## 3 Results and Discussion
### Analysis of Probability Distribution Functions
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Season** & **Distribution** & **Parameters** \\ \hline \multirow{8}{*}{Summer} & GAM & \(\alpha=3.87196207204796\)\(\beta=0.77507456427451\) \\  & GEV & k = \(-0.056960272557\)\(\sigma=1.4972487444338\)\(\mu=1.848955588234\) \\  & GUM & \(\beta=1.4709535966597\)\(\mu=1.8035050553625\) \\  & IGA & \(\lambda=9.9954369211484\)\(\mu=3.0010579509349\) \\  & RAY & \(\sigma=2.4065996370416\) \\  & WEI & \(\alpha=2.0109418096457\)\(\beta=3.4078140596928\) \\ \hline \multirow{8}{*}{Autumn}{umn}{umn}{umn}{c}{} & GAM & \(\alpha=3.9885106615485\)\(\beta=0.6490508105913\) \\  & GEV & k = \(0.0092984086461\)\(\sigma=1.2467280783248\)\(\mu=1.538991787376\) \\ \cline{1-1}  & GUM & \(\beta=1.2502151454179\)\(\mu=1.5383209018954\) \\ \cline{1-1}  & IGA & \(\lambda=9.6627572702393\)\(\mu=2.5888085399449\) \\ \cline{1-1}  & RAY & \(\sigma=2.1079513803782\) \\ \cline{1-1}  & WEI & \(\alpha=1.9027909814916\)\(\beta=2.9407369404527\) \\ \hline \multirow{8}{*}{Winter} & GAM & \(\alpha=3.16024334329771\)\(\beta=0.9410806487361\) \\ \cline{1-1}  & GEV & k = \(0.0992291628189\)\(\sigma=1.3671470841441\)\(\mu=1.7981664820307\) \\ \cline{1-1}  & GUM & \(\beta=1.4179032191099\)\(\mu=1.8725161930694\) \\ \cline{1-1}  & IGA & \(\lambda=8.5461048436524\)\(\mu=2.9740444076619\) \\ \cline{1-1}  & RAY & \(\sigma=2.5135424855173\) \\ \cline{1-1}  & WEI & \(\alpha=1.6904507406495\)\(\beta=3.3661889532314\) \\ \hline \multirow{8}{*}{Spring} & GAM & \(\alpha=3.7247001946047\)\(\beta=0.8304135151953\) \\ \cline{1-1}  & GEV & k = \(0.023269204272\)\(\sigma=1.5140912691744\)\(\mu=1.9235752478768\) \\ \cline{1-1}  & GUM & \(\beta=1.5031457206771\)\(\mu=1.9046835216656\) \\ \cline{1-1}  & IGA & \(\lambda=9.987043439496\)\(\mu=3.0930411052362\) \\ \cline{1-1}  & RAY & \(\sigma=2.5016406862587\) \\ \cline{1-1}  & WEI & \(\alpha=1.9406039977847\)\(\beta=3.5111781389429\) \\ \hline \multirow{8}{*}{Overall} & GAM & \(\alpha=3.5927533461899\)\(\beta=0.8113562688486\) \\ \cline{1-1}  & GEV & k = \(0.0226298979109\)\(\sigma=1.4040697074707\)\(\mu=1.7591867818483\) \\ \cline{1-1}  & GUM & \(\beta=1.4442754819722\)\(\mu=1.7706426185743\) \\ \cline{1-1}  & IGA & \(\lambda=9.3517654063929\)\(\mu=2.9150050416826\) \\ \cline{1-1}  & RAY & \(\sigma=2.3898368796538\) \\ \cline{1-1}  & WEI & \(\alpha=1.8510621376527\)\(\beta=3.3081271593922\) \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Probability distribution function parameters. As shown in Table 12, the GEV distribution consistently demonstrated the best performance across all seasons, as previously seen in Figure 7, with the lowest TE values: 0.00 in summer, 0.00 in autumn, 0.022 in winter, and 0.00 in spring. These values highlight the GEV distribution's superior ability to model the wind speed data effectively. In contrast, the IGA distribution ranked the worst, with the highest TE values of 0.90 in summer and 0.81 in winter, while the RAY distribution was also ranked last in autumn and winter, with TE values of 0.68 and 0.71, respectively. Notably, the dominance of the GEV distribution \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 \multirow{5}{*}{Spring} & GAM & 0.151 & 6 & 1184.74 & 4 & 0.024 & 2 & 0.674 & 4 \\ \cline{2-9}  & GEV & 0.079 & 1 & 45.54 & 1 & 0.017 & 1 & 0.000 & 1 \\ \cline{2-9}  & GUM & 0.081 & 2 & 46.84 & 2 & 0.296 & 6 & 0.343 & 2 \\ \cline{2-9}  & IGA & 0.145 & 4 & 1187.60 & 6 & 0.164 & 5 & 0.814 & 6 \\ \cline{2-9}  & RAY & 0.150 & 5 & 1186.30 & 5 & 0.045 & 3 & 0.695 & 5 \\ \cline{2-9}  & WEI & 0.139 & 3 & 1142.25 & 3 & 0.055 & 4 & 0.642 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: _Cont._  
Figure 7: Histograms with fitted distributions for seasonal wind speed data. remained consistent regardless of seasonal changes. The WEI distribution ranked fourth in summer, autumn, and winter and third in spring.