## 3 Database and Methodology
### Methodology and Model  
Employing SPSS 26.0 statistical software, we construct a frequency distribution histogram illustrating the recurrence probability (\(T/T_{ave}\)) of ancient earthquakes in the northeastern Tibetan Plateau (Figure 4). Figure 4 reveals that while variations in recurrence probabilities among different ancient earthquakes are substantial, they notably diminish after normalization processing, resulting in a distribution skewed towards values near 1.0. The concentration of \(T/T_{ave}\) is confined within a range proximate to 1.0. Furthermore, we posit that this frequency distribution may conform to potential fits with a normal distribution, logarithmic normal distribution, and Weibull distribution. Subsequent sections utilize the Q-Q plots to evaluate potential distribution forms Figures 5-7. Figure 4: Histogram of normalized data of ancient earthquake recurrence intervals in the northeastern Tibetan Plateau T/Tave and the normal distribution fitting curve. T represents recurrence interval of ancient earthquake, Tave represents average recurrence interval, T/Tave represents normalized data of ancient earthquake recurrence intervals. In statistics, a Q-Q plot (quantile-quantile plot) serves as a probability plot, offering a graphical method for comparing two probability distributions by plotting their quantiles against each other. Each point (x, y) on the plot corresponds to a quantile of the second distribution (y-coordinate) plotted against the same quantile of the first distribution (x-coordinate). This results in a parametric curve where the parameter is the index of the quantile interval [20]. The primary purpose of a Q-Q plot is to compare the shapes of distributions, providing a visual representation of how properties such as location, scale, and skewness are either similar or different in the two distributions. Q-Q plots can be applied to compare collections of data or theoretical distributions. Utilizing Q-Q plots for comparing two data samples can be seen as a non-parametric approach to assessing their underlying distributions. While Q-Q plots are generally more diagnostic than comparing sample histograms, they  
Figure 5: Diagram of normal Q-Q plot and reverse trend normal Q-Q plot. A normal Q-Q plot comparing randomly generated, independent standard normal data on the vertical axis to a standard normal population on the horizontal axis. The linearity of the points suggests that the data are normally distributed. Figure 6: Diagram of logarithmic normal Q-Q plot and reverse trend logarithmic normal Q-Q plot. A Q-Q plot of a sample of data versus a logarithmic distribution. The deciles of the distributions are shown in the plot. Many outliers are evident at the high end of the range. are less widely known. Commonly, Q-Q plots are employed to compare a dataset to a theoretical model, offering a graphical assessment of goodness of fit rather than reducing to a numerical summary statistic. Additionally, Q-Q plots are used to compare two theoretical distributions to each other. As Q-Q plots compare distributions, there is no requirement for the values to be observed as pairs, as in a scatter plot, or for the numbers of values in the two groups being compared to be equal [21]. Based on the aforementioned analysis, in conjunction with Figures 5-7, it is evident that the normal distribution yields the most favorable fit, followed by the Weibull distribution, with the logarithmic normal distribution performing the least satisfactorily. Consequently, this study opts for the normal distribution as the probability density function. \(T/T_{ave}\) is expected to adhere to the normal distribution: \(T/T_{ave}\)\(\sim\)N(\(\mu\), \(\sigma^{2}\)), \(\mu\) represents the expected value of the normal distribution; it can be interpreted as a position parameter. \(\sigma\) represents the standard deviation; it can be interpreted as the amplitude of the distribution.