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# 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