void StatNewEPScatteringSample01()
{
 static Int_t nof = 500;                        // number of functions to be generated
 auto can = new TCanvas("c1", "c1", 800,800);   // setting the canvas
 //gStyle->SetOptStat("nerf");
 //gStyle->SetOptStat();
 gStyle->SetOptStat(0);
 can->Draw();

 auto avf = new TH1F("avf", "Average of Functions", 100, 0.0025, 1.0);
 avf->Draw();

//=== generating the functions ===//

 TF1 *fpf[nof], *ppf[nof];
 TString fna;

 for (Int_t i=0; i<nof; i++)
 {
  fna = "f"; fna += i;
  fpf[i] = new TF1("fna","(((2.0*[0]*[0]*[1]*[1]*[2]*[2]*[3]*[3])/(x*x*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)+2.0*[3]*[3]*x*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)+(x*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)*sqrt(x*x*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)+4.0*[3]*[3]*x*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)))))*((2.0*[3]*[3])/(2.0*[3]*[3]+x*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)+sqrt(x*x*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)+4.0*[3]*[3]*x*sin([4]*[5]/360.0)*sin([4]*[5]/360.0))))*((4.0*[3]*[3])/(4.0*[3]*[3]+x))*((0.71)/(0.71+x))*((0.71)/(0.71+x))*((0.71)/(0.71+x))*((0.71)/(0.71+x))*((8.0*[3]*[3]*[3]*[3]*cos([4]*[5]/360.0)*cos([4]*[5]/360.0)+2.0*[3]*[3]*x*[6]*[6]*cos([4]*[5]/360.0)*cos([4]*[5]/360.0)+4.0*[3]*[3]*x*[6]*[6]*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)+x*x*[6]*[6]*sin([4]*[5]/360.0)*sin([4]*[5]/360.0))/(8.0*[3]*[3]*[3]*[3])))", 0.0025, 1.0);
  fpf[i]->SetParameter(0,1.0);
  fpf[i]->SetParameter(1,1.0);
  fpf[i]->SetParameter(2,1.0/137.0);
  fpf[i]->SetParameter(3,gRandom->Gaus(0.938272081,0.000000023));
  fpf[i]->SetParameter(4,10.0);
  fpf[i]->SetParameter(5,TMath::Pi());
  fpf[i]->SetParameter(6,2.793);
 }

 for (Int_t i=0; i<nof; i++)
 {
  fna = "f"; fna += i;
  ppf[i] = new TF1("fna","((2.0*[0]*[0]*[1]*[1]*[2]*[2]*[3]*[3])/(x*x*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)+2.0*[3]*[3]*x*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)+(x*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)*sqrt(x*x*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)+4.0*[3]*[3]*x*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)))))*((2.0*[3]*[3])/(2.0*[3]*[3]+x*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)+sqrt(x*x*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)*sin([4]*[5]/360.0)+4.0*[3]*[3]*x*sin([4]*[5]/360.0)*sin([4]*[5]/360.0))))*((2.0*[3]*[3]*cos([4]*[5]/360.0)*cos([4]*[5]/360.0)+x*sin([4]*[5]/360.0)*sin([4]*[5]/360.0))/(2.0*[3]*[3]))", 0.0025, 1.0);
  ppf[i]->SetParameter(0,1.0);
  ppf[i]->SetParameter(1,1.0);
  ppf[i]->SetParameter(2,1.0/137.0);
  ppf[i]->SetParameter(3,gRandom->Gaus(0.938272081,0.000000023));
  ppf[i]->SetParameter(4,10.0);
  ppf[i]->SetParameter(5,TMath::Pi());
  ppf[i]->SetParameter(6,2.793);
 }

//=== getting the average ===//

 Int_t nop=100;
 Double_t xpt, ypt, del = 0.9975/nop;

 TGraph *av1 = new TGraph();

 for (Int_t j=0; j < nop; j++)
 {
  xpt = del*j + 0.0025*del;
  av1->SetPoint(j, xpt, 0.0);
 }
 for (Int_t i=0; i<nof; i++)
 {
  for (Int_t j=0; j < nop; j++)
  {
   av1->GetPoint(j, xpt, ypt);
   av1->SetPoint(j, xpt, ypt + fpf[i]->Eval(xpt)/(Double_t)nof);
  }
 }

 TGraph *av2 = new TGraph();

 for (Int_t j=0; j < nop; j++)
 {
  xpt = del*j + 0.0025*del;
  av2->SetPoint(j, xpt, 0.0);
 }

 for (Int_t i=0; i<nof; i++)
 {
  for (Int_t j=0; j < nop; j++)
  {
   av2->GetPoint(j, xpt, ypt);
   av2->SetPoint(j, xpt, ypt + ppf[i]->Eval(xpt)/(Double_t)nof);
  }
 }

 TGraph *av4 = new TGraph();
 int j = 0;

 double eps = 0.0001;
 for (Int_t i=0; i<nof; i++)
 {
   av2->GetPoint(i, xpt, ypt);
   if (abs(xpt - 0.409)  < eps ||
       abs(xpt - 0.6085) < eps ||
       abs(xpt - 0.808)  < eps ||
       abs(xpt - 0.9676) < eps ) {
                                                                av4->GetPoint(i, xpt, ypt);
                                                                av4->SetPoint(j, xpt, ypt + ppf[i]->Eval(xpt)/(Double_t)nof);
                                                                j++;
                                                               }
 }

//=== pLotting the average on canvas ===//

 gPad->SetLogy(1);

 av1->SetMarkerStyle(7);
 av1->SetMarkerColor(kBlue);
 av1->SetMarkerSize(1);

 av2->SetMarkerStyle(6);
 av2->SetMarkerColor(kRed);
 av2->SetMarkerSize(1);

 av4->SetMarkerStyle(3);
 av4->SetMarkerColor(kMagenta);
 av4->SetMarkerSize(1);

 TMultiGraph *mgp = new TMultiGraph();
 mgp->SetMinimum(1.e-4);
 mgp->SetMaximum(1.e0);
 mgp->Add(av1,"PL");
 mgp->Add(av2,"PL");
 mgp->Add(av4,"PL");
 mgp->Draw("a");

 avf->SetMaximum(1.e0);
 can->Modified();
 can->Update();
}