Table 2 Density functions of the continuous distributions that are used.

(1) Standard normal; \(f\left(U\right)=\frac{{e}^{-\frac{{U}^{2}}{2}}}{\sqrt{2\pi }}\), where; \(U\in \mathcal{R},{\mu }_{0}=0 \text{ and } {\sigma }^{2}=1\)

(2) Student’s \(t\left(\nu \right); f\left(U\right)=\frac{\Gamma (\frac{\nu +1}{2})}{\Gamma (\frac{\nu }{2})\sqrt{\nu \pi }}{\left(1+\frac{{U}^{2}}{\nu }\right)}^{\frac{\nu +1}{2}}\), where; \(U\in \mathcal{R},{\mu }_{0}=0 \text{ and } {\sigma }^{2}=\frac{\nu }{\nu -2}\) and \(\nu =4\)

(3) Logistic; \(f\left(U\right)=\frac{{e}^{-\frac{\pi U}{\sqrt{3}}}}{\frac{\sqrt{3}}{\pi }{\left(1+{e}^{-\frac{\pi U}{\sqrt{3}}}\right)}^{2}}\), where; \(U\in \mathcal{R},{\mu }_{0}=0\text{ and } {\sigma }^{2}=\frac{3}{{\pi }^{2}}\)

(4) Laplace; \(f\left(U\right)=\frac{1}{2}{e}^{-\left|U\right|}\), where; \(U\in \mathcal{R},{\mu }_{0}=0\text{ and } {\sigma }^{2}=\frac{1}{2}\)

(5) Contaminated Normal (CN); \(f\left(U\right)=\frac{0.95{e}^{-\frac{{U}^{2}}{2}}}{\sqrt{2\pi }}+\frac{{0.05e}^{-\frac{{U}^{2}}{2{\sigma }_{0}^{2}}}}{{\sigma }_{0}^{2}\sqrt{2\pi }}\), where; \(U\in \mathcal{R},{\mu }_{0}=0 \text{ and } {\sigma }^{2}=0.95+0.05{\sigma }_{0}^{2}\)