Comparison Between Parameter Estimation for the Beta Distribution

The beta distribution is useful for modeling continuous random variables that lie Between 0 and 1, such as percentages and percentages. Beta distribution begins Many different shapes can be described by two shape parameters, and, and some statistical properties such as ordinal statistics of the beta distribution and a joint density function have also been shown. It can be challenging to estimate, hence the methods of calculating moments and maximum likelihood estimation have both been researched., although the moment method is more straightforward. We check Both methods here and their comparison is used in MATLAB through code and it was based on the initial parameters (a = 1 and b= 1.5) and for different sample sizes that started from (n = 25, 50, 100, and 200) and using simulation and iteration of 3000 and comparison between the two methods through known statistical measures as mean square error (MSE), correlation coefficient
$(\mathbf{R}^{\wedge}\mathbf{2})$
and the total deviations (TD), so through simulation experiments, we concluded that the MLE method is the best.