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The E-Bayesian Methods for the Inverse Weibull Distribution Rate Parameter Based on Two Types of Error Loss Functions

Author

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  • Hassan M. Okasha

    (Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Abdulkareem M. Basheer

    (Faculty of Administrative Sciences, Albaydha University, Albaydha, Yemen)

  • Yuhlong Lio

    (Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA)

Abstract

Given a sample, E-Bayesian estimates, which are the expected Bayesian estimators over the joint distributions of two hyperparameters in the prior distribution, are developed for the inverse Weibull distribution rate parameter under the scaled squared error and linear exponential error loss functions, respectively. The corresponding expected mean square errors, EMSEs, of E-Bayesian estimators based on the sample are derived. Moreover, the theoretical properties of EMSEs are established. A Monte Carlo simulation study is conducted for the performance comparison. Finally, three data sets are given for illustration.

Suggested Citation

  • Hassan M. Okasha & Abdulkareem M. Basheer & Yuhlong Lio, 2022. "The E-Bayesian Methods for the Inverse Weibull Distribution Rate Parameter Based on Two Types of Error Loss Functions," Mathematics, MDPI, vol. 10(24), pages 1-27, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4826-:d:1007746
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    References listed on IDEAS

    as
    1. Sanjay Kumar Singh & Umesh Singh & Dinesh Kumar, 2013. "Bayesian estimation of parameters of inverse Weibull distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(7), pages 1597-1607, July.
    2. Steve Bennett, 1983. "Log‐Logistic Regression Models for Survival Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(2), pages 165-171, June.
    3. Kundu, Debasis & Howlader, Hatem, 2010. "Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1547-1558, June.
    4. F. Yousefzadeh, 2017. "E-Bayesian and hierarchical Bayesian estimations for the system reliability parameter based on asymmetric loss function," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(1), pages 1-8, January.
    Full references (including those not matched with items on IDEAS)

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