COMPARATIVE BAYESIAN AND CLASSICAL ESTIMATION OF THE SCALE PARAMETER IN THE WEIBULL POWER FUNCTION DISTRIBUTION - Sadiq, Ibrahim Abubakar; Dangana, Hauwa Abdulrahman; Usman, Abubakar; Garba, Jamilu (FUDMA Journal of Sciences, 2025)
We investigate the scale parameter of the Weibull power function distribution (WPFD) via both Bayesian and traditional statistical methodologies. Diverse estimations for the scale parameter were derived from the Bayesian framework, employing three distinct loss functions. The findings revealed that quadratic loss functions, utilising Jeffrey's and Gamma priors, consistently yielded better results than precautionary and squared error loss functions, irrespective of sample size. As the sample size increased, the estimation errors diminished, and the calculated values converged towards the true scale parameter. In conclusion, the Bayesian estimates for the scale parameter, particularly those utilising Jeffrey's and Gamma priors with a quadratic loss function, demonstrated superior performance compared to other estimation techniques
Keywords: Weibull exponential distribution; Maximum likelihood estimation; Bayesian estimation; Gamma prior; Jeffrey prior