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Inference for the Two Parameter Reduced Kies Distribution under Progressive Type-II Censoring

Author

Listed:
  • Mansour Shrahili

    (Department of Statistics and Operations Research, King Saud University, Riyadh 11451, Saudi Arabia
    These authors contributed equally to this work.)

  • Naif Alotaibi

    (Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University, Riyadh 11623, Saudi Arabia
    These authors contributed equally to this work.)

  • Devendra Kumar

    (Department of Statistics, Central University of Haryana, Mahendergarh 123029, India
    These authors contributed equally to this work.)

  • Salem A. Alyami

    (Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University, Riyadh 11623, Saudi Arabia
    These authors contributed equally to this work.)

Abstract

In this paper, we obtained several recurrence relations for the single and product moments under progressively Type-II right censored order statistics and then use these results to compute the means and variances of two parameter reduced Kies distribution. Besides, these moments are then utilized to derived best linear unbiased estimators of the scale and location parameters of two parameter reduced Kies distribution. The parameters of the two parameter reduced Kies distribution are estimated under progressive type-II censoring scheme. The model parameters are estimated using the maximum likelihood estimation method. Further, we explore the asymptotic confidence intervals for the model parameters. Monte Carlo simulations are performed to compare between the proposed estimation methods under progressive type-II censoring scheme. Based on our study, we can conclude that maximum likelihood estimators is decreasing with respect to an increase of the schemes and comparing the three censoring schemes, it is clear that the mean sum of squares, confidence interval lengths are smaller for scheme 1 than schemes 2 and 3.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1997-:d:442003
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    References listed on IDEAS

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    1. Devendra Kumar & Sanku Dey & Saralees Nadarajah, 2017. "Extended exponential distribution based on order statistics," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(18), pages 9166-9184, September.
    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.
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    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. C. Satheesh Kumar & S. Dharmaja, 2014. "On some properties of Kies distribution," METRON, Springer;Sapienza Università di Roma, vol. 72(1), pages 97-122, April.
    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. Balakrishnan, N. & Saleh, H.M., 2011. "Relations for moments of progressively Type-II censored order statistics from half-logistic distribution with applications to inference," Computational Statistics & Data Analysis, Elsevier, vol. 55(10), pages 2775-2792, October.
    8. Robab Aghazadeh Chakherloo & Mohammad Pourgol-Mohammad & Kamran Sepanloo, 2017. "Change points estimations of bathtub-shaped hazard functions," 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(3), pages 553-559, September.
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    Cited by:

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