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In parametric estimates, the maximum likelihood estimation method is the most popular method widely used in the social sciences and psychology, although it is biased in situations where sample sizes are small or the data are heavily censored. Therefore, the main objective of this research is to improve this estimation method using the Runge–Kutta technique. The improved method was applied to derive the estimators of the shape scale family parameters and compare them with Bayesian estimators based on the informative and kernel priors, via Monte Carlo simulation. The simulation results showed that the improved maximum likelihood estimation method is highly efficient and outperforms the Bayesian method for different sample sizes. Finally, from a future perspective, the proposed model could be important for analyzing real data sets including data on COVID-19 deaths in Egypt, for potential comparative studies with other countries.

Improved maximum likelihood estimation of the shape-scale family based on the generalized progressive hybrid censoring scheme