## 4 Results and Discussion
### Analysis of the Fit of the Measured Data
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Estimation Method**} & \multicolumn{6}{c}{**IPIX Radar Measurement Data**} & \multicolumn{6}{c}{**An X-Band Radar Open-Source Measurement Data**} \\ \cline{2-13}  & **MoM** & **ZlogZ** & **MFoM** & **ZlogZ** & **MLE** & **MLE** & **MoM** & **ZlogZ** & **MFoM** & **ZlogZ** & **MLE** & **MLE** \\  & **(2/4)** & **(1)** & **(05/1)** & **(0.25)** & **(1D)** & **(2D)** & **(2/4)** & **(1)** & **(0.5/1)** & **(0.25)** & **(1D)** & **(2D)** \\ \hline Shape parameter & 3.125 & 2.636 & 2.419 & 2.351 & 2.415 & 2.410 & 2.165 & 2.096 & 3.933 & 6.022 & 3.599 & 3.603 \\ Scale Parameter & 0.225 & 0.298 & 0.330 & 0.343 & 0.329 & 0.330 & 0.876 & 0.817 & 0.392 & 0.240 & 0.454 & 0.453 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Estimation results of different parameter estimation methods. important for guiding the construction of statistical models and evaluating the performance of parameter estimation. From the data in Table 4, it can be seen that in terms of moment estimation, the higher-order moment estimation methods (positive 2 nd/4 th-order moments and positive 1 st-order logarithmic moments) result in poorer fitting performance of the generalized Pareto distribution model for the observed data compared to the lower-order moment estimation methods (positive 0.5 th/1 st-order fractional moments and positive 0.25 th-order logarithmic moments). Among them, the positive 0.25 th-order logarithmic moment achieves the best estimation results (MSD test: 4.26 \(\times\) 10\({}^{-5}\); RMSD: 6.40 \(\times\) 10\({}^{-3}\); and K-S test: 1.74 \(\times\) 10\({}^{-2}\)), with estimation errors reduced by 84.98%, 61.21%, and 60.36% compared to the worst performing positive 2 nd/4 th-order moments estimation. The inferior performance of higher-order moment estimation is due to larger accumulated sample errors in higher-order moments. Additionally, the maximum likelihood estimation method shows comparable fitting performance to lower-order moment estimation. Compared to the optimal lower-order moment estimation (i.e., positive 0.25 th-order logarithmic moment), the performance improvements are 4.10% (MSD), 1.59% (RMSD), and \(-\)8.42% (K-S). There is no significant difference in the fitting results of the one-dimensional and two-dimensional non-closed expression search results of the maximum likelihood estimation for the measured data. The fitting results of the sea clutter data in Table 5 yielded conclusions consistent with \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Assessment Metrics**} & **MoM** & **ZlogZ** & **MFoM** & **ZlogZ** & **MLE** & **MLE** \\  & **(2/4)** & **(1)** & **(05/1)** & **(0.25)** & **(1D)** & **(2D)** \\ \hline MSD & \(2.73\times 10^{-4}\) & \(5.98\times 10^{-5}\) & \(4.26\times 10^{-5}\) & \(4.10\times 10^{-5}\) & \(3.96\times 10^{-5}\) & \(3.94\times 10^{-5}\) \\ RMSD & \(1.65\times 10^{-2}\) & \(7.70\times 10^{-3}\) & \(6.50\times 10^{-3}\) & \(6.40\times 10^{-3}\) & \(6.30\times 10^{-3}\) & \(6.30\times 10^{-3}\) \\ K-S & \(4.39\times 10^{-2}\) & \(2.01\times 10^{-2}\) & \(1.91\times 10^{-2}\) & \(1.74\times 10^{-2}\) & \(1.90\times 10^{-2}\) & \(1.90\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The fitting test results of IPIX radar measured data. Figure 11: Fitting effect of generalized Pareto distribution.