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Inferences for Nadarajah–Haghighi Parameters via Type-II Adaptive Progressive Hybrid Censoring with Applications

Author

Listed:
  • Ahmed Elshahhat

    (Faculty of Technology and Development, Zagazig University, Zagazig 44519, Egypt)

  • Refah Alotaibi

    (Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Mazen Nassar

    (Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Statistics, Faculty of Commerce, Zagazig University, Zagazig 44519, Egypt)

Abstract

This study aims to investigate the estimation problems when the parent distribution of the population under consideration is the Nadarajah–Haghighi distribution in the presence of an adaptive progressive Type-II hybrid censoring scheme. Two approaches are considered in this regard, namely, the maximum likelihood and Bayesian estimation methods. From the classical point of view, the maximum likelihood estimates of the unknown parameters, reliability, and hazard rate functions are obtained as well as the associated approximate confidence intervals. On the other hand, the Bayes estimates are obtained based on symmetric and asymmetric loss functions. The Bayes point estimates and the highest posterior density Bayes credible intervals are computed using the Monte Carlo Markov Chain technique. A comprehensive simulation study is implemented by proposing different scenarios for sample sizes and progressive censoring schemes. Moreover, two applications are considered by analyzing two real data sets. The outcomes of the numerical investigations show that the Bayes estimates using the general entropy loss function are preferred over the other methods.

Suggested Citation

  • Ahmed Elshahhat & Refah Alotaibi & Mazen Nassar, 2022. "Inferences for Nadarajah–Haghighi Parameters via Type-II Adaptive Progressive Hybrid Censoring with Applications," Mathematics, MDPI, vol. 10(20), pages 1-19, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3775-:d:941286
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    References listed on IDEAS

    as
    1. Samir K. Ashour & Ahmed A. El-Sheikh & Ahmed Elshahhat, 2022. "Inferences and Optimal Censoring Schemes for Progressively First-Failure Censored Nadarajah-Haghighi Distribution," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 885-923, August.
    2. 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.
    3. Ahmed Elshahhat & Mazen Nassar, 2021. "Bayesian survival analysis for adaptive Type-II progressive hybrid censored Hjorth data," Computational Statistics, Springer, vol. 36(3), pages 1965-1990, September.
    4. 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.
    5. Arne Henningsen & Ott Toomet, 2011. "maxLik: A package for maximum likelihood estimation in R," Computational Statistics, Springer, vol. 26(3), pages 443-458, September.
    6. Refah Alotaibi & Mazen Nassar & Ahmed Elshahhat, 2022. "Computational Analysis of XLindley Parameters Using Adaptive Type-II Progressive Hybrid Censoring with Applications in Chemical Engineering," Mathematics, MDPI, vol. 10(18), pages 1-24, September.
    7. 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.
    8. Hon Keung Tony Ng & Debasis Kundu & Ping Shing Chan, 2009. "Statistical analysis of exponential lifetimes under an adaptive Type‐II progressive censoring scheme," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(8), pages 687-698, December.
    9. M. M. Mohie El-Din & S. E. Abu-Youssef & Nahed S. A. Ali & A. M. Abd El-Raheem, 2016. "Estimation in constant-stress accelerated life tests for extension of the exponential distribution under progressive censoring," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 253-273, August.
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