GPS-X Technical Reference

Table 15-1 – Statistical Measures and Equations
No. Statistical Measure Equation
1 Mean of Residuals
2 Mean of Absolute Residual
3 Mean of Squared Residual
Miscellaneous 416
n
1
n ∑(O i − P i )
i=1
n
1
n ∑|O i − P i |
i=1
n
1
n ∑(O i − P i ) 2
4 Absolute Maximum Residual max [|O i − P i |]
5 Root of Mean Squared Residuals √ 1 n ∑(O i − P i ) 2
6 Mean of Relative Residual
7 Mean of Absolute Relative Residual
8 Mean of Squared Relative Residual
9 Relative Volume Residuals
10 Absolute Relative Volume Residuals
11 Theil's Inequality Coefficient
i=1
n
i=1
n
1
n ∑ (O i − P i )
i=1
n
O i
1
n ∑ |O i − P i |
i=1
n
O i
2
1
n ∑ (O i − P i
)
O i
i=1
∑
n
i=1(O i − P i )
∑n
i=1 O i
∑
n
i=1|O i − P i |
∑n
i=1 O i
∑ n i=1(O i − P i ) 2
∑n
2
i=1 O i
12 Nash-Sutcliffe (R2) 1 − ∑ n i=1
(O i − P i ) 2
∑ n i=1(O i − O m ) 2
13 Standard deviation of Residuals (SDR) √ 1 n ∑(R i − MR) 2
n
i=1
14 Mean of Standardized Residuals
n
1
n ∑ (O i − P i )
i=1 √ 1 n ∑ (O i − P i ) 2
n i=1
Legend:
O i
P i
O m
n
i
R i
MR
= the observed (measured) value
= the predicted (simulated) value
= mean of the observed (measured value)
= number of data points
= the ith observation
= (O i - P i) = residual (error)
= Mean of Residuals
GPS-X Technical Reference