Smooth Transition

Description

A Smooth Transition fit function is defined as:

\[y = A2+\frac{A1-A2}{e^{-\frac{x-M}{G_R}}+1}\]

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