## 3 Analysis of Examples  
### Statistical Result Analysis  
To fulfill the requirements of probability function analysis and fitting tests for pavement performance evaluation metrics, an operational program was developed for analysis and calculation. The statistical results are shown in Table 4. The probability density and fitting analysis results of PCI, RQI, RDI, SRI, and other indicators are presented in Figure 1. The analysis of the results indicated that when comparing PCI, RQI, RDI, and SRI using the Kolmogorov-Smirnov and Anderson-Darling test methods, the Log-Logistic (3P) distribution provided the most suitable fitting results. When using the Chi-Squared method for comparison, the Log-Logistic (3P) distribution yielded the best fitting results for RQI and RDI. The PCI achieved the best result through Logistic fitting method, followed by Log-Logistic (3P) fitting. However, the SRI obtained the best result through Log-Logistic fitting. By comprehensively comparing the calculation results from all three methods, it can be concluded that the probability density distributions of PCI, RQI, RDI, and SRI can be effectively characterized by the Log-Logistic (3P) distribution. The cumulative probability density functions of PCI, RQI, RDI, and SRI, as well as the comparison between measured values and fitting values, are presented in Figures 2 and 3. In the case of the PCI, the Log-Logistic (3P) fitting is not effective in the range of [80; 85], meaning that the fitted function does not accurately represent the distribution of the index within this range. However, the fitting becomes stable and reliable in the range of [85; 100], indicating that the fitted function accurately represents the distribution of the PCI within this range. For the RQI, the Log-Logistic (3P) fitting is not effective in the ranges of [82; 87] and [93; 94], suggesting that the fitted function does not accurately represent the distribution of the index within these ranges. However, the fitting becomes stable and reliable in the range of [87; 93], indicating that the fitted function accurately represents the distribution of the RQI within this range. The overall trend of the RDI obtained through Log-Logistic (3P) fitting to the cumulative probability density function is evident. This suggests that the fitted function accurately represents the distribution of the RDI across its entire range. Similarly, the cumulative probability density function of the SRI obtained through Log-Logistic (3P) fitting shows an ideal effect within the range of [84; 92] and is stable and reliable. This indicates that the fitted function accurately represents the distribution of the SRI within this range. Figure 1: Comparison of probability density of pavement performance indexes and fitting analysis results: (**a**) PCI; (**b**) RQI; (**c**) RDI; (**d**) SRI. The measured and fitted values of pavement performance indicators are compared using Log-Logistic (3P) fitting. In the range of the PCI [0, 0.6], the fitting results fluctuate significantly, and the fitting effect is poor. In the range of [0.6, 0.9], the fitting results fluctuate slightly and are distributed on both sides of the line, indicating relative reliability and stability. For the RQI, in the range of [0, 0.2] and [0.5, 1], the fitting results fluctuate greatly, and the fitting effect is poor. However, in the range of [0.2, 0.5], the fitting results fluctuate slightly and are distributed on both sides of the straight line, indicating stability and reliability. The fitting values obtained for the RDI fluctuate around the actual values, with local fluctuations being significant. In the range of the SRI [0.4, 0.9], the fitting values exhibit a high correlation with the measured values, indicating a better effect. Figure 2: Cumulative probability density function of pavement performance evaluation indexes: (**a**) PCI; (**b**) RQI; (**c**) RDI; (**d**) SRI. Indeed, studying the probability distribution characteristics of asphalt pavement performance evaluation indexes is an important research endeavor.