Evaluating the Performance of Bayesian Estimates for Burr XII Inverse Rayleigh Parameters Using MCMC

Authors

  • Alaa A. Khalaf Ministry of Education, Diyala Education Directorate: Diyala, Iraq Author https://orcid.org/0000-0001-9098-5701
  • Mundher A. Khaleel Department of Mathematics, College of Computer Science and Mathematics, Tikrit University, Tikrit, Iraq. Author
  • Danial Mazarei Department of Statistics, Faculty of Intelligent Systems Engineering and Data Science, Persian GulfUniversity, Bushehr, Iran. Author
  • Ahlam H. Tolba Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt Author
  • Akeem A. Adepoju Department of Statistics, Aliko Dangote University of Science and Technology, Wudil, 713281, Kano. Nigeria Author

DOI:

https://doi.org/10.62933/z56q8971

Keywords:

Burr XII-Family, Bayesian estimator, maximum likelihood estimates, prior distribution, loss function

Abstract

This work applied multiple Bayesian approaches to estimate the parameters of the Burr XII Inverse Rayleigh (BXII-IR) Distribution.  For Bayesian estimators, needed priors distribution for the parameters and certain loss functions such squared error, general entropy, and linear-exponential, owing to the unavailability of closed-form solutions for Bayesian estimates with these loss functions.   Bayesian estimate employing the Markov Chain Monte Carlo (MCMC) approach were assessed for performance.  The simulation results for Bayesian methods indicate that all methods consistently estimate the parameters, with the LN2 loss function estimator demonstrating the highest efficiency as assessed by mean squared error (MSE), root mean squared error (RMSE), bias, Highest Posterior Density Intervals (HPD), average interval length (AIL), and coverage probability (CP).

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Published

2025-07-18

Issue

Vol 2, no. 2, 2025

Section

Original Articles

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Copyright (c) 2025 Alaa A. Khalaf, Mundher A. Khaleel, Danial Mazarei, Ahlam H. Tolba, Akeem A. Adepoju (Author)

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How to Cite

Evaluating the Performance of Bayesian Estimates for Burr XII Inverse Rayleigh Parameters Using MCMC. (2025). Iraqi Statisticians Journal, 2(2), 49-63. https://doi.org/10.62933/z56q8971