in Table \[table1\], mainly for the purpose of interpreting the global shape of the FDFs.

We carried out 800 runs with different realizations of turbulence for each models. To do this, we randomly shift and rotate computational boxes of MHD turbulence simulations when we pile up them. Figure \[fig:f5\] shows 19 examples of FDFs for Model 1. We find that the shape of FDF varies significantly for different configurations of turbulence. For example, some FDFs have a single thin peak and others have multiple peaks. Such variations can be also seen for Models 2 to 4 (Figures \[fig:f6\] to \[fig:f8\]). Therefore, we see no universal shape of the FDF, even if we fix the parameters characterizing the global properties mentioned above.

Apparently, Models 2 (Figure \[fig:f6\]) and 4 (Figure \[fig:f8\]) have broader FDFs and this feature may allow us to probe some global properties of galaxies. Since the reconstructed FDF tends to show a peaked profile with tails, to quantify the features of the global shape of FDFs, we calculate the standard deviation $\sigma$, skewness $\gamma_{\rm s}$ and kurtosis $\gamma_{\rm k}$ of FDFs, defined as, $$\begin{aligned}
\sigma^2 &=& \frac{\sum_i |F(\phi_i)| (\phi_i-\mu)^2}{\sum_i |F(\phi_i)|} \\
\gamma_{\rm s} &=& \frac{\sum_i |F(\phi_i)| (\phi_i-\mu)^3}{\sigma^3 \sum_i 