// Toy Monte Carlo example.
// Check pull distribution to compare chi2 and binned
// log-likelihood methods.

pull( int n_toys = 10000,
      int n_tot_entries = 100,
      int nbins = 40,
      bool do_chi2=true ){

    TString method_prefix("Log-Likelihood ");
    if (do_chi2)
        method_prefix="#chi^{2} ";

    // Create histo
    TH1F* h4 = new TH1F(method_prefix+"h4",
                        method_prefix+" Random Gauss",
                        nbins,-4,4);
    h4->SetMarkerStyle(21);
    h4->SetMarkerSize(0.8);
    h4->SetMarkerColor(kRed);

    // Histogram for sigma and pull
    TH1F* sigma = new TH1F(method_prefix+"sigma",
                           method_prefix+"sigma from gaus fit",
                           50,0.5,1.5);
    TH1F* pull = new TH1F(method_prefix+"pull",
                          method_prefix+"pull from gaus fit",
                          50,-4.,4.);

    // Make nice canvases
    TCanvas* c0 = new TCanvas(method_prefix+"Gauss",
                            method_prefix+"Gauss",0,0,320,240);
    c0->SetGrid();

    // Make nice canvases
    TCanvas* c1 = new TCanvas(method_prefix+"Result",
                            method_prefix+"Sigma-Distribution",
                            0,300,600,400);
    c0->cd();

    float sig, mean;
    for (int i=0; i<n_toys; i++){
     // Reset histo contents
        h4->Reset();
     // Fill histo
        for ( int j = 0; j<n_tot_entries; j++ )
        h4->Fill(gRandom->Gaus());
     // perform fit
        if (do_chi2) h4->Fit("gaus","q"); // Chi2 fit
        else h4->Fit("gaus","lq"); // Likelihood fit
     // some control output on the way 
        if (!(i%100)){
            h4->Draw("ep");
            c0->Update();}

     // Get sigma from fit
        TF1 *fit = h4->GetFunction("gaus");
        sig = fit->GetParameter(2);
        mean= fit->GetParameter(1);
        sigma->Fill(sig);
        pull->Fill(mean/sig * sqrt(n_tot_entries));
       } // end of toy MC loop
     // print result
        c1->cd();
        pull->Draw();
}

void macro9(){
    int n_toys=10000;
    int n_tot_entries=100;
    int n_bins=40;
    cout << "Performing Pull Experiment with chi2 \n";
    pull(n_toys,n_tot_entries,n_bins,true);
    cout << "Performing Pull Experiment with Log Likelihood\n";
    pull(n_toys,n_tot_entries,n_bins,false);
    }