Numerical Method on the Generalized Gamma Distribution Parameters Using Picard’s Method

AbstractRecently, in the literature, many modifications have been introduced to improve the maximum likelihood estimation method. However, most of them are less efficient than the Bayes’ method, especially for small samples. Therefore, in this study, a numerical method based on Picard’s method has been introduced for estimating the generalized gamma distribution parameters and comparing them with Bayes’ method based on the informative gamma and kernel priors. A comparison between these estimates is provided by an extensive Monte Carlo simulation study based on two criteria: absolute bias and mean squared error. The simulation results indicated that Picard’s method is highly favourable, which provides better estimates and outperforms the Bayes’ method using different loss functions based on the generalized progressive hybrid censoring scheme. Finally, two real dataset analyses for the COVID-19 epidemic in Egypt are presented to illustrate the efficiency of the proposed methods.