Additive absolute error

If you encounter these functions, you can reformulate them as equivalent smooth functions by introducing additional constraints and variables. For example, consider the problem of fitting a model to n data points by minimizing the sum of weighted absolute errors between the measured and model outputs. This can be formulated as follows ... 

Comparisons between calculated and experimental absolute acidities are provided in Table 6-6. The reactions are even more endothermic than those for absolute basicity, due to the additional penalty arising from charge separation. With the exception of the local density 6-311+G model, mean absolute errors here are significantly larger than those uncovered in absolute basicity comparisons, even though... 

None of the semi-empirical models are as successful. Mean absolute errors are two to three times larger than for other models, and individual molecules often show errors larger than the dipole moments themselves. In addition, a number of subtle effects are not properly reproduced. Overall, semi-empirical models do not offer a good choice for dipole moment calculations in hydrocarbons (and presumably as well in other molecules of low polarity). 

Dipole moments in amines obtained from the same set of models used in previous comparisons are compared with experimental values in Table 10-3. These and further data (on oxygen, silicon, phosphorous and sulfur compounds) are given in Appendix AlO (Tables AlO-9 to AlO-16), and mean absolute errors corresponding to the full set are summarized in Table 10-4. In addition, graphical comparisons of calculated and experimental dipole moments have been provided for selected models (Figures 10-1 to 10-11). Circular markers (o) designate molecules with heteroatoms. 

Structure 21 was subsequently synthesized by Porco, " its X-ray structure obtained, and its NMR spectra was found to be completely consistent with the original hexacyclinol compound reported by Grafe. In addition, Bagno recomputed the and chemical shifts of 17 and 21 at B97-2/cc-pVTZ/B3LYP/6-31G(d,p). The mean absolute error between the experimental and computed stractures is half that for 21 than for the originally proposed structure 17. The computed coupling constants also are in much better agreement with 21. 

Additionally, the (oB97X-D functional shows promise. Eor example, its mean absolute error for Reaction 3.8a is 0.48 kcal mol" and for the isomerization energy... 

The real zirconia gas sensor fnnction is located between two dotted lines due to the inconsistency of both sensitivity and the initial level of output signal of the sensor. The uncertainty of measurements is restricted by the value 2Aq + where A() is the absolute error of the zero level, or additive absolute error is the absolute sensitivity error, or multiplicative absolute error and is the relative sensitivity error, or relative multiphcative error. 

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