Curve fitting tool does not respect the upper and lower limits of parameters of custom equation
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Luciano Montanelli on 11 Aug 2022
Hi. I hope you can help me. I have the data from measurements in vectors vel_3_Hor and tau_fr_3_Hor:
vel_3_Hor = [206.5139956
tau_fr_3_Hor = [0.137735032
The elements with same index in the previous vectors correspond to each other. I want to fit these points to this custom equation:
y = tau_C + (T_S - tau_C)*exp(-(x/vel_S)^delta_S) + c_vel*x
I tried to fit, manually, this function to my data with this page and I got these results:
(There is a value of tau_fr_3_Hor at vel_3_Hor = 0 here, but please ignore it. tau_fr_3_Hor = 0.1208 is an average result that I got from several experiments at vel_3_Hor where I measured tau_fr_3_Hor. I cannot rely on this average for specific reasons, but still it works as an estimate).
I set this values in Curve Fitting Tool:
Then I got these results:
It just seems to be something wrong with the confidence bounds in each parameter. For instance, vel_S cannot be negative, and also should be less than 80 at first sight. Also, tau_C should be between 0.10 - 0.12.
Thanks in advance.
John D'Errico on 12 Aug 2022
Sorry, but the confidence limits are not impacted by the bounds. To get better confidence limits they would need to do considerably more work. Those confidence limits were computed using a fairly simplistic scheme.