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Estimation using hybrid censored data from a two-parameter distribution with bathtub shape

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  • Rastogi, Manoj Kumar
  • Tripathi, Yogesh Mani

Abstract

The problem of estimating unknown parameters of a two-parameter distribution with bathtub shape is considered under the assumption that samples are hybrid censored. The maximum likelihood estimates are obtained using an EM algorithm. The Fisher information matrix is obtained as well and the asymptotic confidence intervals are constructed. Further, two bootstrap interval estimates are also proposed for the unknown parameters. Bayes estimates are evaluated under squared error loss function. Approximate explicit expressions for these estimates are derived using the Lindley method as well as using the Tierney and Kadane method. An importance sampling scheme is then proposed to generate Markov Chain Monte Carlo samples which have been used to compute approximate Bayes estimates and credible intervals for the unknowns. A numerical study is performed to compare the proposed estimates. Finally, two data sets are analyzed for illustrative purposes.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:67:y:2013:i:c:p:268-281
    DOI: 10.1016/j.csda.2013.05.022
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    References listed on IDEAS

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    1. Kundu, Debasis & Joarder, Avijit, 2006. "Analysis of Type-II progressively hybrid censored data," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2509-2528, June.
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    3. Shuo-Jye Wu, 2008. "Estimation of the two-parameter bathtub-shaped lifetime distribution with progressive censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(10), pages 1139-1150.
    4. Balakrishnan, N. & Kundu, Debasis, 2013. "Hybrid censoring: Models, inferential results and applications," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 166-209.
    5. Howlader, Hatem A. & Hossain, Anwar M., 2002. "Bayesian survival estimation of Pareto distribution of the second kind based on failure-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 38(3), pages 301-314, January.
    6. 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.
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    Cited by:

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    2. Wenjie Zhang & Wenhao Gui, 2022. "Statistical Inference and Optimal Design of Accelerated Life Testing for the Chen Distribution under Progressive Type-II Censoring," Mathematics, MDPI, vol. 10(9), pages 1-21, May.
    3. Raj Kamal Maurya & Yogesh Mani Tripathi & Chandrakant Lodhi & Manoj Kumar Rastogi, 2019. "On a generalized Lomax distribution," 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(5), pages 1091-1104, October.
    4. Bhattacharya, Ritwik & Pradhan, Biswabrata & Dewanji, Anup, 2015. "Computation of optimum reliability acceptance sampling plans in presence of hybrid censoring," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 91-100.
    5. Zihui Zhang & Wenhao Gui, 2022. "Statistical Analysis of the Lifetime Distribution with Bathtub-Shaped Hazard Function under Lagged-Effect Step-Stress Model," Mathematics, MDPI, vol. 10(5), pages 1-23, February.
    6. Wang, Liang & Tripathi, Yogesh Mani & Lodhi, Chandrakant & Zuo, Xuanjia, 2022. "Inference for constant-stress Weibull competing risks model under generalized progressive hybrid censoring," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 70-83.

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