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Bayesian Inference for the Reliability Parameter under the Inverse Rayleigh Distribution

Year 2026, Volume: 47 Issue: 1, 194 - 201, 27.02.2026

Asuman Yılmaz

https://doi.org/10.17776/csj.1719303
https://izlik.org/JA24UK95SF

Abstract

The parameter estimation problem of the probability  for the inverse Rayleigh distribution is the main focus of this study. The maximum likelihood and Bayesian estimation methods are taken into consideration. Importance sampling and Lindley approximation techniques are used in Bayesian inference. The maximum likelihood approximation is used to generate asymptotic confidence intervals. The importance sampling approximation is also used to obtain Bayesian credible intervals. A simulation study is conducted to evaluate and compare the performance of the proposed estimation methods. The results indicate that Bayesian estimators perform better than maximum likelihood estimators in many cases. Moreover, Bayesian credible intervals are shorter than the asymptotic confidence intervals, especially for small sample sizes.  Finally, a real-world application is conducted to improve the methods presented in this study

Keywords

Bayesian inference Inverse Rayleigh distribution Monte-Carlo simulation System reliability

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There are 33 citations in total.

Details

Primary Language English
Subjects Applied Statistics
Journal Section Research Article
Authors

Asuman Yılmaz 0000-0002-8653-6900

Submission Date June 14, 2025
Acceptance Date February 5, 2026
Publication Date February 27, 2026
DOI https://doi.org/10.17776/csj.1719303
IZ https://izlik.org/JA24UK95SF
Published in Issue Year 2026 Volume: 47 Issue: 1

Cite

APA Yılmaz, A. (2026). Bayesian Inference for the Reliability Parameter under the Inverse Rayleigh Distribution. Cumhuriyet Science Journal, 47(1), 194-201. https://doi.org/10.17776/csj.1719303

As of 2026, Cumhuriyet Science Journal will be published in six issues per year, released in February, April, June, August, October, and December