Fit Errors too large

Roofit and RooStats
#1

I have a pull distribution to which I am trying to fit a crystal ball line-shape. The data (a binned histogram) has been normalised, so effectively is weighted. As such, I used a min-chi2 fit.

When I perform the fit it converges successfully and the fit looks fine. However, the values and their errors are reported as:

EXT PARAMETER INTERNAL INTERNAL
NO. NAME VALUE ERROR STEP SIZE VALUE
1 alpha 5.43082e-01 1.76769e+01 6.66050e-05 -1.23972e+00
2 cbmean 9.14488e-02 1.46364e+00 6.06855e-07 9.14488e-04
3 cbsigma 3.69025e-01 1.03026e+00 3.76384e-06 -1.51646e+00
4 n 2.68776e+00 5.30508e+01 3.36110e-04 -1.24142e+00

I.e. the errors seem far too large. For example, the error on the mean places it outside the range of the fit!

Here is the code I am using:

using namespace RooFit;

double fitPull(std::string fileName, std::string histName, int rebin = 1) {
  RooRealVar x("x","pull", -1, 1);
  RooPlot* xframe = x.frame();  

  RooRealVar cbmean("cbmean", "cbmean" , 0.0,-100,100);
  RooRealVar cbsigma("cbsigma", "cbsigma" , 0.5, 0,500) ;
  RooRealVar n("n","", 3,0,100);
  RooRealVar alpha("alpha","alpha", 0.53,0,20);

  RooCBShape cball("cball", "crystal ball", x, cbmean, cbsigma, alpha, n);
  RooGaussian gaus("gaus","gaus",x,cbmean,cbsigma);
  
  TFile f(fileName.c_str());
  TH1F *h = (TH1F*) f.Get((histName).c_str());
  RooDataHist d("data","data",x,h);
  RooChi2Var chi2("chi2","chi2",cball,d,DataError(RooAbsData::SumW2));
  RooMinuit minuit(chi2);
  minuit.migrad();
  minuit.hesse();
  
  d.plotOn(xframe);
  cball.plotOn(xframe);
  cball.paramOn(xframe);
  
  xframe->Draw();
  std::cout << xframe->chiSquare(4) << std::endl;
  xframe->GetYaxis()->SetTitleOffset(1.5);
  return 0;
}

Can anyone tell me if I am missing some important option in the fit?

Cheers,

Cameron