New technique to estimate the parameters for extended exponential distribution

In this paper, a new modified technique is proposed to ascertain the estimation of two parameters associated with the extended exponential distribution, this method was called the method of regression, and the new method (Modified Multiple Regression Least Squares Estimator) was compared with the other two methodologies employing comprehensive datasets, specifically the technique known as Maximum Likelihood Estimation (MLE), are utilized in this context and the method of moments (ME), and after these methods were derived and a general mathematical formula was calculated for each parameter, these three methods were compared through Monte Carlo simulation and using the mean square error (MSE) criterion on multiple samples of different sizes and values of varying parameters, the comparative analysis conducted in this research indicates that the Modified Multiple Regression Least Squares Estimator methodology outperforms alternative approaches.