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CombiStats: Five-parameter curves

CombiStats v6.1 offers the possibility to fit asymmetric curves such as the 5-parameter logistic curve defined by the equation y=d+a×f(b(x-c))g  where the additional parameter g>0 is used to model the asymmetry of the curve. The other parameters are the same as in the 4-parameter models, but a is allowed to be negative in 5-parameter models whereas a is forced to be positive in 4-parameter models to remove redundancy with the sign of slope in symmetrical curves.

To illustrate this model, example 5.4.1 from the European Pharmacopoeia is shown here. If sigmoid models are selected in the options wizard, an additional checkbox will appear in the transformation options. Tick this box to include g in the model.

The output shows the best fitting values for the asymptotes, the slope, and the asymmetry factor. The best fitting curve with positive a would have asymmetry factor 1.13889 with asymptotes 0.155355 and 3.22287 and a slope factor of 1.06970. There is however a better fit for negative a with values as shown in the output. Although the output does not explicitly show that a is negative, it can nonetheless be seen from the inversion in the order of asymptotes. In 4-parameter models, the lower asymptote is always shown first, whereas, in 5-parameter models, the order depends on the sign of a.

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