Recently, numerical analysis has been used effectively for estimating the lifetime distribution parameters in the literature. Therefore, the main objective of this paper is to introduce a new numerical estimation technique, such as Picard’s method. This method has been used to estimate the Weibull model parameters and compare them with the most common estimation method in statistical inference, which is the Bayes’ method based on the informative gamma and kernel priors, via Monte Carlo simulations. The simulation results indicated that Picard’s method outperformed Bayes’ method using different loss functions. Finally, two real data sets have been analyzed for illustrations and TO compare the proposed methods.