Smooth Transition

Description

A Smooth Transition fit function is defined as:

y=A2+A1A2exMGR+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

  • GR - 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