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Smooth Transition¶
Description¶
A Smooth Transition fit function is defined as:
where
\(A1\) - the limit of the function as x tends to zero
\(A2\) - the limit of the function as x tends to infinity
\(M\) - the sigmoid midpoint
\(G_R\) - the growth rate
This models a logistic function.
Examples¶
The logistic function has been used in modelling Covid-19 infection trajectory[1]. It has also been used for examining the muonium state of CdS at low temperatures[2].
Properties (fitting parameters)¶
Name |
Default |
Description |
|---|---|---|
A1 |
0.0 |
the limit of the function as x tends to zero |
A2 |
0.1 |
the limit of the function as x tends to infinity |
Midpoint |
100.0 |
Sigmoid Midpoint |
GrowthRate |
1.0 |
Growth rate |
References¶
[1]Lee, Se Yoon et al. (2020) “Estimation of COVID-19 spread curves integrating global data and borrowing information.” PloS one vol. 15,7 doi:10.1371/journal.pone.0236860.
[2] Gil, J.M et al (1999). Novel Muonium State in CdS. Phys. Rev. Lett., Vol 83 Issue 25, 5294-5297 doi: 10.1103/PhysRevLett.83.5294.
Categories: FitFunctions | Muon\MuonModelling
Source¶
C++ header: SmoothTransition.h
C++ source: SmoothTransition.cpp