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AIMS Mathematics

2024, Volume 9, Issue 11: 31868-31881. doi: 10.3934/math.20241531
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Generalized Bayesian inference study based on type-Ⅱ censored data from the class of exponential models

  • 1.
    Department of Mathematics, College of Science, Taibah University, Saudi Arabia
  • 2.
    Department of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt
  • 3.
    Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
  • 4.
    Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, Saudi Arabia
  • Received: 24 August 2024 Revised: 26 October 2024 Accepted: 04 November 2024 Published: 08 November 2024

  • MSC : 62F10, 62F15

  • Generalized Bayesian (GB) is a Bayesian approach based on the learning rate parameter (LRP) ($ 0 < \eta < 1 $) as a fraction of the power of the likelihood function. In this paper, we consider the GB method to perform inference studies for a class of exponential distributions. Generalized Bayesian estimators (GBE) and generalized empirical Bayesian estimators (GEBE) for the parameters of the considered distributions are obtained based on the censored type Ⅱ samples. In addition, generalized Bayesian prediction (GBP) and generalized empirical Bayesian prediction (GEBP) are considered using a one-sample prediction scheme. Monte Carlo simulations and illustrative example are performed for one parameter models to compare the performance of the GBE and GEBE estimation results and the GBP and GEBP prediction results for different values of the LRP.

    Citation: Yahia Abdel-Aty, Mohamed Kayid, Ghadah Alomani. Generalized Bayesian inference study based on type-Ⅱ censored data from the class of exponential models[J]. AIMS Mathematics, 2024, 9(11): 31868-31881. doi: 10.3934/math.20241531

    Related Papers:

  • Generalized Bayesian (GB) is a Bayesian approach based on the learning rate parameter (LRP) ($ 0 < \eta < 1 $) as a fraction of the power of the likelihood function. In this paper, we consider the GB method to perform inference studies for a class of exponential distributions. Generalized Bayesian estimators (GBE) and generalized empirical Bayesian estimators (GEBE) for the parameters of the considered distributions are obtained based on the censored type Ⅱ samples. In addition, generalized Bayesian prediction (GBP) and generalized empirical Bayesian prediction (GEBP) are considered using a one-sample prediction scheme. Monte Carlo simulations and illustrative example are performed for one parameter models to compare the performance of the GBE and GEBE estimation results and the GBP and GEBP prediction results for different values of the LRP.



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