## 3 Results and Discussion
### Probability Characteristics of Extreme Pressure Coefficients
#### 3.1.2 Probability Distribution Modelling of Extreme Pressure Coefficient
Figure 6 shows the fitting for the Gumbel and GEV distribution with minimum wind pressure coefficients of 2 m\({}^{2}\) area in the north facade of the building at several typical wind direction angles (45\({}^{\circ}\), 60\({}^{\circ}\), 90\({}^{\circ}\), 120\({}^{\circ}\), 135\({}^{\circ}\), 180\({}^{\circ}\)). As can be seen from Figure 6, the fitting departs considerably from the fitted line for the case of the Gumbel distribution. The fitting is reasonable in the case of the GEV distribution for all wind directions, and the shape parameter value K in the GEV parameter estimation is less than 0. Figure 6: _Cont._  
The K-S test and the AIC method are used to investigate the fitting goodness for the extreme pressure coefficient. Figure 7 shows the probability distribution fitting test chart of the extreme pressure coefficients for different wind directions. It can be seen from Figure 7 that for the wind angle of 60\({}^{\circ}\), the D\({}_{\rm K}\) of the Gumbel distribution fitting is slightly larger than that of the GEV distribution, but the difference is small. Combined with the probability plot, it can be seen that the performance for the fitting based on the GEV distribution is better than that based on the Gumbel distribution, and for the wind direction of 90\({}^{\circ}\), the D\({}_{\rm K}\) of the Gumbel distribution fitting is significantly greater than that of the extreme value Type III distribution. The fitting goodness for the extreme value Type III distribution is significantly better than that for the Gumbel distribution. There are the same conclusions for the other wind directions. The AIC test can obtain the same conclusions as the K-S test. Therefore, in general, it can be concluded that the wind direction has little effect on the distribution model for peak pressure coefficients. The extreme value Type III distribution is preferred for the extreme pressure coefficient. Figure 6: Fitting results of the probability distribution of extreme pressure coefficient under different wind direction angles: (**a**) Fitting results between Gumbel and GEV distribution for 45\({}^{\circ}\), (**b**) Fitting results between Gumbel and GEV distribution for 60\({}^{\circ}\), (**c**) Fitting results between Gumbel and GEV distribution for 90\({}^{\circ}\), (**d**) Fitting results between Gumbel and GEV distribution for 180\({}^{\circ}\). Figure 7: D\({}_{\rm K}\) value and AIC value of extreme pressure coefficients for different wind angles. (**a**) D\({}_{\rm K}\) of K-S test; (**b**) AIC of AIC method. (3) Attribution of the probability distribution of the extreme wind pressure on the building envelope. The case of a wind angle of 0\({}^{\circ}\) is selected to study the probability model of the extreme pressure coefficient for an area of 2 m\({}^{2}\) on the building envelope. Figure 8 shows the ratio of D\({}_{\text{K}}\) that is based on the Gumbel distribution to the GEV distribution for the building envelope. Table 2 provides the fitting distribution percent of the extreme pressure coefficients on the building envelope. It can be observed from Figure 8 that the D\({}_{\text{K}}\) value obtained by the Gumbel distribution is larger than that based on the GEV distribution. The GEV fitting goodness will be better, and all the minimum wind pressure coefficients belong to the GEV distribution and follow the extreme value Type III distribution. For the maximum pressure coefficient, it is affected by the separation of airflow. The percent of probability distribution for the maximum value is 7%, 55%, and 38% by considering Type I, II, and III distributions consequently.