Fit a time series to a best-fitting logistic function.
Updated 25 Jan 2016

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Fit time series Q(t) to a logistic function.
Inputs (vectors of same size): t (time) & Q
Outputs: Qpre (logistic model fit to data) and three independent parameters: thalf, Qinf, and a, describing the logistic
Q(t) = Qinf/(1 + exp(-a*(t-thalf)))
Qinf is value as t --> infinity
thalf is time of symmetric inflection point
a is time decay constant
Written by James Conder, Southern Illinois University, Oct. 2010
Cleaned up for publishing May 16, 2013

Cite As

James Conder (2024). fit_logistic(t,Q) (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2013a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes

Added confidence limits for parameters.

1) condensed output of three individual parameters: thalf, Qinf, and alpha into one 3 element vector, p
2) fixed typo in comments

Added a check to avoid the flatlining (Qpre goes to the mean) that has occasionally occurred.

Fixed bug for reversing time when fitting a decreasing logistic.
Added an example in help comments.

accidentally included debugging code in last update. update is debugged AND cleaned version

Fixed instability for short or long time frames

Fixed signs of coefficients for decreasing logistic and added screenshot

Fixed signs of coefficients for decreasing logistic.