TY - JOUR
TI - A dual approach to parameter estimation classical vs. Bayesian methods in power Rayleigh modelling
AU - Mudasir Sofi
AU - Bhat Ajaz A
AU - Ahmad Sheikh P
AU - Rehman Aasimeh
AU - Jawa Taghreed M
AU - Sayed-Ahmed Neveen
AU - Tolba Ahlam H
JN - Thermal Science
PY - 2024
VL - 28
IS - 6
SP - 4877
EP - 4894
PT - Article
AB - 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.