Bayesian Inference for the Reliability Parameter under the Inverse Rayleigh Distribution

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