[hist] Chi-square computation in Binned likelihood fits

[lmoneta]

As reported in https://root-forum.cern.ch/t/chi-square-definition-in-root/51083/3,
the reported chi-square from TF1::GetChisquare and from FitResult is not correct.
A Neyman chi-square is computed but using also the empty bins.
See https://github.com/root-project/root/blob/master/math/mathcore/src/FitResult.cxx#L183

We should return in this case as chi-square the value suggested by Baker-Cousins, i.e. 2 * MinNLL.

In addition we have also :

• Documentation for TF1::GetChisquare and ROOT::Fit::FitResult::Chi2 is missing.
• TH1::Chisquare and ROOT::Fit::Chisquare should compute also the Pearson chi-square

[atolosadelgado]

Hi,

I have tested the method TH1::Chisquare and seems to calculate the Pearson Chi2 properly

// File: test.cxx
// test TH1::Chisquare function. Pearson Chi2 is calculated as expected
// To run the script: root test.cxx
void test()
{

    int nbins = 100;
    double xmin =-5;
    double xmax = 5;

    TF1 * f = new TF1("f","gausn");
    double nentries = 1000;
    double binwidth = (xmax-xmin)/nbins;
    f->SetParameters(nentries*binwidth,0.,1.);
    f->SetRange(-10,10);

    TH1D *h = new TH1D("h","", nbins, xmin,xmax);
    h->FillRandom("f2",nentries);
    h->Draw();
    f->Draw("same");

    //-- Chi2 Pearson
    double chi2_th1 = h->Chisquare( f , "P");

    // note: below it is assumed that "bin error" = sqrt( f("bin center") )
    double chi2_P = 0.;
    for (int i = 1; i <= h->GetNbinsX(); i++) {
        double v = f->Eval(h->GetBinCenter(i));
        if (v) chi2_P += TMath::Sq(v - h->GetBinContent(i)) / TMath::Abs(v);
    }
    std::cout << "hand calculated Pearson chi2 = " << chi2_P << "\n";
    std::cout << "ROOT TH1::Chisquare     chi2 = " << chi2_th1 << "\n";

}

Question: Should ROOT::Fit::FitResult::Chi2 call TH1::Chisquare to avoid writing the same piece of code in two different places?

[lmoneta]

ROOT::Fit::FitResult::Chi2() returns the chi2 after fitting, TH1::Chisquare calls the function ROOT::Fit::Chisquare which compute the chi2 with an arbitrary function and histogram. The implementation is the same using the ROOT::Fit::Chi2FCN class.