Bayesian Inference for the Reliability Parameter under the Inverse Rayleigh Distribution

Asuman Yılmaz

doi:10.17776/csj.1719303

Bayesian Inference for the Reliability Parameter under the Inverse Rayleigh Distribution

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

References

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Details

Primary Language

English

Subjects

Applied Statistics

Journal Section

Research Article

Authors

Asuman Yılmaz ^*
0000-0002-8653-6900
Türkiye

Publication Date

February 27, 2026

Submission Date

June 14, 2025

Acceptance Date

February 5, 2026

Published in Issue

Year 2026 Volume: 47 Number: 1

DOI

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

IZ

https://izlik.org/JA24UK95SF

Cite

RIS / Bibtex

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