In this study, numerical analysis has been used to estimate the lifetime distribution parameters based on the Picard iteration technique. The point estimates of the generalized Weibull model parameters were derived using Picard and Bayes methods based on the generalized progressive hybrid censoring scheme, via a Monte Carlo simulation. The Simulation results indicated that Picard’s method is highly efficient and outperforms Bayes’ method based on the informative and kernel priors using different loss functions. Finally, two real datasets, including COVID-19 data, were studied to ensure Picard’s method can be used more effectively than the most popular estimation methods in fitting and analyzing real-life data.