Fitting data to Gaussian function forced to have zero mean

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matnewbie
matnewbie 2018-7-11
评论： matnewbie 2018-7-12
I am trying to fit experimental data to a Gaussian function forced to have zero mean. I tried to use the explicit expression for the Gaussian and nlinfit, but the sigmoidal shape of the Gaussian disappears (it behaves like an exponential decay function). I also tried to use fit with the 'gauss1' option, but I don't know how to set a zero value for the mean and the Gaussian distribution I obtain has the mean where it fits better the data (therefore shifted with respect to zero). What is the best approach to obtain what I need?

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回答（1 个）

dpb
dpb 2018-7-11
Use mle; there are some examples in the doc fitting distributions with fixed parameters...
Given x is your observation vector, and under the assumption the offset is relatively small in comparison to the variance,
[phat,pci] = mle(x,'pdf',@(x,sigma) pdf('normal',x,0,sigma),'start',std(x));
should give reasonable estimates.
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matnewbie
matnewbie 2018-7-12
Thank you, but I solved in another way, since I had x,y data to fit... I used this code snippet:
meanval=sum(x.*y)/sum(y);
sigma0=sqrt(sum(y.*(x-meanval).^2)/sum(y));
CenteredGaussian=@(b,x)(b(1)*exp(-x.^2/(2*b(2)^2)));
sol=nlinfit(x,y,CenteredGaussian,[max(y) sigma0]);

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