// -------- ROOT baseDistributions ------------------
// Description:  plot basic statistical distributions
//
// Author:       G. Quast, Dec. 2013
// last modified: 
//
// dependencies: ROOT 
//---------------------------------------------------

#ifndef __CINT__     // These include-statements are needed if the program is
#include <iostream>  // run as a "stand-alone application", i.e. if it is not 
#include <math.h>    // called from an interactive ROOT session
#include "TStyle.h"
#include "TFile.h"    
#include "TH1.h"      
#include "TH2.h"
#include "TF1.h"
#include "TRandom.h"
#include "TMath.h"
#include "TCanvas.h"
#include "TPad.h"
#include "TText.h"
//-----end headers -------------------------------------------------
#endif     // from here on, the code can also be used as a macro

Double_t NormBinomial(Double_t *x, Double_t *par)
 // Binomial distribution
{ 
   int n,k; double p,norm;
   n=par[1]; k=x[0]; p=par[0]; norm=par[2];
   return norm*TMath::Binomial(n,k)*TMath::Power(p,k)*TMath::Power(1-p,n-k);
}

Double_t NormPoisson(Double_t *x, Double_t *par)
 // Poisson distribution
{
  double norm=par[1], mu=par[0], x0=int(x[0]); 
   return norm*TMath::Poisson(x0,mu);
}

Double_t NormGauss(Double_t *x, Double_t *par)
 // Gaussdistribution
{
  double norm=par[2], mu=par[0], sigma=par[1]; 
  return norm*TMath::Gaus(x[0],mu,sigma,kTRUE);
}

void baseDistributions(double n=1000.,double p=0.05) 
{
  // plot basic statistical distribuions
  //double n=1000., p=0.05; // input
  //
  double  mu=n*p, sigma=sqrt(n*p*(1.-p)) ;

  // create canvas and pads
 TCanvas *c1=new TCanvas("c1","Basic distributions"
             ,10, 10, 710, 710);

 TPad *p1=new TPad("Pad3","Pad3",0.0,0.5,0.5,1.);   
 p1->Draw();  
 TPad *p2=new TPad("Pad4","Pad4",0.5,0.5,1.,1.);   
 p2->Draw();  
 TPad *p3=new TPad("Pad1","Pad1",0.,0.,0.5,0.5); 
 p3->Draw();  
 TPad *p4=new TPad("Pad2","Pad2",0.5,0.0,1.,0.5);   
 p4->Draw();  

 double xmin=mu-3.5*sigma;
 double xmax=mu+3.5*sigma;

 //binomial
 TF1 *binom = new TF1("binom",NormBinomial,xmin,xmax,400);
 binom->SetTitle("Binomial distribution");
 binom->SetParameter(0,p); 
 binom->SetParameter(1,n); 
 binom->SetParameter(2,1.); // normalisation
 // poisson
 TF1 *poiss = new TF1("binom",NormPoisson,xmin,xmax,400);
 poiss->SetTitle("Poisson distribution");
 poiss->SetParameter(0,mu); 
 poiss->SetParameter(1,1.); // normalisation
 //gauss
 TF1 *gauss = new TF1("NormGauss",NormGauss,xmin,xmax,400);
 gauss->SetTitle("Normal distribution");
 gauss->SetParameter(0,mu);      
 gauss->SetParameter(1,sigma); 
 gauss->SetParameter(2,1.);        // normalisation

 p1->cd();
 binom->DrawCopy();

 p2->cd();
 poiss->DrawCopy();

 p3->cd();
 gauss->DrawCopy();

 p4->cd(); // draw all in same pad
 p4->SetLogy();

 TLegend* legend = new TLegend(0.35, 0.15, 0.65, 0.3);
 TObject* copied;

 char txt[50];
 sprintf(txt,"p=%1.3g , n=%3g",p,n);
 binom->SetTitle(txt);

 binom->SetLineColor(2);
 copied = binom->DrawCopy(); 
 legend->AddEntry(copied, "Binomial");
 
 poiss->SetLineColor(3);
 copied = poiss->DrawCopy("SAME"); 
 legend->AddEntry(copied, "Poisson");
 
 gauss->SetLineColor(4);
 copied = gauss->DrawCopy("SAME");
 legend->AddEntry(copied, "Gauss");

 legend->Draw();

}

#ifndef __CINT__   // needed if the program is compiled stand-alone
//_________________________________________________________________

int main()
{
  baseDistributions();
  return 0;
}
#endif