Error Function

Abbreviation

Formula

References

Residual Root Mean Square Error

RMSE

$\sqrt{\frac{1}{n-2}{\displaystyle \sum _{i=1}^N{\left(Q_{e,exp}-Q_{e,cal}\right)}^2}}$

[35]

Chi-Square Test

χ²

${\displaystyle \sum _{i=1}^N\frac{{\left(Q_{e,exp}-Q_{e,cal}\right)}^2}{Q_{e,cal}}}$

[35]

Sum Square of Errors

ERRSQ

${\displaystyle \sum _{i=1}^N{\left(Q_{e,exp}-Q_{e,cal}\right)}_i^2}$

[35]

Hybrid Fractional Error Function

HYBRID

$\frac{100}{N-p}{\displaystyle \sum _{i=1}^N\left[\frac{{\left(Q_{e,i,exp}-Q_{e,i,cal}\right)}^2}{Q_{e,i,exp}}\right]}$

[33]

Average Relative Error

ARE

$\frac{100}{N}{\displaystyle \sum _{i=1}^N\left|\frac{Q_{e,i,cal}-Q_{e,i,exp}}{Q_{e,i,exp}}\right|}$

[33]

Marquardt’s Percent Standard Deviation

MPSD

$100{\sqrt{\frac{1}{N-p}{\displaystyle \sum _{i=1}^N\left(\frac{Q_{e,exp}-Q_{e,cal}}{Q_{e,exp}}\right)}}}^2$

[33]

Sum of Absolute Errors

EABS

${\displaystyle \sum _{i=1}^N{\left|Q_{e,exp}-Q_{e,cal}\right|}_i}$

[35]

Coefficient of Determination

R²

$\frac{{\displaystyle \sum _{i=1}^N{\left(Q_{e,cal}-Q_{mexp}\right)}^2}}{{\displaystyle \sum _{i=1}^N{\left(Q_{e,cal}-Q_{mexp}\right)}^2+{\left(Q_{e,cal}-Q_{mexp}\right)}^2}}$

[33]