Bayesian estimation of two-parameter power Rayleigh distribution and its application

This paper explores classical and Bayesian approaches to the estimation of unknown parameters and reliability functions for the power Rayleigh distribution. The maximum likelihood estimator (MLE) method is considered in classical estimation. The Bayesian estimation, on the other hand uses several loss functions under informative and non-informative prior distributions, utilizing the Lindley technique and Markov chain Monte Carlo (MCMC) methods for Bayesian computations. Approximate confidence i ntervals a re e stablished based on the MLEs using the delta technique, while Bayes credible intervals are determined using the MCMC method. A simulation study is conducted to compare the performance of these methods in terms of biases and mean square errors, revealing that Bayesian estimators outperform their classical counterparts. Additionally, two real datasets are presented for illustrative purposes.