改进自适应渐进 II 型删失下 Chen 分布的贝叶斯分析
Bayesian Analysis of Chen Distributionunder Improved Adaptive ProgressiveType-II Censoring
摘要: 本文基于改进的自适应渐进 II 型删失，对 Chen 分布进行了贝叶斯分析。首先利用 EM 算法得 到了参数的极大似然估计。针对共轭和非共轭的四种信息先验，运用大方差和遗传算法确定了先 验的超参数。进而根据 Metropolis-Hastings 算法实现了后验分布样本的抽取。最后，通过真实 数据集对不同先验下的贝叶斯估计性能进行比较并得出了相应的结论。
Abstract: This paper presents a Bayesian analysis of the Chen distribution based on an improved adaptive progressive Type-II censoring. Initially, the EM algorithm is used to obtain the maximum likelihood estimation of the parameters. Four types of informative priors, including conjugate and non-conjugate, are then determined using large variance and genetic algorithms. Subsequently, the Metropolis-Hastings algorithm is employed to extract samples from the posterior distribution. Finally, a comparison of the Bayesian estimation performance under different priors is conducted using real datasets, leading to corresponding conclusions.
文章引用：张莉. 改进自适应渐进 II 型删失下 Chen 分布的贝叶斯分析[J]. 理论数学, 2024, 14(1): 400-415. https://doi.org/10.12677/PM.2024.141040

参考文献

[1] Klein, J.P. and Moeschberger, M.L. (1997) Survival Analysis: Techniques for Censored and Truncated Data. Springer, New York.
[2] Balakrishnan, N. and Aggarwala, R. (2000) Progressive Censoring: Theory, Methods, and Applications. Birkhäuser Boston, MA.
https://doi.org/10.1007/978-1-4612-1334-5
[3] Ng, H.K.T., Kundu, D. and Chan, P.S. (2009) Statistical Analysis of Exponential Lifetimes under an Adaptive Type-II Progressive Censoring Scheme. Naval Research Logistics, 56, 687- 698.
https://doi.org/10.1002/nav.20371
[4] Yan, W., Li, P. and Yu, Y. (2021) Statistical Inference for the Reliability of Burr-Xii Distribution under Improved Adaptive Type-II Progressive Censoring. Applied Mathematical Modelling, 95, 38-52.
https://doi.org/10.1016/j.apm.2021.01.050
[5] 马金歌. 基于截尾样本的可靠性统计推断研究 [D]: [硕士学位论文]. 西安: 西安电子科技大学, 2021.
[6] Ranjan, R., Sen, R. and Upadhyay, S.K. (2021) Bayes Analysis of Some Important Lifetime Models Using MCMC Based Approaches When the Observations Are Left Truncated and Right Censored. Reliability Engineering and System Safety, 214, Article 107747.
https://doi.org/10.1016/j.ress.2021.107747
[7] Lv, Q., Tian, Y. and Gui, W. (2022) Statistical Inference for Gompertz Distribution under Adaptive Type-II Progressive Hybrid Censoring. Journal of Applied Statistics, 1-30.
https://doi.org/10.1080/02664763.2022.2136147
[8] Nassar, M. and Elshahhat, A. (2023) Estimation Procedures and Optimal Censoring Schemes for an Improved Adaptive Progressively Type-II Censored Weibull Distribution. Journal of Applied Statistics, 1-25.
https://doi.org/10.1080/02664763.2023.2230536
[9] Balakrishnan, N. and Mitra, D. (2012) Left Truncated and Right Censored Weibull Data and Likelihood Inference with an Illustration. Computational Statistics and Data Analysis, 56, 4011-4025.
https://doi.org/10.1016/j.csda.2012.05.004
[10] Shang, X. and Ng, H.K.T. (2020) On Parameter Estimation for the Generalized Gamma Distribution Based on Left-Truncated and Right-Censored Data. Computational and Mathematical Methods, 3, e1091.
https://doi.org/10.1002/cmm4.1091
[11] Okasha, H., Nassar, M. and Dobbah, S.A. (2021) E-Bayesian Estimation of Burr Type-XII Model Based on Adaptive Type-II Progressive Hybrid Censored Data. AIMS Mathematics, 6, 4173-4196.
https://doi.org/10.3934/math.2021247
[12] Zhang, Y., Liu, K. and Gui, W. (2021) Bayesian and E-Bayesian Estimations of Bathtub- Shaped Distribution under Generalized Type-I Hybrid Censoring. Entropy, 23, Article 934.
https://doi.org/10.3390/e23080934
[13] Algarni, A. and Almarashi, A.M. (2021) E-Bayesian Estimation of Reliability Characteristics of Two-Parameter Bathtub-Shaped Lifetime Distribution with Application. Quality and Reliability Engineering International, 37, 1635-1649.
https://doi.org/10.1002/qre.2817
[14] Shi, W. and Gui, W. (2023) Reliability Analysis of Bathtub-Shaped Distribution Using Empirical Bayesian and E-Bayesian Estimations under Progressive Type-II Censoring. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability.
[15] Dey, S., Elshahhat, A. and Nassar, M. (2023) Analysis of Progressive Type-II Censored Gamma Distribution. Computational Statistics, 38, 481-508. https://doi.org/10.1007/s00180-022-01239-y
[16] Chen, Z. (2000) A New Two-Parameter Lifetime Distribution with Bathtub Shape or Increasing Failure Rate Function. Statistics and Probability Letters, 49, 155-161.
https://doi.org/10.1016/S0167-7152(00)00044-4
[17] Noori Asl, M., Belaghi, R.A. and Bevrani, H. (2017) On Burr-Xii Distribution Analysis under Progressive Type-II Hybrid Censored Data. Methodology and Computing in Applied Probability, 19, 665-683.
https://doi.org/10.1007/s11009-016-9514-7
[18] Natarajan, R. and McCulloch, C.E. (1998) Gibbs Sampling with Diffuse Proper Priors: A Valid Approach to Data-Driven Inference? Journal of Computational and Graphical Statistics, 7, 267-277.
https://doi.org/10.1080/10618600.1998.10474776
[19] Hand, D., Daly, F., McConway, K., Lunn, D. and Ostrowski, E. (1993) A Handbook of Small Data Sets. Chapman and Hall/CRC, London.
[20] Algarni, A., Almarashi, A. M., Okasha, H. and Ng, H.K.T. (2020) E-Bayesian Estimation of Chen Distribution Based on Type-I Censoring Scheme. Entropy, 22, Article 636.
https://doi.org/10.3390/e22060636

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