// example of CrystalBall Function and its distribution (pdf and cdf)
void CrystalBall() {
auto c1 = new TCanvas();
c1->Divide(1,3);
// crystal ball function
c1->cd(1);
auto f1 = new TF1("f1","crystalball",-5,5);
f1->SetParameters(1, 0, 1, 2, 0.5);
f1->SetLineColor(kRed);
f1->Draw();
// use directly the functionin ROOT::MATH note that the parameters definition is different is (alpha, n sigma, mu)
auto f2 = new TF1("f2","ROOT::Math::crystalball_function(x, 2, 1, 1, 0)",-5,5);
f2->SetLineColor(kGreen);
f2->Draw("same");
auto f3 = new TF1("f3","ROOT::Math::crystalball_function(x, 2, 2, 1, 0)",-5,5);
f3->SetLineColor(kBlue);
f3->Draw("same");
auto legend = new TLegend(0.7,0.6,0.9,1.);
legend->AddEntry(f1,"N=0.5 alpha=2","L");
legend->AddEntry(f2,"N=1 alpha=2","L");
legend->AddEntry(f3,"N=2 alpha=2","L");
legend->Draw();
c1->cd(2);
auto pdf1 = new TF1("pdf","crystalballn",-5,5);
pdf1->SetParameters(2, 0, 1, 2, 3);
pdf1->Draw();
auto pdf2 = new TF1("pdf","ROOT::Math::crystalball_pdf(x, 3, 1.01, 1, 0)",-5,5);
pdf2->SetLineColor(kBlue);
pdf2->Draw("same");
auto pdf3 = new TF1("pdf","ROOT::Math::crystalball_pdf(x, 2, 2, 1, 0)",-5,5);
pdf3->SetLineColor(kGreen);
pdf3->Draw("same");
legend = new TLegend(0.7,0.6,0.9,1.);
legend->AddEntry(pdf1,"N=3 alpha=2","L");
legend->AddEntry(pdf2,"N=1.01 alpha=3","L");
legend->AddEntry(pdf3,"N=2 alpha=3","L");
legend->Draw();
c1->cd(3);
auto cdf = new TF1("cdf","ROOT::Math::crystalball_cdf(x, 1.2, 2, 1, 0)",-5,5);
auto cdfc = new TF1("cdfc","ROOT::Math::crystalball_cdf_c(x, 1.2, 2, 1, 0)",-5,5);
cdf->SetLineColor(kRed-3);
cdf->SetMinimum(0.);
cdf->SetMaximum(1.);
cdf->Draw();
cdfc->SetLineColor(kMagenta);
cdfc->Draw("Same");
legend = new TLegend(0.7,0.7,0.9,1.);
legend->AddEntry(cdf,"N=1.2 alpha=2","L");
legend->AddEntry(cdfc,"N=1.2 alpha=2","L");
legend->Draw();
}