The Moyal Trick for Approximating Landau Distributions

Method to analytically approximate the MPV of the Landau distribution, e.g. for charge deposited.
When filling histogram, fill with Moyal distribution instead of charge directly:

qMoyalvsxmym->fill( xmod, ymod, exp(- Q0 / 3.5) );

where 3.5 is a normalization factor corresponding to <>

After filling the histogram, rebin using

for(Int_t i = 1; i <= h->GetNbinsX(); i++) {
    for(Int_t j = 1; j <= h->GetNbinsY(); j++) {
      double qx = h->GetBinContent(i,j);
      h->SetBinEntries(h->GetBin(i,j),1);
      h->SetBinContent(i,j,-3.5*log(qx));
    }
  }