Wind potential estimation is a crucial aspect of wind energy applications, often relying on the two-parameter ( k ,  c ) of the Weibull distribution (WD). By comparing the Root Mean Square Error (RMSE), chi-squared (χ 2), correlation coefficient (R), and determination coefficient (R 2), we can identify the most reliable and efficient methods for estimating these parameters and understanding the Weibull probability distribution (WPD). In this study, we selected seven methods: the Maximum Likelihood Method (MLM), the Energy Pattern Factor Method (EPFM), the L-moment Estimation Method (L-MOM), the Empirical Justus (EMJ), the Method of Moment (MOM), the Mean-standard deviation Method (MSDM), and the Curve Fitting Method (CFM) to evaluate the two-parameter of the WD. These methods were applied to the unique wind conditions of Al-Mukha City, Yemen, using the 2013 daily wind speed measured at 10 meters. The results indicate that the L-MOM represents the highest accuracy for all heights, while the EPFM represents the lowest accuracy. Furthermore, our analysis reveals that the two parameters increase with height.

For the aim of determining the wind speed characteristics and wind power density, the performance of five numerical approaches to identify the shape (k) and scale (c) parameters of the Weibull distribution function is assessed in this work. The chosen methods are the empirical Justus method (EMJ), the maximum likelihood method (ML), the energy pattern factor method (EPF), the moment method (MOM), and L-moment estimation method (L-MOM). In order to calculate the mean wind speed, wind speed standard deviation, and wind power density for Al-Hodeidah in West Yemen, the best suitable method must be determined. Daily mean wind speeds collected from January to December 2014 are used in this study. The findings show that using various parameter estimating techniques alters the precision of the values derived for mean wind speed, mean wind power density and their standard deviation, skewness and kurtosis. For this site, all of the methods: EMJ, EPF, ML, MOM, and L-MOM present a very good accuracy for predicting mean wind speed on both daily and monthly basis. For forecasting standard deviation of wind speed, the EMJ method performs the best one on both daily and monthly scales. The ML method is recommended for assessing the wind energy potential since it presents better performance in terms of forecasting the daily and monthly average power density at the study site. All methods showed a notable error with relative percent error (RPE) larger than 10% at the study site for the skewness and kurtosis of both wind speed and power density except the EPM method is sufficient for predicting the kurtosis of power with relative percent errors (RPE) smaller than 3%. For the standard deviation of power density analyses, all of the methods show remarkable errors with relative percent errors (RPE) greater than 11%.