Table 9 Statistical metrics used for evaluating the prediction efficiency of gas geothermometers (new and existing)

Percent difference (DIFF%)

\(DIFF\% = \left[ {\left( {\frac{{BHT_{CALC\left( i \right)} - BHT_{m\left( i \right)} }}{{BHT_{m\left( i \right)} }}} \right) \times 100} \right]\)

(6)

García-López et al. (2014)

Root mean square error (RMSE)

\(RMSE = \sqrt{{\frac{1}{n}\mathop \sum \limits_{i = 1}^{n} \left( {BHT_{m\left( i \right)} - BHT_{CALC\left( i \right)} } \right)^{2} }}\)

(7)

Willmott et al. (2009)

Mean absolute error (MAE)

\(MAE = \frac{1}{n}\mathop \sum \limits_{i = 1}^{n} \left| {BHT_{m\left( i \right)} - BHT_{CALC\left( i \right)} } \right|\)

(8)

Wang and Lu (2018)

Mean absolute percentage error (MAPE)

\(MAPE = \left( {\frac{1}{n}\mathop \sum \limits_{i = 1}^{n} \left| {\frac{{BHT_{m\left( i \right)} - BHT_{CALC\left( i \right)} }}{{BHT_{m\left( i \right)} }}} \right|} \right) \times 100\)

(9)

Li and Shi (2010)

Difference coefficient (Theil's U)

\(Theil^{\prime}s U = \frac{{\sqrt{{\mathop \sum \nolimits_{i = 1}^{n} \left( {BHT_{m\left( i \right) - } BHT_{GaS\_GeoT\left( i \right) } } \right)^{2} }}}}{{\sqrt{{\mathop \sum \nolimits_{i = 1}^{n} \left( {BHT_{m\left( i \right) - } BHT_{GasGeo\_Lit\left( i \right) } } \right)^{2} }}}}\)

(10)

Álvarez del Castillo et al. (2012)