Improved Maximum Likelihood Estimator of the Extended Rama Distribution with Application to Lifetime Data
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Maximum Likelihood Estimator, Extended Rama Distribution, Cox-Snell Bias-Correction, Bootstrap Bias-Correction, Monte Carlo Simulation
Abstract
Lifetime data are involved in numerous applied sciences, and the extended Rama (ER) distribution can be used to model such data. The maximum likelihood method is widely used for estimating the parameters of any distribution, particularly with large sample sizes. However, its effectiveness diminishes for small or moderate sample sizes due to the potential for biased estimates. This study improves the maximum likelihood estimator (MLE) of the extended Rama distribution by using two bias-corrected methods based on the Cox-Snell and parametric bootstrap approaches. Monte Carlo simulation was examined in terms of average bias and root mean square error (RMSE). The results indicate that the proposed bias-corrected estimators perform well in reducing both bias and root mean square error, thereby improving the accuracy of the estimates. Conversely, the maximum likelihood estimator exhibits relatively poor performance. Overall, the parametric bootstrap method outperformed the others, even when applied to small and moderate sample sizes. Additionally, the bias-corrected estimators were applied to a real dataset.
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