## 3 Database and Methodology
### Methodology and Model
Based on the statistical analysis results based on Figure 4, \(\mu\) = 0.9538, \(\sigma\) = 0.3879, \(T/T_{ave}\) is expected to adhere to the normal distribution N(0.9538, 0.38792), and the fitting result successfully passes the \(\chi^{2}\) test within the 95% confidence interval. This implies that recurrent events in the same location possess an approximate 95% confidence interval falling within \([\mu-2\sigma,\mu+2\sigma]\). Subsequently, the probability density function for \(T/T_{ave}\) conforming to the normal distribution can be derived as follows:  
\[f(T/T_{ave})=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{(T/T_{ave}-\mu)^{2}}{2\sigma^ {2}}} \tag{1}\]  
The probability distribution function for the northeastern margin of the Tibetan Plateau can be derived as follows:  
\[F(t)=\Phi\left[\frac{t/R-0.9538}{0.3879}\right] \tag{2}\]  
In Equation (2), \(\Phi\) represents the standard normal distribution function, \(R\) denotes the average recurrence interval of earthquakes at a given location, and \(t\) signifies the elapsed time (the duration between the last earthquake and the present). Figure 7: Diagram of Weibull distribution Q-Q plot and reverse trend Weibull distribution Q-Q plot. A Q-Q plot of a sample of data versus a Weibull distribution. The deciles of the distributions are shown in the plot. many outliers are evident at the high end of the range. Employing the aforementioned probability distribution function, the conditional probability (\(P\)) of earthquake recurrence can be expressed by the following equation:  
\[P=\frac{F(t+\Delta t)-F(t)}{1-F(t)} \tag{3}\]  
In Equation (3), \(t\) represents the elapsed time (the duration between the last earthquake and the present), \(R\) denotes the average recurrence interval of earthquakes, while \(\Delta t\) signifies the time increment used to project the probability of future earthquake occurrences. To compute the conditional probability of earthquake recurrence, only the three fundamental parameters--\(t\), \(R\), and \(\Delta t\)--are required. Regarding the conditional probability model for earthquake recurrence, [PERSON] (1996) [12] conducted a comprehensive analysis by collating recurrence interval data from 46 ancient earthquakes within the continental interior. Employing the logarithmic normal distribution, [PERSON] fitted the cumulative frequency and established a universal distribution relationship applicable to all active faults within dynamic continents [12]:  
\[f(T/T_{ave})=\frac{T_{ave}}{T\sigma\sqrt{2\pi}}\exp\left[\frac{-1}{2\sigma^{2 }}\left(\ln\frac{T}{T_{ave}}-\mu\right)^{2}\right] \tag{4}\]  
Applying the maximum likelihood method, we obtain estimates for the mean (\(\mu\) = 0.1206) and standard deviation (\(\sigma\) = 0.5054). The resulting probability distribution function is as follows:  
\[F(t)=\Phi\left[\frac{\ln(t/R)+0.1206}{0.5054}\right] \tag{5}\]  
In the subsequent sections, we employ the previously mentioned two distribution models to examine the earthquake risk within the Maqin-Maqu segment of the Eastern Kunlun fault zone. Subsequently, we conduct a comparative analysis and discussion of the results, thereby mutually validating their feasibility.