## 3 Results and Discussion  
### Descriptive Statistics of the Wind Speed  
Table 9 presents the annual and monthly wind speed statistics for the University of Fort Hare, detailing the data size (N), range (R), mean wind speed (\(\overline{\sigma}_{obs}\)), variance (\(\sigma^{2}_{obs}\)) standard deviation (\(\sigma_{obs}\)), coefficient of variation (CoV), skewness (S), kurtosis (K), and the minimum (Min) and maximum (Max) wind speeds based on the observed data. The mean \begin{table}
\begin{tabular}{l l} \hline \hline
**Distribution** & **Wind Power Density for Each Distribution** \\ \hline WEI & WPD\({}_{WEI}=0.5 pc^{3}\Gamma\left(1+3\alpha^{-1}\right)\) \\ RAY & WPD\({}_{RAY}=0.5p\)\(\cdot\)3.76\(\sigma^{3}\) \\ GAM & WPD\({}_{GAM}=0.5\rho\alpha^{3}\beta(\beta+2)(\beta+1)\) \\ GEV & WPD\({}_{GEV}=0.5p\frac{1}{\lambda^{2}}\left[(\mu k-\sigma)^{3}+\sigma^{3}\Gamma(1 -3k)+3(\mu k-\sigma)\sigma(\sigma\Gamma(1-2k)+(\mu k-\sigma)\Gamma(1-k))\right]\) \\ IGA & WPD\({}_{IGA}=0.5p\frac{3h^{5}}{\lambda^{2}}+\frac{3h^{4}}{\lambda}+\mu^{3}\) \\ GUM & WPD\({}_{GUM}=0.5\rho\mu^{3}+3\gamma\mu^{2}\beta+3\left(\frac{\pi^{2}}{6}+\gamma^{2} \right)\mu\beta^{2}-\left(\frac{n^{2}}{3}-\frac{n^{2}}{6}\gamma+2\gamma^{3}+ \gamma^{2}-2\zeta(3)\right)\beta^{3}\) \\  & where \(\zeta(3)\) is the Riemann zeta function at 3 = 1.202057 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Wind power density (WPD) formula for each distribution. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Wind Power Class** & **Mean Wind Speed (m/s)** & **Wind Power Density (W/m\({}^{2}\))** \\ \hline
1 (Poor) & 0–4.4 & 0–100 \\
2 (Marginal) & 4.4–5.1 & 100–500 \\
3 (Moderate) & 5.1–5.6 & 200–250 \\
4 (Good) & 5.6–6.0 & 200–250 \\
5 (Excellent) & 6.0–6.4 & 250–300 \\
6 (Excellent) & 6.4–7.0 & 300–400 \\
7 (Excellent) & 7.0–9.4 & 400–1000 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Wind resource availability classification [60; 61; 62; 63]. wind speed (\(\overline{v}_{obs}\)) peaked in July at 13.8m/s and was lowest in February at 8.3m/s. The observed \(\sigma_{obs}^{2}\) ranged from 2.119 in May to 2.872 in September, indicating fluctuations in wind speed consistency. The standard deviation (\(\sigma_{obs}\) ) generally showed similar trends, with the highest values in July (4.83 m/s) and lowest values in May (2.44 m/s). The variability in the wind speeds across the months demonstrated significant fluctuations, as the CoV values indicate. In July, the wind speed variability was at its peak, with a CoV of 77%, marking it as the most unpredictable month. This was followed by May and August, each with a CoV of 74%, reflecting similarly extreme variability [19; 34]. Conversely, January and September exhibited relatively lower CoV values of 63% and 67%, respectively, though still above the threshold for high variability (>40%) [64]. The positive skewness suggests that the measured wind speeds were typically above the mean, indicating better wind performance at this location and a right-skewed distribution [1; 34]. These results are similar to other studies [29; 64]. The kurtosis values were positive and less than 3, except in January. The maximum wind speed recorded was 13.8 m/s, reflecting a steady upper limit across the observations. Overall, these results indicate clear seasonal variation in wind characteristics, with notable mid-year peaks and a general trend of increasing variability during the summer months. As illustrated in Figure 3, the monthly mean wind speed values typically ranged from 2.6 to 2.9 m/s, with only a few instances falling below 2.4 m/s. The highest monthly mean value, 2.872 m/s, was recorded in September. Figure 4 depicts a comparison of four statistical metrics, namely, the mean, variance, skewness, and kurtosis, across the six distributions (GAM, GEV, GUM, IGA, WEI, RAY) relative to the actual wind data. The actual wind data's mean was 2.603 m/s, which was closely approximated by most distributions with minimal variation. The GEV distribution had the closest mean of 2.602 m/s. The actual data had a variance of 3.424.