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An Optimal Bayesian Sampling Plan for Two-Parameter Exponential Distribution Under Type-I Hybrid Censoring

Author

Listed:
  • Kiran Prajapat

    (Indian Institute of Technology Kanpur)

  • Arnab Koley

    (Indian Institute of Management Indore)

  • Sharmishtha Mitra

    (Indian Institute of Technology Kanpur)

  • Debasis Kundu

    (Indian Institute of Technology Kanpur)

Abstract

The Bayesian sampling plan for two-parameter exponential distribution has been considered by Lam (Statistician, 39, 53–66, 1990) under the conventional Type-II censoring. Lin et al. (Commun. Stat.—Simul. Comput., 37, 1101–1116, 2008b) have obtained an exact Bayesian sampling plan for one-parameter exponential distribution under Type-I and Type-II hybrid censoring schemes. In this paper, we obtain an optimal Bayesian sampling plan for the two-parameter exponential distribution under Type-I hybrid censoring scheme based on a four-parameter conjugate prior, introduced by Varde (J. Am. Stat. Assoc., 64, 621–631 1969). Bayes risk expressions of Lam (Statistician, 39, 53–66, 1990) for the conventional Type-II censoring scheme can be obtained as special cases of the Type-I hybrid censoring scheme. The optimal Bayesian sampling plan cannot be obtained analytically, we provide a numerical algorithm to compute the optimal Bayesian sampling plan. Different optimal Bayesian sampling plans have been reported.

Suggested Citation

  • Kiran Prajapat & Arnab Koley & Sharmishtha Mitra & Debasis Kundu, 2023. "An Optimal Bayesian Sampling Plan for Two-Parameter Exponential Distribution Under Type-I Hybrid Censoring," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 512-539, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-021-00263-2
    DOI: 10.1007/s13171-021-00263-2
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    References listed on IDEAS

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    1. Huang, Wen-Tao & Lin, Yu-Pin, 2004. "Bayesian sampling plans for exponential distribution based on uniform random censored data," Computational Statistics & Data Analysis, Elsevier, vol. 44(4), pages 669-691, January.
    2. Chen, Jianwei & Li, Kim-Hung & Lam, Yeh, 2007. "Bayesian single and double variable sampling plans for the Weibull distribution with censoring," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1062-1073, March.
    3. Chen, Jianwei & Choy, S. T. B. & Li, Kim-Hung, 2004. "Optimal Bayesian sampling acceptance plan with random censoring," European Journal of Operational Research, Elsevier, vol. 155(3), pages 683-694, June.
    4. A. Childs & B. Chandrasekar & N. Balakrishnan & D. Kundu, 2003. "Exact likelihood inference based on Type-I and Type-II hybrid censored samples from the exponential distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(2), pages 319-330, June.
    5. Yu-Pin Lin & TaChen Liang & Wen-Tao Huang, 2002. "Bayesian Sampling Plans for Exponential Distribution Based on Type I Censoring Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 100-113, March.
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