Attempting to fit data with a sigmoid curve, but not an option in curvefitter toolbox

Question

Levi Matsushima 2024-8-21，19:04

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回答： Image Analyst 2024-8-21，22:16

I am working on fitting data with a sigmoidal curve, but my CurveFitter toolbox does not have the sigmoidal option under fit types. I have tried a custom fit, but it is not giving me any useable fits.

eqn:

'a/(1+exp(-b*(x-c)))'

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Answer 1

Star Strider 2024-8-21，19:15

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Perhaps something like this —

s = fittype('a/(1+exp(-b*(x-c)))', 'Coefficients',{'a','b','c'}, 'Independent','x', 'Dependent','y')

s =

General model: s(a,b,c,x) = a/(1+exp(-b*(x-c)))

x = linspace(0, 10, 20);

y = rand(size(x));

sfit = fit(x(:), y(:), s)

Warning: Start point not provided, choosing random start point.

sfit =

General model: sfit(x) = a/(1+exp(-b*(x-c))) Coefficients (with 95% confidence bounds): a = 58.84 (-1.583e+05, 1.584e+05) b = 0.05918 (-1.317, 1.435) c = 85.92 (-4.764e+04, 4.781e+04)

figure

plot(sfit, x, y)

grid

.

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Answer 2

Sam Chak 2024-8-21，20:01

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Hi @Levi Matsushima

The latest Curve Fitting Toolbox has only three Sigmoidal Curves in its library of models.

rng(0,"twister")

x = linspace(-1, 1, 101)';

y = 1./(1 + exp(- 10*x)) + 0.02*randn(101, 1);

y(y>1) = 1;

y(y<0) = 0;

logsigm = fit(x, y, 'logistic')

logsigm =

General model Logistic: logsigm(x) = a/(1 + exp(-b*(x-c))) Coefficients (with 95% confidence bounds): a = 0.9933 (0.9863, 1) b = 10.2 (9.769, 10.63) c = -0.001955 (-0.006753, 0.002844)

plot(logsigm, x, y), grid on, grid minor

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Answer 3

Image Analyst 2024-8-21，22:16

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Attach your actual data so we can work with it. In the meantime, I'm attaching my demo of fitting a sigmoid, though it uses a different formula than yours. However, you can adapt it to use your formula.