TH1F *h_ExpGauss = new TH1F("h_ExpGauss", "Exponential convoluted by Gaussian", 100, 0., 5.);
for (int i = 0; i < 1e6; i++) {
   // Gives a alpha of -0.3 in the exp.
   double x = gRandom->Exp(1. / 0.3);
   x += gRandom->Gaus(0., 3.);
   // Probability density function of the addition of two variables is the
   // convolution of two density functions.
   h_ExpGauss->Fill(x);
}

TF1Convolution *f_conv = new TF1Convolution("expo", "gaus", -1, 6, true);
f_conv->SetRange(-1., 6.);
f_conv->SetNofPointsFFT(1000);
TF1 *f = new TF1("f", *f_conv, 0., 5., f_conv->GetNpar());
f->SetParameters(1., -0.3, 0., 1.);

h_ExpGauss->Fit("f");

%jsroot on
gROOT->GetListOfCanvases()->Draw()