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Bayesian Analysis of Generalized Inverted Exponential Distribution Based on Generalized Progressive Hybrid Censoring Competing Risks Data

Author

Listed:
  • Amal S. Hassan

    (Cairo University)

  • Rana M. Mousa

    (Cairo University)

  • Mahmoud H. Abu-Moussa

    (Cairo University)

Abstract

In this study, a competing risk model was developed under a generalized progressive hybrid censoring scheme using a generalized inverted exponential distribution. The latent causes of failure were presumed to be independent. Estimating the unknown parameters is performed using maximum likelihood (ML) and Bayesian methods. Using the Markov chain Monte Carlo technique, Bayesian estimators were obtained under gamma priors with various loss functions. ML estimate was used to create confidence intervals (CIs). In addition, we present two bootstrap CIs for the unknown parameters. Further, credible CIs and the highest posterior density intervals were constructed based on the conditional posterior distribution. Monte Carlo simulation is used to examine the performance of different estimates. Applications to real data were used to check the estimates and compare the proposed model with alternative distributions.

Suggested Citation

  • Amal S. Hassan & Rana M. Mousa & Mahmoud H. Abu-Moussa, 2024. "Bayesian Analysis of Generalized Inverted Exponential Distribution Based on Generalized Progressive Hybrid Censoring Competing Risks Data," Annals of Data Science, Springer, vol. 11(4), pages 1225-1264, August.
    • Handle: RePEc:spr:aodasc:v:11:y:2024:i:4:d:10.1007_s40745-023-00488-y
    DOI: 10.1007/s40745-023-00488-y
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    References listed on IDEAS

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    1. M. M. Mohie El-Din & M. Nagy & M. H. Abu-Moussa, 2019. "Estimation and Prediction for Gompertz Distribution Under the Generalized Progressive Hybrid Censored Data," Annals of Data Science, Springer, vol. 6(4), pages 673-705, December.
    2. N. Balakrishnan, 2007. "Rejoinder on: Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 290-296, August.
    3. Amal S. Hassan & Said G. Nassr & Sukanta Pramanik & Sudhansu S. Maiti, 2020. "Estimation in Constant Stress Partially Accelerated Life Tests for Weibull Distribution Based on Censored Competing Risks Data," Annals of Data Science, Springer, vol. 7(1), pages 45-62, March.
    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. Hon Ng & Ping-Shing Chan, 2007. "Comments on: Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 287-289, August.
    6. Amal S. Hassan & Said G. Nassr & Sukanta Pramanik & Sudhansu S. Maiti, 2020. "Correction to: Estimation in Constant Stress Partially Accelerated Life Tests for Weibull Distribution Based on Censored Competing Risks Data," Annals of Data Science, Springer, vol. 7(3), pages 547-547, September.
    7. James M. Tien, 2017. "Internet of Things, Real-Time Decision Making, and Artificial Intelligence," Annals of Data Science, Springer, vol. 4(2), pages 149-178, June.
    8. Arnab Koley & Debasis Kundu, 2017. "On generalized progressive hybrid censoring in presence of competing risks," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(4), pages 401-426, May.
    9. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 211-259, August.
    10. Amulya Kumar Mahto & Chandrakant Lodhi & Yogesh Mani Tripathi & Liang Wang, 2022. "Inference for partially observed competing risks model for Kumaraswamy distribution under generalized progressive hybrid censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(8), pages 2064-2092, June.
    11. Abd El-Raheem M. Abd El-Raheem & Mona Hosny & Mahmoud H. Abu-Moussa, 2021. "On Progressive Censored Competing Risks Data: Real Data Application and Simulation Study," Mathematics, MDPI, vol. 9(15), pages 1-17, July.
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