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Likelihood and Bayesian estimation of using lower record values from the generalized exponential distribution

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  • Baklizi, Ayman

Abstract

We consider the likelihood and Bayesian estimation of the stress-strength reliability based on lower record values from the generalized exponential distribution. The estimators are derived and their properties are studied. Confidence intervals, exact and approximate, as well as the Bayesian credible sets for the stress-strength reliability are obtained. A simulation study is conducted to investigate and compare the performance of the intervals.

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  • Baklizi, Ayman, 2008. "Likelihood and Bayesian estimation of using lower record values from the generalized exponential distribution," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3468-3473, March.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3468-3473
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    References listed on IDEAS

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    1. J. Ahmadi & N. Arghami, 2003. "Nonparametric confidence and tolerance intervals from record values data," Statistical Papers, Springer, vol. 44(4), pages 455-468, October.
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    Cited by:

    1. William Volterman & R. Arabi Belaghi & N. Balakrishnan, 2018. "Joint records from two exponential populations and associated inference," Computational Statistics, Springer, vol. 33(1), pages 549-562, March.
    2. M. S. Kotb & M. Z. Raqab, 2021. "Estimation of reliability for multi-component stress–strength model based on modified Weibull distribution," Statistical Papers, Springer, vol. 62(6), pages 2763-2797, December.
    3. A. James & N. Chandra & Nicy Sebastian, 2023. "Stress-strength reliability estimation for bivariate copula function with rayleigh marginals," 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. 14(1), pages 196-215, March.
    4. EryIlmaz, Serkan, 2010. "On system reliability in stress-strength setup," Statistics & Probability Letters, Elsevier, vol. 80(9-10), pages 834-839, May.
    5. Wang, Bing Xing & Ye, Zhi-Sheng, 2015. "Inference on the Weibull distribution based on record values," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 26-36.
    6. Saralees Nadarajah, 2011. "The exponentiated exponential distribution: a survey," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(3), pages 219-251, September.
    7. Ayush Tripathi & Umesh Singh & Sanjay Kumar Singh, 2021. "Inferences for the DUS-Exponential Distribution Based on Upper Record Values," Annals of Data Science, Springer, vol. 8(2), pages 387-403, June.
    8. Wong, Augustine C.M. & Wu, Yan Yan, 2009. "A note on interval estimation of P(X," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3650-3658, August.
    9. Jana, Nabakumar & Bera, Samadrita, 2022. "Interval estimation of multicomponent stress–strength reliability based on inverse Weibull distribution," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 95-119.
    10. Abhimanyu Singh Yadav & S. K. Singh & Umesh Singh, 2019. "Bayesian estimation of $$R=P[Y," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(5), pages 905-917, October.
    11. Mustafa Nadar & Fatih Kızılaslan, 2014. "Classical and Bayesian estimation of $$P(X>Y)$$ P ( X > Y ) using upper record values from Kumaraswamy’s distribution," Statistical Papers, Springer, vol. 55(3), pages 751-783, August.
    12. A. Asgharzadeh & M. Kazemi & D. Kundu, 2017. "Estimation of $$P(X>Y)$$ P ( X > Y ) for Weibull distribution based on hybrid censored samples," 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. 8(1), pages 489-498, January.

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