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Bayesian and Non-Bayesian Estimation for the Parameter of Bivariate Generalized Rayleigh Distribution Based on Clayton Copula under Progressive Type-II Censoring with Random Removal

Author

Listed:
  • El-Sayed A. El-Sherpieny

    (Cairo University)

  • Ehab M. Almetwally

    (Delta University of Science and Technology)

  • Hiba Z. Muhammed

    (Cairo University)

Abstract

In this paper, the bivariate generalized Rayleigh distribution is introduced based on Clayton copula and denoted as (Clayton-BGR). The likelihood function for progressive Type-II censoring scheme with random removal is derived and applied on the Clayton-BGR distribution. Bayesian and non -Bayesian estimation methods based on progressive Type-II censoring have been discussed. Asymptotic confidence intervals and bootstrap confidence intervals for the unknown parameters are obtained. Also, a simulation study has been conducted to compare the performances between censoring schemes. Also, two real data sets are analyzed to investigate the models and useful results are obtained for illustrative purposes.

Suggested Citation

  • El-Sayed A. El-Sherpieny & Ehab M. Almetwally & Hiba Z. Muhammed, 2023. "Bayesian and Non-Bayesian Estimation for the Parameter of Bivariate Generalized Rayleigh Distribution Based on Clayton Copula under Progressive Type-II Censoring with Random Removal," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1205-1242, August.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:2:d:10.1007_s13171-021-00254-3
    DOI: 10.1007/s13171-021-00254-3
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    References listed on IDEAS

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    1. Kundu, Debasis & Gupta, Arjun K., 2013. "Bayes estimation for the Marshall–Olkin bivariate Weibull distribution," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 271-281.
    2. Ehab Mohamed Almetwally & Hiba Zeyada Muhammed & El-Sayed A. El-Sherpieny, 2020. "Bivariate Weibull Distribution: Properties and Different Methods of Estimation," Annals of Data Science, Springer, vol. 7(1), pages 163-193, March.
    3. Kundu, Debasis & Dey, Arabin Kumar, 2009. "Estimating the parameters of the Marshall-Olkin bivariate Weibull distribution by EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 956-965, February.
    4. M. El-Morshedy & Ziyad Ali Alhussain & Doaa Atta & Ehab M. Almetwally & M. S. Eliwa, 2020. "Bivariate Burr X Generator of Distributions: Properties and Estimation Methods with Applications to Complete and Type-II Censored Samples," Mathematics, MDPI, vol. 8(2), pages 1-31, February.
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