Table 7 Statistical equations for evaluation metrices.
\(RMSE=\sqrt{\frac{\sum_{c=1}^{w}{({m}_{c}-{g}_{c})}^{2}}{w}}\) (3) |
\(MAE=\frac{\sum_{c=1}^{w}\left|{m}_{c}-{g}_{c}\right|}{w}\) (4) |
\(MAE=\frac{\sum_{c=1}^{w}\left|{m}_{c}-{g}_{c}\right|}{w}\) (5) |
\(RSE=\frac{\sum_{c=1}^{w}{({g}_{c}-{m}_{c})}^{2}}{\sum_{c=1}^{w}{(\overline{m}-{m}_{c})}^{2}}\) (6) |
\(RRMSE=\frac{1}{\left|\overline{\overline{m} }\right|}\sqrt{\frac{\sum_{c=1}^{w}{({m}_{c}-{g}_{c})}^{2}}{w}}\) (7) |
\(R=\frac{\sum_{c=1}^{w}({m}_{c}-{\overline{m}}_{c})({g}_{c}-{\overline{g}}_{c})}{\sqrt{\sum_{c=1}^{w}{({m}_{c}-{\overline{m}}_{c})}^{2}\sum_{k=1}^{u}{({g}_{c}-{\overline{g}}_{c})}^{2}}}\) (8) |
\(\rho =\frac{RRMSE}{(1+R)}\) (9) |
\(MSE=\frac{1}{w}{\sum }_{c=1}^{w}{({m}_{c}-{g}_{c})}^{2}\) (10) |
\(U95= \frac{1.96}{w}\sqrt{\sum_{c=1}^{w}{({m}_{c}-{g}_{c})}^{2}+\sum_{i=1}^{w}{({m}_{c}-{g}_{c})}^{2}}\) (11) |
\(A10-index=\frac{w10}{w}\) (12) |
\(AI=\frac{\sum_{c=1}^{w}{({m}_{c}-{g}_{c})}^{2}}{\sum_{c=1}^{w}+{({{|m}_{c}-{\overline{g}}_{c}|+|g}_{c}-{\overline{g}}_{c}|)}^{2}}\) (13) |
\(VAF=1-\frac{var \left({m}_{c}-{g}_{c}\right)}{var \left({m}_{c}\right)}\times 100\)% (14) |
\({R}^{2}=\frac{{\left(\sum_{c=1}^{w}({m}_{c}-{\overline{m}}_{c})({g}_{c}-{\overline{g}}_{c}\right)}^{2}}{\sum_{c=1}^{w}{({m}_{c}-{\overline{m}}_{c})}^{2}\sum_{c=1}^{w}{({g}_{c}-{\overline{g}}_{c})}^{2}}\) (15) |
