## 3 Results and Discussion
### Statistical Characteristics of Acceleration Peaks  
In Figure 8, the PDF plots of the recorded acceleration data are presented for the vertical direction. Appendix A contains the numerical data for all kurtosis and skewness values in all three orientations and for all layers and FM space amounts. Here it has to be noted that presenting the kurtosis and skewness values is very important due to the fact that the random vibration testing controller in the  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**FM** & **Location** & **Lateral** & **Longitudinal** & **Vertical** \\ \hline \multirow{4}{*}{**0\%**} & Floor & 0.064 & 0.037 & 0.136 \\  & 1 st & 0.085 & 0.051 & 0.166 \\  & 2 nd & 0.101 & 0.069 & 0.170 \\  & 3 rd & 0.118 & 0.095 & 0.181 \\ \hline \multirow{4}{*}{**10\%**} & Floor & 0.063 & 0.044 & 0.146 \\  & 1 st & 0.068 & 0.057 & 0.193 \\  & 2 nd & 0.079 & 0.067 & 0.216 \\  & 3 rd & 0.098 & 0.070 & 0.217 \\ \hline \multirow{4}{*}{**20\%**} & Floor & 0.059 & 0.036 & 0.149 \\  & 1 st & 0.081 & 0.070 & 0.182 \\ \cline{1-1}  & 2 nd & 0.090 & 0.073 & 0.204 \\ \cline{1-1}  & 3 rd & 0.135 & 0.075 & 0.216 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Overall G\({}_{\text{rms}}\) for various layers and FM space, in all three orientations (1–200 Hz).  
Figure 7: Transmissibility plots of the various layers in the vertical direction for (**a**) FM 0%, (**b**) FM 10%, and (**c**) FM 20%.  
laboratory, when engineers want to simulate vibration circumstances, mostly generates a control signal from a normal distribution, so field-measured kurtosis can be used as an input parameter to perform realistic variability for the random signal during vibration simulations.  
The recorded acceleration events at each measurement and in each layer were positively peaked (positive kurtosis) and showed a difference (CI: 95%) from a normal Gaussian distribution (where the kurtosis is zero). This indicates a so-called \"heavy-tailed\" distribution. The reason for this phenomenon is that the field-recorded acceleration values (used with positive or negative orientation) did not follow the normal Gaussian distribution as a function of time. The kurtosis values of vertical recorded events were between 1.18 and 6.76. These values for the floor confirm the results of previous papers presented on the non-Gaussian nature of random vehicle vibration in delivery vehicles [17; 18; 19]. However, the values of kurtosis in higher layers approached zero, which means that in a stack unit, the higher layers suffer such random vibration that it almost follows a normal distribution. The kurtosis values of longitudinal and lateral recorded events were 8.08-19.83 and 5.97-15.86, respectively, for higher layers and various FM amounts.  
Figure 8: Distributions of vertical acceleration records from this study for (**a–d**) FM 0%, (**e–h**) FM 10%, and (**i–l**) FM 20%.  
In each case, skewness values showed deviation from zero, which indicates asymmetric distributions. These values were between \(-0.74\) and \(1.10\) in the vertical direction, \(1.99\)-\(3.43\) in the lateral direction, and \(2.15\)-\(3.87\) in the longitudinal direction. On the floor and in the vertical direction, the vehicle vibration was negatively skewed; these distributions thereby went towards the right dissymmetry. This can be attributed to more acceleration events in the vertical negative direction.