Estimating parameters and reliability features in various situations is a key challenge for statistical researchers in many disciplines. The prime goal of this paper is to investigate the flexibility of the newly compound three-parameter Rayleigh Gamma Gompertz for estimating unknown parameters and the reliability function under different estimation methods, sample sizes, and datasets. Simulation experiments are presented to investigate how the different estimators behave under various sample sizes and parameter values. The estimators’ performance is measured using mean squared error. The empirical results demonstrated the outperforming, flexibility, and consistency of maximum likelihood and maximum product of spacing estimates to estimate the parameters and reliability function, with marked superiority of maximum likelihood for estimating the reliability function, confirming that this approach is still the most often used estimating technique due to its theoretical and practical features.