • M. Arashi
  • S. M. M. Tabatabaey

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.

Suggested Citation

  • R. Arabi Belaghi & M. Arashi & S. M. M. Tabatabaey, 2015. "On the Construction of Preliminary Test Estimator Based on Record Values for the Burr XII Model," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(1), pages 1-23, January.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:1:p:1-23
    DOI: 10.1080/03610926.2012.733473
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    Cited by:

    1. Ajit Chaturvedi & Ananya Malhotra, 2017. "Estimation and testing procedures for the reliability functions of a family of lifetime distributions based on records," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 8(2), pages 836-848, November.
    2. R. Arabi Belaghi & M. Noori Asl, 2019. "Estimation based on progressively type-I hybrid censored data from the Burr XII distribution," Statistical Papers, Springer, vol. 60(3), pages 761-803, June.
    3. Ajit Chaturvedi & Reza Arabi Belaghi & Ananya Malhotra, 2018. "Preliminary test estimators of the reliability characteristics for the three parameters Burr XII distribution based on records," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 9(6), pages 1260-1278, December.

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