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Inference on unknown parameters of a Burr distribution under hybrid censoring

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  • Manoj Rastogi
  • Yogesh Tripathi

Abstract

Based on hybrid censored data, the problem of making statistical inference on parameters of a two parameter Burr Type XII distribution is taken up. The maximum likelihood estimates are developed for the unknown parameters using the EM algorithm. Fisher information matrix is obtained by applying missing value principle and is further utilized for constructing the approximate confidence intervals. Some Bayes estimates and the corresponding highest posterior density intervals of the unknown parameters are also obtained. Lindley’s approximation method and a Markov Chain Monte Carlo (MCMC) technique have been applied to evaluate these Bayes estimates. Further, MCMC samples are utilized to construct the highest posterior density intervals as well. A numerical comparison is made between proposed estimates in terms of their mean square error values and comments are given. Finally, two data sets are analyzed using proposed methods. Copyright Springer-Verlag 2013

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  • Manoj Rastogi & Yogesh Tripathi, 2013. "Inference on unknown parameters of a Burr distribution under hybrid censoring," Statistical Papers, Springer, vol. 54(3), pages 619-643, August.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:3:p:619-643
    DOI: 10.1007/s00362-012-0452-3
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    References listed on IDEAS

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    1. Ng, H. K. T. & Chan, P. S. & Balakrishnan, N., 2002. "Estimation of parameters from progressively censored data using EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 371-386, June.
    2. M. Mousa & Z. Jaheen, 2002. "Bayesian prediction for progressively censored data from the Burr model," Statistical Papers, Springer, vol. 43(4), pages 587-593, October.
    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. Min Kim & Bong-Jin Yum, 2011. "Life test sampling plans for Weibull distributed lifetimes under accelerated hybrid censoring," Statistical Papers, Springer, vol. 52(2), pages 327-342, May.
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    Cited by:

    1. Hanieh Panahi, 2019. "Estimation for the parameters of the Burr Type XII distribution under doubly censored sample with application to microfluidics data," 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. 10(4), pages 510-518, August.
    2. Saieed F. Ateya & Abdulaziz S. Alghamdi & Abd Allah A. Mousa, 2022. "Future Failure Time Prediction Based on a Unified Hybrid Censoring Scheme for the Burr-X Model with Engineering Applications," Mathematics, MDPI, vol. 10(9), pages 1-23, April.
    3. Rastogi, Manoj Kumar & Tripathi, Yogesh Mani, 2013. "Estimation using hybrid censored data from a two-parameter distribution with bathtub shape," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 268-281.
    4. M. Noori Asl & R. Arabi Belaghi & H. Bevrani, 2017. "On Burr XII Distribution Analysis Under Progressive Type-II Hybrid Censored Data," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 665-683, June.
    5. Tanmay Sen & Yogesh Mani Tripathi & Ritwik Bhattacharya, 2018. "Statistical Inference and Optimum Life Testing Plans Under Type-II Hybrid Censoring Scheme," Annals of Data Science, Springer, vol. 5(4), pages 679-708, December.
    6. 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.

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