Use a convolution of two gaussians as a custom fit

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Bill Francois 2015-6-3

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https://ww2.mathworks.cn/matlabcentral/answers/222175-use-a-convolution-of-two-gaussians-as-a-custom-fit

评论： Bill Francois 2015-6-11

Hi I want to create a function that is the convolution product of two gaussian probability density functions:

f1=normpdf(x,(1-tau)*m,(1-tau*sigma)) 
and 
f2=normpdf(x,tau*m,tau*P*sigma)  
where P, sigma and m will be given, and tau will be the fit parameter.

I want to obtain the convolution product: a fuction of x that is the sum from i=0 to x of

f1(i)*f2(x-i)
And use it as a custom fit model with parameter tau.
How can I do this?

I have tried using the conv function:

function[c]=gaussienneconv3(P,tau,sigma,mu,x)
c=conv(normpdf(x,(1-tau)*mu,(1-tau)*sigma),normpdf(x,tau*mu,P*tau*sigma));
end

And then fit wit cftool and a custom fit model but even when I adjusted the size of the data vectors the fit tool did not work with this expression (he said all the points were NaN)

Then I tried with a sum expression:

function[d]=gaussienneconv4(tau,P,sigma,mu,x)
compteur=0;
for i=0:1:x
compteur=compteur+gaussienneconv1(tau,sigma,mu,i)*gaussienneconv2(P,tau,sigma,mu,x-i);
end;
d=compteur;
end

But in this case the fit tool worked but gave me a very bad fit, with a negative R-square, even when using some data computed so that they should have given me an accurate value.

Thanks in advance

Bill

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Bill Francois 2015-6-11

Can anyone please help me with this issue? I am sure it is very easy for you, but I do not manage to make this fit work and it is a major problem in my biology research project.

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