I'm currently attempting to convolve two exponential(one gaussian) functions in order to create a convolved equation in Matlab that I can then use in the custom equation section of the Curve Fitting application to fit to a distribution in order to extract certain parameter values for multiple datasets. The convolve functions in Matlab that I have examined seem to only work when utilizing matrices and there doesn't seem to be a method to convolve symbolic functions. Since my understanding of advanced convolutions and the corresponding integrals that go along with it is weak, I'm concerned my initial attempt at convolving the two equations contains errors.
f(equation1) = a*exp((-x)/(b))+1
f(equation2) = (1/(4*pi*c^2))*exp((-x^2)/(4*c^2))
f(convolveattempt1) = (1/(4*sqrt(pi)*c)) + (a/(2*sqrt(pi)*c))*exp(((b*x-2*c^2)^2-(b^2)*(x^2))/(4*c^2*b^2))*(1-normcdf(((2*c^2-b*x)/(c*b*sqrt(2))),mu,sigma))
My first attempt at convolution (by hand) seems to return unexpected values for certain parameters (namely c) when I fit it to the distributions. I'm wondering if there is a method to let Matlab perform the convolution and allow me to fit my dataset (preferably in the curve fitting function where I can adjust parameter limits and bounds) without having to rely on my math and parenthetical placement.
Any help would be greatly appreciated.