Fit Normalised Gaussian to data

Hi,

I am trying to fit a nromalised Gaussian to my data, using

f(x) = a/sqrt(2pi*sigma^2) * exp (-(x-mu)^2/sigma^2)

However the fit function in matla does not accound for the sigma coefficient. Is there a way to modify the equation of the fit function? I tried to do a manual fit but it doesn't seem to work.

Thanks

[Alex Sha]

Hi, post out your data please.

[Matt J]

I am trying to fit a nromalised Gaussian to my data, using

Shouldn't it be,

f(x) = a/sqrt(2pi*sigma^2) * exp (-0.5*(x-mu)^2/sigma^2)

Answer 1

[Matt J]

You can use,

https://www.mathworks.com/matlabcentral/fileexchange/69116-gaussfitn

Example:

%% Synthetic data
fn=@(x,a,mu,sigma) a./sqrt(2*pi*sigma^2) .* exp (-(x(:)-mu).^2/2/sigma^2);
xdata=linspace(-3,9,20).';
ydata=fn(xdata,1,3,2)+0.006*randn(size(xdata));

%% Do the fit
ulb={0,[],[],[]};
[params,resnorm, residual,exitflag,output]=gaussfitn(xdata,ydata,[],ulb,ulb);

Local minimum possible.

lsqcurvefit stopped because the final change in the sum of squares relative to 
its initial value is less than the value of the function tolerance.

[A,mu,variance]=deal(params{2:4});

sigma=sqrt(variance);
a=A*sqrt(2*pi*variance);

%% Verify
xs=linspace(min(xdata),max(xdata),1000);
plot(xdata,ydata,'o',xs, fn(xs,a,mu,sigma));shg