# Finding sigma from fit using Curve Toolbox gaussian?

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Gary on 22 Jan 2013
Commented: Fynn Reinbacher on 5 Nov 2020
I am using the gaussin fitting functions in the Matlab curve fitting toolbox, which uses the model:
ans(x) = a1*exp(-((x-b1)/c1)^2) + a2*exp(-((x-b2)/c2)^2)
This all works well for my data and I get the fits, but now I want to know what sigma is for these two gaussians? That isn't just c, is it? Can someone tells me how the fit coefficients relate to sigma?
Much appreciation.
Gary

Shashank Prasanna on 22 Jan 2013
Edited: Shashank Prasanna on 22 Jan 2013
If you look at the gaussian equation the curve fitting toolbox fits:
you will notice that it is different from the standard normal/gaussian distribution equation given here:
which means you can equate the coefficients you can equate them and get the value of sigma.
a1 = 1/sigma*sqrt(2*pi)
-1/c^2 = -1/2*sigma^2
Fynn Reinbacher on 5 Nov 2020
sigma = 1/(a*sqrt(2*pi));
Has to be used with caution.
This works only for normalized datasets.
In the matlab version of the gaussian: where f(x) is the data you fitted.
For nomalized data and the above answer is indeed valid
In order to get σ from a you'd need to integrate your data first
% if:
[x, cnts] = load('mydata.mat'); % data you are fitting
f1 = fit(x, cnts, 'gauss1');
% then:
mu = f1.b1;
sigma = f1.c1/sqrt(2);
% or:
intergral = trapz(x, cnts);
sigma = integral/(f.a1*sqrt(2*pi));
This has me bugged for a long time.