Comparative Analysis of Picard and Bayesian Methods for Generalized Weibull: Parameter Estimation with Real Data Applications

Bayesian methods are widely employed for parameter estimation but often depend on subjective prior specifications, which can impact their robustness. This study evaluates Picard’s approach as a numerical estimation methodology for the generalized Weibull model, comparing its performance against the Bayesian method with informative gamma, characteristic, and kernel priors. Using Monte Carlo simulations based on the generalized progressive hybrid censoring scheme, we demonstrate that Picard’s method achieves competitive performance, particularly for sparse or censored datasets, where it achieves lower mean squared errors without requiring strong prior assumptions. Analysis of two real datasets, including vinyl chloride and COVID-19 mortality data, further confirms that Picard’s method offers reliable and efficient parameter estimation, often outperforming Bayesian approaches in scenarios with limited or skewed data. Our findings demonstrate that Picard's method delivers superior performance, achieving up to 15% reduction in mean squared error compared to Bayesian approaches, particularly for small sample sizes. These findings highlight Picard’s approach as a valuable statistical modeling tool, especially in reliability and survival analysis.