Estimation of the Weibull Distribution Parameters and Reliability Using Runge-Kutta Method based on Interval-Censored Data

Abstract

Abstract In parameter estimation techniques, distribution parameters are usually independent, but theoretically, the distribution parameters are dependent because they are estimated from the same sampling group. Thus, based on this dependence, we provide an optimal technique using the Runge-Kutta method to estimate the Weibull model parameters and reliability and compare them with the Bayesian estimators based on the informative and kernel priors, via Monte Carlo simulations based on the interval-censored data. The simulation results indicated that the Runge-Kutta method provides better estimates and outperforms the Bayesian method using different loss functions. Finally, from a future perspective, the proposed model can be used to analyze some real data on COVID-19 deaths in Egypt using these methods, for potential comparative studies of this epidemic.