Fig. 1
Description of the relationship between \({\text{Z}}={\text{log}}\left(\frac{1+{\text{R}}}{1-{\text{R}}}\right)\) and \({\text{R}}=\widehat{{\text{cor}}}\left({\widetilde{\mathbf{g}}}_{2},{\mathbf{y}}_{2}\right)=\frac{{{\text{e}}}^{{\text{Z}}}-1}{{{\text{e}}}^{{\text{Z}}}+1}\), highlighting the regions in which \({\text{R}}={\text{f}}({\text{Z}})\) is a convex (in red) or concave (in blue) function of \(\mathrm{Z }\sim \mathrm{ N}\left({\text{log}}\left(\frac{1+\uprho }{1-\uprho }\right),\frac{4}{{{\text{n}}}_{2}-3}\right)\)