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Improved confidence intervals for the scale parameter of Burr XII model based on record values

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

Abstract

In this paper some different sorts of confidence intervals are considered for the scale parameter of the Burr type XII distribution based on the upper record values. In this regard, the coverage probability is adopted as a measure of improvement when the endpoints are the same for all types of confidence intervals. Proposed confidence intervals are based on the preliminary test estimator, Thompson shrinkage estimator and Bayes estimator with conjugate prior information. It is nicely demonstrated that the confidence intervals based on the above methodologies are superior to the equal tail confidence interval on specific intervals. Subsequently, to construct a uniformly dominant confidence interval, the result of Kubokawa (Ann Stat 22(1):290–299, 1994 ) is extended for dependent observations by making use of the information that exists in a covariate record value. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • R. Arabi Belaghi & M. Arashi & S. Tabatabaey, 2014. "Improved confidence intervals for the scale parameter of Burr XII model based on record values," Computational Statistics, Springer, vol. 29(5), pages 1153-1173, October.
    • Handle: RePEc:spr:compst:v:29:y:2014:i:5:p:1153-1173
    DOI: 10.1007/s00180-014-0484-3
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    References listed on IDEAS

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    1. Constantinos Petropoulos & Stavros Kourouklis, 2012. "New classes of improved confidence intervals for the variance of a normal distribution," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(4), pages 491-506, May.
    2. Abdel-Hamid, Alaa H., 2009. "Constant-partially accelerated life tests for Burr type-XII distribution with progressive type-II censoring," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2511-2523, May.
    3. Dallas Wingo, 1993. "Maximum likelihood methods for fitting the burr type XII distribution to multiply (progressively) censored life test data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 203-210, December.
    4. B. Kibria & A. Saleh, 2010. "Preliminary test estimation of the parameters of exponential and Pareto distributions for censored samples," Statistical Papers, Springer, vol. 51(4), pages 757-773, December.
    5. Shao, Quanxi, 2004. "Notes on maximum likelihood estimation for the three-parameter Burr XII distribution," Computational Statistics & Data Analysis, Elsevier, vol. 45(3), pages 675-687, April.
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    Cited by:

    1. 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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