164 views (last 30 days)

Show older comments

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.

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!