Objective Bayesian analysis using reparameterization for Type-II hybrid censored Rayleigh data†
Young Eun Jeon1 · Jung-In Seo2
12Department of Data Science, Andong National University
Correspondence to: † This work was supported by a Research Grant of Andong National University.
1 Researcher, Department of Data Science, Andong National University, Andong 36729, Korea.
2 Corresponding author: Associate professor, Department of Data Science, Andong National University, Andong 36729, Korea. E-mail: leehoo1928@gmail.com
1 Researcher, Department of Data Science, Andong National University, Andong 36729, Korea.
2 Corresponding author: Associate professor, Department of Data Science, Andong National University, Andong 36729, Korea. E-mail: leehoo1928@gmail.com
Received September 15, 2024; Revised October 6, 2024; Accepted October 10, 2024.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
- Abstract
- In a Rayleigh distribution, a scale parameter is a crucial determinant of data variability, making its accurate estimation essential for enhancing the predictive performance of statistical models. However, under a hybrid censoring scheme, obtaining a corresponding marginal distribution function is notoriously complex and often inefficient. This complexity poses significant challenges in deriving an exact form of the expected Fisher information which is foundational for constructing a frequentist confidence interval and defining objective priors in a Bayesian framework. This study develops an objective Bayesian approach that effectively circumvents the computational complexities inherent in a Type-II hybrid censoring framework, thereby facilitating the estimation of the scale parameter in the Rayleigh distribution. A key aspect of our approach is the straightforward derivation of the Jeffreys prior through reparameterization. Using the derived Jeffreys prior, Bayes estimators of the scale parameter and their posterior risks are obtained under both squared error and general entropy loss functions. In addition to point estimation, interval estimation for the scale parameter is performed. For comparison, the results derived from a conjugate prior are provided together, and the validity and applicability of our approach are demonstrated through Monte Carlo simulations and analysis of COVID-19 mortality rates in Italy.
- Keywords : Bayesian estimation, censoring scheme, posterior risk, Rayleigh distribution
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