Applying Bias-Correction Methods to Parameter Estimation for the Zeghdoudi Distribution in Medical Data

Abstract

The Zeghdoudi distribution (ZD) is a valuable model for analyzing lifetime data. It has been further developed for modeling various data types and for constructing related lifetime models. In statistical inference, the maximum likelihood method is well known for estimating the parameters of different distributions using large samples. However, when applied to small or moderate samples, the bias of the maximum likelihood estimator (MLE) can become problematic. This study proposes point estimators for the Zeghdoudi distribution using two bias-correction methods: the Cox-Snell method and the parametric bootstrap. The performance of these estimators is evaluated using average bias and root mean square error (RMSE) in simulation studies. The results demonstrate that the point estimators derived from the bias-correction methods improve finite-sample accuracy by reducing the bias of the maximum likelihood estimator to second order. In addition, the findings indicate that the parametric bootstrap technique outperformed the others under various conditions, whereas the MLE can be biased for small or moderate sample sizes. Furthermore, analyses of two medical datasets were conducted to validate the performance of the proposed estimators.