## 2 Materials and Methods
### PAWN Method  
One of the advantages of the PAWN method is that the sensitivity indices derived from its application are independent of the probability distribution function and the cumulative distribution function. Therefore, they do not use a specific moment of output distribution to characterize the uncertainty, making them applicable regardless of the shape of the distribution. PAWN uses density-based sensitivity indices, which are \"moment-independent\" indices because, by definition, they consider the entire probability distribution of the output rather than just one part of it [16]. The advantage of PAWN over other \"independent-moment\" methods is that it characterizes the output distributions by their cumulative distribution functions rather than their probability density functions, which makes PAWN easier to implement [36]. PAWN has the common use of the cumulative distribution function (CDF) with regional sensitivity analysis (RSA). However, it is very different in terms of the methods and purposes by which CDF is applied. The RSA considers variations in the CDF of the inputs, whereas PAWN considers variations in the CDF of the output. In RSA,  
Figure 5: (a) Design spectrum of NCh2745, LIdleo’s spectrum scaled to NCh2745 and LIdleo’s original spectrum. (b) LIdleo’s earthquake original and scaled to fit NCh2745 spectrum of design. the focus is on the input space and how the input distributions vary by conditioning the output. In contrast, the focus in PAWN is on the output and how the output distribution varies when an input is conditioned. With respect to variance-based sensitivity analysis indices, the main advantage of PAWN is that it can be applied regardless of the type of output distribution [16]. In contrast, in other SA methods (e.g., [PERSON]'s method, [37]), if the output distribution is multimodal or if it is highly skewed, the use of variance as a proxy for uncertainty can lead to contradictory results [22; 38]. In order to identify the design parameters of the FBR and BIR with the greatest influence on the maximum responses of drift, displacement of the top storage level, and base shear load, the PAWN global sensitivity analysis method was used. This method generates a prioritization of the input parameters, quantitatively determining which parameters are the most influential in the model outputs by means of a sensitivity index \(T_{i}\). This index is not conditioned to any assumed input value, because the dependence of the Kolmogorov-Smirnov statistic [39; 40] on the value of \(x_{i}\) is eliminated by the statistic on \(x_{i}\), as can be seen in Equation (4). PAWN performs a sensitivity analysis of a model by characterizing the distribution of outputs by its CDF. The method measures the sensitivity of a parameter \(x_{i}\) as the distance between the unconditional probability distribution of the output variable, \(Y\), which is obtained when all inputs vary simultaneously, and the conditional distributions obtained by varying all inputs except \(x_{i}\)[16]. To measure the distance between unconditional and conditional CDFs, the Kolmogorov-Smirnov statistic is used [39; 40]:  
\[KS(x_{i})=\max_{y}\Big{|}F_{y}(y)-F_{y|x_{i}}(y)\Big{|} \tag{4}\]  
where, the unconditional CDF of the output \(Y\) is called \(F_{y}(y)\), and the conditional CDF when \(x_{i}\) is set is called \(F_{y|x_{i}}(y)\). Since \(F_{y|x_{i}}(y)\) explains what happens when variability due to \(x_{i}\) is removed, the difference between this and \(F_{y}(y)\) provides a measure of the effects of \(x_{i}\) on \(Y\). The limiting case occurs when \(F_{y|x}(y)\) coincides with \(F_{y}(y)\). In this case, it is deduced that by eliminating the uncertainty on \(x_{i}\), the output distribution is not affected, and it can be concluded that \(x_{i}\) has no influence on \(Y\) (e.g., see Figure 6 left). On the other hand, if the difference between \(F_{y|x}(y)\) and \(F_{y}(y)\) increases, the influence of \(x_{i}\) also increases, which indicates that it is a conditional CDF, as seen in Figure 6 on the right.