## 3 Results and Discussion
### Fitting and Testing of the Key Parameters  
This study employs the Kolmogorov-Smirnov (KS) test to identify optimal probability distributions for key typhoon parameters. The hypothesis tests are conducted at the 5% or 1% significance level. If neither level yields statistical significance, empirical distributions are adopted, ultimately establishing optimal probabilistic models for typhoon parameters in Guangzhou. Since the negative binomial distribution is suitable for overdispersed data (variance \(>\) mean), it is not applicable to the historical typhoon data characteristics of Guangzhou; therefore, this distribution is not considered. The goodness-of-fit test results for Guangzhou's typhoon parameters are summarized in Table 1, while statistical models comparing the simulated and observed key parameters are illustrated in Figure 5.  
Parameter distribution selection follows rigorous statistical validation. The annual occurrence rate (\(\lambda\)) is estimated from 75 samples, whereas the other four key parameters are derived from 2834 samples. As shown in the table, the optimal distributions are identified as follows: the Poisson distribution for the annual occurrence rate, the gamma distribution for the translational velocity (\(V_{T}\)), and the generalized linear distribution for the minimum distance (\(D_{min}\)). The central pressure deficit (\(\Delta p\)) and movement direction (\(\theta\)) were not statistically validated; thus, empirical distributions were employed for these parameters.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \begin{tabular}{c} **Key** \\ **Parameters** \\ \end{tabular} & \begin{tabular}{c} **Alternative Probability** \\ **Distribution** \\ \end{tabular} & \begin{tabular}{c} **\(p\)-Value** \\ **\end{tabular} & \begin{tabular}{c} **Test** \\ **Statistic** \\ \end{tabular} & \begin{tabular}{c} **Critical** \\ **Value** \\ **(5\%)** \\ \end{tabular} & \begin{tabular}{c} **Critical** \\ **Value** \\ **(1\%)** \\ \end{tabular} & \
\begin{tabular}{c} **Optimal** \\ **Probability** \\ **Distribution** \\ \end{tabular} &
\begin{tabular}{c} **Distribution** \\ **Parameters** \\ \end{tabular} \\ \hline \(\lambda\) & Poisson & 0.9516 & 0.0182 & 0.1568 & 0.1880 & Poisson & \(\lambda=2.52\) \\  & Binomial & 0.9098 & 0.0251 & & & \\  & Lognorm & \(\sim\)0 & 0.0459 & & & \\ \(\Delta p\) & Gamma & \(\sim\)0 & 0.0662 & 0.0255 & 0.0306 & Empirical & - \\  & Weibull & \(\sim\)0 & 0.0946 & & & & \\  & Logorm & \(\sim\)0 & 0.0530 & & & & \\ \(V_{T}\) & Gamma & 0.1193 & 0.0194 & 0.0255 & 0.0306 & Gamma & \(k=3.988\) \\  & Normal & \(\sim\)0 & 0.0708 & & & & \(\theta=4.477\) \\  & Normal & \(\sim\)0 & 0.1623 & & & & \\ \(\theta\) & von Mises & \(\sim\)0 & 0.0922 & 0.0255 & 0.0306 & Empirical & - \\  & BimodalVM & \(\sim\)0 & 0.0436 & & & & \\  & Uniform & \(\sim\)0 & 0.0860 & & & & \\ \(D_{min}\) & Trapezoid & \(\sim\)0 & 0.0644 & 0.0255 & 0.0306 & General & \(c=2.527\) \\  & General linear & 0.1391 & 0.0187 & & & linear & \(d=1.451\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Goodness-of-fit test for the typhoon key parameters and the optimal probability distributions at Guangzhou.  
Figure 5: Statistical models comparing the simulated and observed key parameters.