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fitting a Gaussian curve convoluted with exponential decay

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I have to fit a gaussian curve convoluted with an expoential tail to the attached data. For the curve i have the below equation but it does not produce the desired shape. The attached image shows the curve shape I am aiming to achieve using these values and curve equation the exponential section dominates such that the gaussian component cannot even be seen. How would i go about getting the desired curve shape?
y2=0.5*exp(-a*(x2-(0.5*o^2*a))).*(1+erf((x2-o^2*a)/sqrt(2)*o));
using values;
a=exp(-1);
o=0.009931621960609;
where a is a place holder for the decay constant (it may be the issue if it is a very incorrect guess but i am unsure) and o is teh standard deviation of the data.

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Idris Phillips-Fry
Idris Phillips-Fry on 10 Dec 2020
The data file may not open as i have since discovered it is damaged. However that is not of great consequence as i mainly wish to know the general form of the equation i will need to form the desired curve shape shown in the image. Any assistance would be greatly appreciated.

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Accepted Answer

Jeff Miller
Jeff Miller on 11 Dec 2020
It sounds like you want what is often called the "ex-Gaussian" distribution. Its density function is on Wikipedia.
Cupid will fit it for you, if you don't want to write the code yourself.

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