# mathStudent¶

Tutorial illustrating the use of the Student and F distributions

Author: Anna Kreshuk
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Wednesday, August 17, 2022 at 09:34 AM.

drawing the set of student density functions normal(0, 1) density drawn for comparison

In [1]:
TCanvas *DistCanvas = new TCanvas("DistCanvas", "Distribution graphs", 10, 10, 800, 650);
DistCanvas->SetFillColor(17);
DistCanvas->Divide(2, 2);
DistCanvas->cd(1);
TLegend *leg = new TLegend(0.6, 0.7, 0.89, 0.89);

TF1* fgaus = new TF1("gaus", "TMath::Gaus(x, [0], [1], [2])", -5, 5);
fgaus->SetTitle("Student density");
fgaus->SetLineStyle(2);
fgaus->SetLineWidth(1);
fgaus->SetParameters(0, 1, kTRUE);

TF1* student = new TF1("student", "TMath::Student(x,[0])", -5, 5);


student->SetTitle("Student density");

In [2]:
student->SetLineWidth(1);
student->SetParameter(0, 10);
student->SetLineColor(4);
leg->AddEntry(student->DrawCopy("lsame"), "10 degrees of freedom", "l");

student->SetParameter(0, 3);
student->SetLineColor(2);
leg->AddEntry(student->DrawCopy("lsame"), "3 degrees of freedom", "l");

student->SetParameter(0, 1);
student->SetLineColor(1);
leg->AddEntry(student->DrawCopy("lsame"), "1 degree of freedom", "l");

leg->Draw();


drawing the set of student cumulative probability functions

In [3]:
DistCanvas->cd(2);
TF1 *studentI = new TF1("studentI", "TMath::StudentI(x, [0])", -5, 5);
studentI->SetTitle("Student cumulative dist.");
studentI->SetLineWidth(1);
TLegend *leg2 = new TLegend(0.6, 0.4, 0.89, 0.6);

studentI->SetParameter(0, 10);
studentI->SetLineColor(4);
leg2->AddEntry(studentI->DrawCopy(), "10 degrees of freedom", "l");

studentI->SetParameter(0, 3);
studentI->SetLineColor(2);
leg2->AddEntry(studentI->DrawCopy("lsame"), "3 degrees of freedom", "l");

studentI->SetParameter(0, 1);
studentI->SetLineColor(1);
leg2->AddEntry(studentI->DrawCopy("lsame"), "1 degree of freedom", "l");
leg2->Draw();


drawing the set of F-dist. densities

In [4]:
TF1* fDist = new TF1("fDist", "TMath::FDist(x, [0], [1])", 0, 2);
fDist->SetTitle("F-Dist. density");
fDist->SetLineWidth(1);
TLegend* legF1 = new TLegend(0.7, 0.7, 0.89, 0.89);

DistCanvas->cd(3);

fDist->SetParameters(1, 1);
fDist->SetLineColor(1);

fDist->SetParameter(1, 10);
fDist->SetLineColor(2);

fDist->SetParameters(10, 1);
fDist->SetLineColor(8);

fDist->SetParameters(10, 10);
fDist->SetLineColor(4);

legF1->Draw();


drawing the set of F cumulative dist.functions

In [5]:
TF1* fDistI = new TF1("fDist", "TMath::FDistI(x, [0], [1])", 0, 2);
fDistI->SetTitle("Cumulative dist. function for F");
fDistI->SetLineWidth(1);
TLegend* legF2 = new TLegend(0.7, 0.3, 0.89, 0.5);

DistCanvas->cd(4);
fDistI->SetParameters(1, 1);
fDistI->SetLineColor(1);

fDistI->SetParameters(1, 10);
fDistI->SetLineColor(2);

fDistI->SetParameters(10, 1);
fDistI->SetLineColor(8);

fDistI->SetParameters(10, 10);
fDistI->SetLineColor(4);

gROOT->GetListOfCanvases()->Draw()