Table 3 Random characteristics of material parameters

\({f\left(x\right)=\frac{1}{\sigma \sqrt{2\pi }}e}^{-\frac{{\left(x-\mu \right)}^{2}}{{2\sigma }^{2}}}\)

\({f\left(x\right)=\frac{1}{x\sigma \sqrt{2\pi }}e}^{-\frac{{\left(\mathrm{ln}x-\mu \right)}^{2}}{{2\sigma }^{2}}}\)

\(\begin{array}{cc}{f\left(x\right)=\frac{1}{\sigma }\left[1+\xi \left(\frac{x-\mu }{\sigma }\right)\right]}^{-\frac{1}{\xi }-1}& {e}^{{-\left[1+\xi \left(\frac{x-\mu }{\sigma }\right)\right]}^{-\frac{1}{\xi }}}\end{array}\)

\(f\left(x\right)=\frac{{\beta }^{\alpha }}{\Gamma \left(\alpha \right)}{x}^{\alpha -1}{e}^{-\beta x}\)

\(f\left(x\right)=\left\{\begin{array}{c}{\frac{k}{\lambda }\left(\frac{x}{\lambda }\right)}^{k-1}{e}^{{-\left(x/\lambda \right)}^{k}},x\ge 0\\ 0,x<0\end{array}\right. \)