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

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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.

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Acknowledgments

We would like to thank the editor and anonymous referees for their helpful suggestions which greatly improved the presentation of the paper.

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Authors and Affiliations

  1. Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, P.O. Box 91775-1159, Mashhad, Iran

    R. Arabi Belaghi & S. M. M. Tabatabaey

  2. Department of Statistics, School of Mathematical Sciences, Shahrood University of Technology, P.O. Box 316-3619995161, Shahrood, Iran

    M. Arashi

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  1. R. Arabi Belaghi
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  2. M. Arashi
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  3. S. M. M. Tabatabaey
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Correspondence to R. Arabi Belaghi.

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Arabi Belaghi, R., Arashi, M. & Tabatabaey, S.M.M. Improved confidence intervals for the scale parameter of Burr XII model based on record values. Comput Stat 29, 1153–1173 (2014). https://doi.org/10.1007/s00180-014-0484-3

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  • DOI: https://doi.org/10.1007/s00180-014-0484-3

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