Convolve and fitting

Question

I want to convolve two equation, then I want to find the parameters. But it doesn't give the answer and Takes too much time. What is the wrong with my code?

nlm = NonlinearModelFit[
   data, {Convolve[
     a*UnitStep[x - b]*c*Sqrt[x - b]*
       Divide[Pi*Divide[Sqrt[d], Sqrt[x - b]]*
         Exp[Pi*Divide[Sqrt[d], Sqrt[x - b]]], 
        Sinh[Pi*Divide[Sqrt[d], Sqrt[x - b]]]] + 
      a*d*Sum[Divide[4*Pi, n^3]*DiracDelta[x - b + d/n^2], {n, 1, 1}],
      VoigtDistribution, x, y], b < Min[data[[All, 1]]], 
    b < Min[data[[All, 1]]]}, {{a, 10}, {b, -1}, c, d}, x];
nlm["BestFitParameters"]

meneken17 · Answer

I neither know the context of your calculation nor do I know properties of the Voigt distribution so I cannt help you choose those:
According to the reference and the wikipedia-article it should be VoigtDistribution[sigma,delta] where sigma is the standard-error of the underlying gauss distributionand delta is the $gamma$ of the unerdlying Lorentz distribution.

As VoigtDistribution[sigma,delta] gives you a distribution you have to use

PDF[VoigtDistribution[sigma,delta],x]

Secondly you should test around if your expression within the NonlinearModel fit evaluates and trace the error piece by piece.

Convolve and fitting

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