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. 2018 Apr 17;15(4):780. doi: 10.3390/ijerph15040780

Table 3.

The definitions and formulas of indexes involved in this paper.

Metric Definition Equation
MAE The mean absolute error of N forecasting results MAE=1Ni=1N|FiAi|
MSE The mean squared error of N forecasting results MSE=1ni=1n(FiAi)2
RMSE The square root of average of the error squares RMSE=1N×i=1N(FiAi)2
NMSE The normalized average of the squares of the errors NMSE= 1Ni=1N(FiAi)2FiAi
MAPE The average of N absolute percentage error MAPE= 1Ni=1N|AiFiAi|×100%
IA The index of agreement of forecasting results IA= 1i=1N(FiAi)2/i=1N(|FiĀ|+|Ai+Ā|)2
R The correlation coefficient R= (AiĀ)(FiF¯)σFσA
AE The absolute error of forecasting results AE= |FiAi|
FB The fractional bias of N forecasting results FB= 2(ĀF¯)/(Ā+F¯)
IOA The index of agreement IOA=1i=1N(FiAi)2i=1N(|FiF¯|+|Ai+Ā|)2