## 5 Conclusions  
In this study, we propose a new stochastic approach for generating probability distribution of Peak Ground Acceleration (PGA) based on recorded data from a single seismic event in regions with limited strong ground motion data. Conventional ground motion prediction techniques often fall short in these areas because they rely on historical data \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multirow{2}{*}{**Station**} & \multicolumn{2}{c}{**Source-to-Site**} & \multirow{2}{*}{**PGA (g)**} & \multicolumn{2}{c}{**Median PGA**} & \multicolumn{2}{c}{**Median PGA**} \\  & & **Distance (km)** & & **of Records (g)** & **of Simulations (g)** \\ \hline
1 & PHA2 & 11.56 & 0.27 & 0.27 & 0.24 \\ \hline \multirow{3}{*}{2} & HAK & 24.04 & 0.036 & \multirow{3}{*}{0.039} \\  & CHS & 25.96 & 0.028 & & \\  & DKJ & 30.50 & 0.048 & & \\ \hline \multirow{3}{*}{3} & YOCB & 41.06 & 0.015 & \multirow{3}{*}{0.012} \\  & CSO & 41.35 & 0.059 & & \\  & YODB & 47.72 & 0.014 & & \\  & ADO2 & 49.69 & 0.042 & 0.015 & 0.012 \\  & USN2 & 51.63 & 0.035 & & \\  & JEJB & 53.40 & 0.0045 & & \\  & DAG2 & 57.63 & 0.015 & & \\ \hline \multirow{3}{*}{4} & YEYB & 62.99 & 0.014 & \multirow{3}{*}{0.0058} \\  & UL2 & 65.31 & 0.0058 & \\  & EUSB & 67.32 & 0.0065 & \\  & GUWB & 70.56 & 0.0050 & \\  & ADOA & 79.29 & 0.0090 & 0.0065 & 0.0053 \\ \cline{1-1}  & CIGB & 89.47 & 0.0040 & & \\ \cline{1-1}  & GUM & 98.15 & 0.052 & & \\ \cline{1-1}  & UJN & 98.40 & 0.080 & & \\ \cline{1-1}  & BUS2 & 99.80 & 0.0036 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of empirical and simulated PGAs by source-to-site distances. from seismically active regions. To address these limitations, the present study incorporates local site characteristics, source characteristics, and seismic wave propagation from a single seismic event into a stochastic point-source model, enabling the simulation of multiple artificial earthquakes. In the proposed approach, it is assumed that the source parameters, \(f_{c}\) and \(M_{0}\), which are recorded data from a single seismic event, are random variables. These parameters are demonstrated to be independent of the source-to-site distance, thereby incorporating the inherent uncertainty associated with them. It is also shown that the optimal copula function for capturing the relationship between \(f_{c}\) and \(M_{0}\), is the Frank copula function. This function was selected from five copula functions based on the highest log-likelihood. By using the Frank copula function for sampling points, the reliability of the generated artificial earthquakes is significantly enhanced. It is concluded that the present approach, utilizing Monte Carlo Simulation (MCS) with random sampling of the two key parameters, successfully generates sets of artificial ground motions and their corresponding PGA distributions. The method's effectiveness is validated by comparing the median PGAs of artificial earthquakes, generated from a single seismic event, across four different source-to-site distances with recorded data. The derived probability distributions of PGA provide a rational method for selecting an appropriate set of artificial earthquakes for seismic safety assessments for high-rise buildings, large dams, nuclear power plants, and other critical infrastructures in regions like the Korean Peninsula, where strong seismic records are extremely rare. Given the scarcity of large-amplitude recorded ground motions in this region, the ability to generate and select reasonable artificial earthquakes from a single seismic event is particularly valuable. Consequently, the proposed stochastic approach is expected to significantly enhance the reliability of seismic safety assessments and provide a solid foundation for future research on earthquake ground motion prediction in regions with limited strong motion records. To further enhance the method's reliability and broader applicability, future work should include validation against multiple seismic events of varying magnitudes.