tStudent.C: Example macro describing the student t distribution

// Example macro describing the student t distribution
//
// root[0]: .x tStudent.C 
//
// It draws the pdf, the cdf and then 10 quantiles of the t Student distribution
//
// Author: Magdalena Slawinska

#include "TH1.h"
#include "TF1.h"
#include "TCanvas.h"
#include "TSystem.h"
#include "TLegend.h"
#include "TLegendEntry.h"
#ifndef __CINT__
#include "Math/DistFunc.h"
#endif


void tStudent()
{
   gSystem->Load("libMathCore");
   gSystem->Load("libMathMore");

  int n=100;
  double a=-5.;
  double b=5.;
  //double r  = 3; 
  TF1* pdf = new TF1("pdf", "ROOT::Math::tdistribution_pdf(x,3.0)", a,b);
  TF1* cum = new TF1("cum", "ROOT::Math::tdistribution_cdf(x,3.0)", a,b);


  TH1D* quant = new TH1D("quant", "", 9, 0, 0.9);
  

  for(int i=1; i < 10; i++)
     quant->Fill((i-0.5)/10.0, ROOT::Math::tdistribution_quantile((1.0*i)/10, 3.0 ) );

  double xx[10];
  xx[0] = -1.5;
  for(int i=1; i<9; i++)
    xx[i]= quant->GetBinContent(i);
  xx[9] = 1.5;
  TH1D* pdfq[10];
  //int nbin = n/10.0;
  for(int i=0; i < 10; i++)
  {
    int nbin = n * (xx[i+1]-xx[i])/3.0+1.0; 
    TString name = "pdf" + i; 
    pdfq[i]= new TH1D(name, "", nbin,xx[i],xx[i+1] );
    for(int j=1; j<nbin; j++)
    {
       double x= j*(xx[i+1]-xx[i])/nbin + xx[i];
       pdfq[i]->SetBinContent(j, ROOT::Math::tdistribution_pdf(x,3));

    }
 
  }

 TCanvas *Canvas = new TCanvas("DistCanvas", "Student Distribution graphs", 10, 10, 1000, 800); 
 pdf->SetTitle("Student t distribution function");
 cum->SetTitle("Cumulative for Student t");
 quant->SetTitle("10-quantiles  for Student t");
 Canvas->Divide(2, 2);
 Canvas->cd(1);
 pdf->SetLineWidth(2);
 pdf->DrawCopy();
 Canvas->cd(2);
 cum->SetLineWidth(2);
 cum->SetLineColor(kRed);
 cum->Draw();
 Canvas->cd(3);
 quant->Draw();
 quant->SetLineWidth(2);
 quant->SetLineColor(kBlue);
 quant->SetStats(0);
 Canvas->cd(4);
 pdfq[0]->SetTitle("Student t & its quantiles");
 pdf->SetTitle("");
 pdf->Draw();
 //pdfq[0]->SetAxisRange(-1.5, 0, 1.5,1.0);
 pdfq[0]->SetTitle("Student t & its quantiles");
 for(int i=0; i < 10; i++)
 {
   pdfq[i]->SetStats(0);
   pdfq[i]->SetFillColor(i+1);
   pdfq[i]->Draw("same");
 }
 Canvas->Modified();
 Canvas->cd();
}