## 3 Results and Discussion
### Analysis of Probability Distribution Functions
In Figure 8, the TE for each distribution listed in Table 13 is represented by individual bars, with different colors within each bar indicating the contribution of each normalized test statistic metric (KSS, AD, and WPDE) to the TE. Based on the analysis in Table 13 and Figure 8, which show the TE for each distribution, the GEV distribution emerged as the best-performing model, with the lowest TE of 0.0202, primarily influenced by the WPDE metric. Its three-parameter structure allowed it to capture rare and high-impact wind events, crucial for accurately representing variability in wind regimes. Additionally, it ranked first in KSS with a value of 0.0995, second in AD with 276.95, and third in WPDE with 0.024, demonstrating consistent performance across multiple indicators. The GUM distribution followed with a moderate TE of 0.3394, primarily driven by WPDE, as shown in Figure 8. The WEI distribution, with a TE of 0.5421, showed major contributions from KSS and AD. The IGA distribution had a TE of 0.5622, dominated by AD contributions, while the RAY distribution, with the highest TE of 0.6667, was mainly influenced by AD and KSS contributions. These findings align with the seasonal performance trends, confirming the GEV distribution as the most effective and robust model overall. It is worth noting that the RAY distribution performed poorly both seasonally and overall, further emphasizing its inadequacy. Its dismal performance can be attributed to its single-parameter structure, which assumes a zero mean wind vector an overly simplistic \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Distribution** & **KSS** & **Rank** & **AD** & **Rank** & **WPDE** & **Rank** & **TE** & **Overall Rank** \\ \hline GAM & 0.1699 & 5 & 4910.418 & 5 & 0.042 & 4 & 0.6005 & 5 \\ GEV & 0.0995 & 1 & 276.9513 & 2 & 0.024 & 3 & 0.0202 & 1 \\ GUM & 0.1012 & 2 & 272.8823 & 1 & 0.367 & 6 & 0.3394 & 2 \\ IGA & 0.1526 & 3 & 4868.478 & 4 & 0.072 & 5 & 0.5622 & 4 \\ RAY & 0.1917 & 6 & 5259.141 & 6 & 0.003 & 1 & 0.6667 & 6 \\ WEI & 0.1622 & 4 & 4735.565 & 3 & 0.022 & 2 & 0.5421 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Performance comparison of the six distributions for the entire period of 2021–2023. Figure 8: Contributions of normalized KSS, AD, and WPDE to TE for each distribution in Table 13.  
approach that failed to capture the variability and extremes present in real-world wind speed data. Although the Weibull distribution ranked third out of six in this analysis, it remains a historically popular choice for wind speed modeling due to its simplicity and flexibility. Its two-parameter structure makes it easy to apply and compatible with various parameter estimation methods. For instance, the Weibull distribution, combined with the OpenWind method, has demonstrated notable effectiveness at sites such as Fort Beaufort and Upper Blinkwater in the Eastern Cape [1,4]. However, in this study, the GEV and GUM distributions, both designed to model extreme wind speeds, proved to be the most effective in fitting the wind data. Additionally, the performance of the Weibull distribution could potentially be improved using advanced optimization techniques, such as artificial intelligence, to refine its scale and shape parameter estimation.