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

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)))'

Answer 1

[Star Strider]

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

.

Answer 2

[Sam Chak]

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

Answer 3

[Image Analyst]

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.