An Optimal Estimation Method on the Analysis of the Generalized Gamma Distribution Parameters Using Runge-Kutta Method

Abstract

Abstract Recently, in the literature many modifications introduced to improve the maximum likelihood estimation method, however most of them are less efficient than the Bayesian method especially for small samples. Therefore, in this study an improvement method based on the Runge-Kutta technique has been introduced for estimating the generalized gamma distribution parameters and compare them with the Bayesian estimates based on the informative gamma and kernel priors. A comparison between these estimators is provided by using an extensive Monte Carlo simulation based on two criteria, namely, the absolute bias and mean squared error. The simulation results indicated that the Runge-Kutta method is highly favorable, which provides better estimates and outperforms the Bayesian estimates using different loss functions based on the generalized progressive hybrid censoring scheme. Finally, two real datasets analyses for COVID-19 epidemic in Egypt are presented to illustrate the efficiency of the proposed methods.