Ibution function in the coefficients of influencing aspects of 15 was 9 described to clarify the heterogeneity with the 3 variables on passenger decision-making utility, as shown in Figure 3a .(a)(b)(c) Figure 3. The marginal probability of estimated coefficients. (a) The marginal probability of estimated coefficient “Dist”; Figure 3. The marginal probability of estimated coefficients. (a) The marginal probability of estimated coefficient “Dist”; (b) The marginal probability of estimated coefficient “Betamethasone disodium Description Pedestrian (c) The marginal probability of estimated estimated (b) The marginal probability of estimated coefficient “Pedestrian flow”; flow”; (c) The marginal probability of coefficient coefficient “Crowd density”. “Crowd density”.4.three. The Verification of Preferencemarginal probability distribution on the “Dist” coefficient Figure 3a shows that the Heterogeneitywas the this section, we useindicating that theskewness coefficient and kernel density In most concentrated, the approaches of estimated coefficient of the “Dist” element showed the lowest the passengers’ preference most of the people estimation to confirm heterogeneity level; that is,heterogeneity.will decide on the nearest exit The skewness coefficient [38] could be the characteristic worth that represents the asymmetry degree from the probability distribution density curve PK 11195 Technical Information relative for the average value. The calculation formula of skewness is as follows: =-(7)Sustainability 2021, 13,9 offor evacuation. Figure 3b,c showed that the marginal probability distribution with the coefficients of “Pedestrian flow” and “Crowd density” had been reasonably dispersed, and their heterogeneity levels had been greater than that of “Dist”, indicating that passengers’ perception of these two influencing variables is reasonably dispersed. four.3. The Verification of Preference Heterogeneity Within this section, we use the procedures of skewness coefficient and kernel density estimation to verify the passengers’ preference heterogeneity. The skewness coefficient [38] is the characteristic value that represents the asymmetry degree from the probability distribution density curve relative towards the typical value. The calculation formula of skewness is as follows: SK ( X ) = u – M0 (7) (8) (9)= EX 2 = EX two – exactly where Skew( X ) is the skewness coefficient of influencing elements, X could be the value of influencing elements, may be the mean worth of influencing factors and 2 is the variance of influencing factors. When Skew( X ) 0, it implies that the worth of influencing things is concentrated inside a smaller variety, and when Skew( X ) 0, it suggests that the value of influencing factors is concentrated within a huge variety. The higher the absolute value of skewness, the higher the skewness of its information distribution. In Table 5, we calculate not simply the imply and also the median, but also the skewness coefficient.Table five. The coefficient of skewness of influence factors. Independent Variable Dist Pedestrian flow Crowd density Skewness Coefficient 0.93 -0.01 0.19 Imply Worth 27.00 3.69 4.01 Median 20.89 three.70 3.The kernel density estimation [39] is actually a method utilised to study the qualities of data distribution in the data sample itself, which can be a nonparametric technique for estimating the probability density function. Hence, it has been extremely valued in the field of statistical theory and application. The calculation formula from the kernel density is as follows: f h (x) = 1 n x – xi ( K nh i h =1 (10)where K (.) would be the kernel function, h is usually a smoothing parameter, and h 0, and n is.