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Progressive Type-II Censored Data and Associated Inference with Application Based on Li–Li Rayleigh Distribution

Author

Listed:
  • Devendra Kumar

    (Central University of Haryana)

  • M. Nassar

    (King Abdulaziz University
    Zagazig University)

  • Sanku Dey

    (St. Anthony’s College)

Abstract

Based on progressive Type-II censored samples, we first derive the recurrence relations for the single and product moments of progressively Type-II censored order statistics from two parameter Rayleigh distribution. These recurrence relations enable us to compute the mean and variances of all progressively Type-II censored order statistics for all sample sizes in a simple and efficient manner. Further, an algorithm is discussed which enable us to compute all the means and variances of two parameter Rayleigh progressive Type-II censored order statistics for all sample sizes and all censoring schemes. Next, we obtain the maximum likelihood estimators of the unknown parameters and the approximate confidence intervals of the parameters of the Rayleigh distribution. Finally, we consider Bayes estimation under five different types of loss functions (symmetric and asymmetric loss functions) using independent gamma priors for both the unknown parameters. Monte Carlo simulations are performed to compare the performance of the proposed methods, and one data set has been analyzed for illustrative purposes.

Suggested Citation

  • Devendra Kumar & M. Nassar & Sanku Dey, 2023. "Progressive Type-II Censored Data and Associated Inference with Application Based on Li–Li Rayleigh Distribution," Annals of Data Science, Springer, vol. 10(1), pages 43-71, February.
    • Handle: RePEc:spr:aodasc:v:10:y:2023:i:1:d:10.1007_s40745-021-00339-8
    DOI: 10.1007/s40745-021-00339-8
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    References listed on IDEAS

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    1. Manoj Kumar & Anurag Pathak & Sukriti Soni, 2019. "Bayesian Inference for Rayleigh Distribution Under Step-Stress Partially Accelerated Test with Progressive Type-II Censoring with Binomial Removal," Annals of Data Science, Springer, vol. 6(1), pages 117-152, March.
    2. Mahmoud R. Mahmoud & Khalaf S. Sultan & Hassan M. Saleh, 2006. "Progressively censored data from the linear exponential distribution: moments and estimation," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 199-215.
    3. Mansour Shrahili & Naif Alotaibi & Devendra Kumar & Salem A. Alyami, 2020. "Inference for the Two Parameter Reduced Kies Distribution under Progressive Type-II Censoring," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    4. 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.
    5. Hui Jiang & Qingshan Yang, 2016. "Moderate deviations for the moment estimators in Rayleigh distribution with two parameters," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(2), pages 330-339, January.
    6. Mansoor Rashid Malik & Devendra Kumar, 2017. "Relations For Moments Of Progressively Type-Ii Right Censored Order Statistics From Erlang-Truncated Exponential Distribution," Statistics in Transition New Series, Polish Statistical Association, vol. 18(4), pages 651-668, December.
    7. 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.
    8. Tanmay Sen & Yogesh Mani Tripathi & Ritwik Bhattacharya, 2018. "Statistical Inference and Optimum Life Testing Plans Under Type-II Hybrid Censoring Scheme," Annals of Data Science, Springer, vol. 5(4), pages 679-708, December.
    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. Hui Jiang & Xin Yun & Chen Xie, 2016. "Asymptotic properties for the moment estimators in Rayleigh distribution with two parameters," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(16), pages 4760-4770, August.
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