## 3 Results and Discussion
### Descriptive Statistics of the Wind Speed
However, the variance of the distributions showed more variation, indicating differences in data spread. The GEV distribution closely matched this variance with a value of 3.447, while the GAM distribution deviated the most, showing a significantly lower variance of 2.365. The skewness of the actual data was 1.12, a positive value, and the skewness values calculated from all the distributions were also positive. The GEV distribution, with a skewness of 1.28, and the GUM distribution, with a skewness of 1.14, were closer to the actual data, while the IGA distribution exhibited the highest skewness at 1.675, indicating a more pronounced right-skewed distribution. The GAM distribution, on the other hand, had the lowest skewness at 0.366, indicating less asymmetry than the actual data. In terms \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Month** & **N** & **R** & \(\overline{v}_{obs}\) & \(\sigma^{2}_{obs}\) & \(\sigma_{obs}\) & **CoV(\%)** & **S** & **K** & **Min** & **Max** \\ \hline Jan & 2232 & 9.5 & 2.756 & 3.04 & 1.74 & 63 & 0.59 & \(-\)0.04 & 0 & 9.5 \\ Feb & 2016 & 8.3 & 2.481 & 3.12 & 1.77 & 71 & 0.71 & 0.09 & 0 & 8.3 \\ Mar & 2232 & 9.5 & 2.456 & 2.94 & 1.72 & 70 & 0.87 & 0.63 & 0 & 9.5 \\ Apr & 2160 & 9.6 & 2.234 & 2.48 & 1.57 & 70 & 1.12 & 1.61 & 0 & 9.6 \\ May & 2232 & 11.5 & 2.119 & 2.44 & 1.56 & 74 & 1.52 & 3.69 & 0 & 11.5 \\ Jun & 2160 & 11.1 & 2.653 & 3.57 & 1.89 & 71 & 1.39 & 2.09 & 0 & 11.1 \\ Jul & 2232 & 13.8 & 2.848 & 4.83 & 2.20 & 77 & 1.58 & 2.61 & 0 & 13.8 \\ Aug & 2232 & 12.0 & 2.710 & 3.97 & 1.99 & 74 & 1.36 & 2.10 & 0 & 12.0 \\ Sept & 2160 & 10.6 & 2.872 & 3.67 & 1.92 & 67 & 1.15 & 1.48 & 0 & 10.6 \\ Oct & 2232 & 10.9 & 2.762 & 3.61 & 1.90 & 69 & 0.76 & 0.43 & 0 & 10.9 \\ Nov & 2160 & 9.4 & 2.669 & 3.32 & 1.82 & 68 & 0.63 & 0.05 & 0 & 9.4 \\ Dec & 2232 & 10.2 & 2.670 & 3.46 & 1.86 & 70 & 0.74 & 0.32 & 0 & 10.2 \\ Annual & 26,280 & 13.8 & 2.603 & 3.42 & 1.85 & 71 & 1.12 & 1.56 & 0 & 13.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Annual and monthly statistical wind data for University of Fort Hare at 10 m AGL. of kurtosis, the actual data showed a value of 1.57, suggesting that the wind speed data had few extreme values. The GEV distribution exhibited a kurtosis of 6.14, which was significantly higher than the kurtosis of the actual wind data, indicating a more pronounced peak and steeper tails. The IGA distribution demonstrated an even higher kurtosis of 7.68, suggesting an exceptionally sharp peak. Also, the GUM, GAM, WEI, and RAY distributions showed kurtosis values that were also higher than the actual wind data but not as extreme as the IGA and GEV distributions. While most of the distributions aligned reasonably well with the actual wind data in terms of mean and variance, the IGA and GEV distributions deviated the most in their kurtosis, highlighting their tendency for sharper peaks and heavier tails. The results also showed a similar trend to the findings of [43], where the distributions exhibited variations in these statistical properties compared to the values obtained from actual wind speed data, especially when the parameters were estimated using the maximum likelihood method. Figure 4: Comparison of statistical metrics for the six distributions. Figure 3: Monthly average wind speed at 10m AGL for the University of Fort Hare. The diurnal variation in the mean wind speed, as shown in Figure 5, illustrated a clear daily cycle over a 24 h period. During the early morning hours, from midnight to around 8 a.m., the wind speeds were relatively low and remained almost constant. At around 8:30 a.m., the wind speed began to increase gradually, followed by a sharp rise after 9:00 a.m., peaking in the late afternoon at 5 p.m. with a maximum value of 4.28 m/s. After this peak, the wind speeds steadily declined as the day transitioned into evening, reaching a minimum of 1.65 m/s early at 8 a.m.