A dual approach to parameter estimation classical vs. Bayesian methods in power Rayleigh modelling

Abstract

In this article, we investigated the problem of estimating the parameters of power Rayleigh distribution using a range of classical and Bayesian estimate strategies. For applied statisticians and reliability engineers, parameter estimation provides a guide for choosing the best method of estimating the model parameters. Six frequentist estimation methods, including maximum likelihood estimation, Cramer-von Mises estimation, Anderson-Darling estimation, least square estimation, weighted least square estimation, and maximum product of spacing estimation, were taken into consideration when estimating the parameters of the power Rayleigh model. The expressions for Bayes estimators of the scale parameter are derived under squared error and precautionary loss functions and utilizing extensions of Jeffrey?s prior and natural conjugate priors. To investigate the finite sample properties of the parameter estimations, Monte Carlo simulations are also performed. Finally, two applications to real data are used to highlight the versatility of the suggested model and the comparison is made with the Rayleigh and some of its well-known extensions such as exponentiated Rayleigh and weighted Rayleigh distributions.