Marshall–Olkin Exponentiated Inverse Rayleigh Distribution Using Bayesian and Non-Bayesian Estimation Methods

In this paper, a new generalization of continuous distributions using the Marshall–Olkin distribution as a generator is proposed and studied. Many important mathematical properties are derived from the proposed distribution, including moments, the moment generating function, order statistics, entropy, and the quantile function. Two different estimation methods are used, namely, maximum likelihood estimation and Bayesian methods. A Monte Carlo simulation is conducted to estimate the parameters and study the behavior of the proposed distribution. Bayesian estimation is obtained using the Gibbs sampler and Metropolis–Hastings algorithm. Finally, two real-world datasets are used to compare the performance of non-Bayesian and Bayesian methods.