The procedure of selecting the values of hyper-parameters for prior distributions in Bayesian estimate has produced many problems and has drawn the attention of many authors, therefore the expected Bayesian (E-Bayesian) estimation method to overcome these problems. These approaches are used based on the step-stress acceleration model under the Exponential Type-I hybrid censored data in this study. The values of the distribution parameters are derived. To compare the E-Bayesian estimates to the other estimates, a comparative study was conducted using the simulation research. Four different loss functions are used to generate the Bayesian and E-Bayesian estimators. In addition, three alternative hyper-parameter distributions were used in E-Bayesian estimation. Finally, a real-world data example is examined for demonstration and comparative purposes.
Citation: M. Nagy, M. H. Abu-Moussa, Adel Fahad Alrasheedi, A. Rabie. Expected Bayesian estimation for exponential model based on simple step stress with Type-I hybrid censored data[J]. Mathematical Biosciences and Engineering, 2022, 19(10): 9773-9791. doi: 10.3934/mbe.2022455
The procedure of selecting the values of hyper-parameters for prior distributions in Bayesian estimate has produced many problems and has drawn the attention of many authors, therefore the expected Bayesian (E-Bayesian) estimation method to overcome these problems. These approaches are used based on the step-stress acceleration model under the Exponential Type-I hybrid censored data in this study. The values of the distribution parameters are derived. To compare the E-Bayesian estimates to the other estimates, a comparative study was conducted using the simulation research. Four different loss functions are used to generate the Bayesian and E-Bayesian estimators. In addition, three alternative hyper-parameter distributions were used in E-Bayesian estimation. Finally, a real-world data example is examined for demonstration and comparative purposes.
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Figures(2) / Tables(4)
M. Nagy, M. H. Abu-Moussa, Adel Fahad Alrasheedi, A. Rabie. Expected Bayesian estimation for exponential model based on simple step stress with Type-I hybrid censored data[J]. Mathematical Biosciences and Engineering, 2022, 19(10): 9773-9791. doi: 10.3934/mbe.2022455
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