## From \$ROOTSYS/tutorials/roofit/rf201_composite.C

```/////////////////////////////////////////////////////////////////////////
//
// 'ADDITION AND CONVOLUTION' RooFit tutorial macro #201
//
// Composite p.d.f with signal and background component
//
// pdf = f_bkg * bkg(x,a0,a1) + (1-fbkg) * (f_sig1 * sig1(x,m,s1 + (1-f_sig1) * sig2(x,m,s2)))
//
//
// 07/2008 - Wouter Verkerke
//
/////////////////////////////////////////////////////////////////////////

#ifndef __CINT__
#include "RooGlobalFunc.h"
#endif
#include "RooRealVar.h"
#include "RooDataSet.h"
#include "RooGaussian.h"
#include "RooChebychev.h"
#include "TCanvas.h"
#include "TAxis.h"
#include "RooPlot.h"
using namespace RooFit ;

void rf201_composite()
{
// S e t u p   c o m p o n e n t   p d f s
// ---------------------------------------

// Declare observable x
RooRealVar x("x","x",0,10) ;

// Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and their parameters
RooRealVar mean("mean","mean of gaussians",5) ;
RooRealVar sigma1("sigma1","width of gaussians",0.5) ;
RooRealVar sigma2("sigma2","width of gaussians",1) ;

RooGaussian sig1("sig1","Signal component 1",x,mean,sigma1) ;
RooGaussian sig2("sig2","Signal component 2",x,mean,sigma2) ;

// Build Chebychev polynomial p.d.f.
RooRealVar a0("a0","a0",0.5,0.,1.) ;
RooRealVar a1("a1","a1",-0.2,0.,1.) ;
RooChebychev bkg("bkg","Background",x,RooArgSet(a0,a1)) ;

////////////////////////////////////////////////////
// M E T H O D   1 - T w o   R o o A d d P d f s  //
////////////////////////////////////////////////////

// A d d   s i g n a l   c o m p o n e n t s
// ------------------------------------------

// Sum the signal components into a composite signal p.d.f.
RooRealVar sig1frac("sig1frac","fraction of component 1 in signal",0.8,0.,1.) ;

// A d d  s i g n a l   a n d   b a c k g r o u n d
// ------------------------------------------------

// Sum the composite signal and background
RooRealVar bkgfrac("bkgfrac","fraction of background",0.5,0.,1.) ;

// S a m p l e ,   f i t   a n d   p l o t   m o d e l
// ---------------------------------------------------

// Generate a data sample of 1000 events in x from model
RooDataSet *data = model.generate(x,1000) ;

// Fit model to data
model.fitTo(*data) ;

// Plot data and PDF overlaid
RooPlot* xframe = x.frame(Title("Example of composite pdf=(sig1+sig2)+bkg")) ;
data->plotOn(xframe) ;
model.plotOn(xframe) ;

// Overlay the background component of model with a dashed line
model.plotOn(xframe,Components(bkg),LineStyle(kDashed)) ;

// Overlay the background+sig2 components of model with a dotted line
model.plotOn(xframe,Components(RooArgSet(bkg,sig2)),LineStyle(kDotted)) ;

// Print structure of composite p.d.f.
model.Print("t") ;

////////////////////////////////////////////////////////////////////////////////////////////////////
// M E T H O D   2 - O n e   R o o A d d P d f   w i t h   r e c u r s i v e   f r a c t i o n s  //
////////////////////////////////////////////////////////////////////////////////////////////////////

// Construct sum of models on one go using recursive fraction interpretations
//
//   model2 = bkg + (sig1 + sig2)
//

// NB: Each coefficient is interpreted as the fraction of the
// left-hand component of the i-th recursive sum, i.e.
//
//   sum4 = A + ( B + ( C + D)  with fraction fA, fB and fC expands to
//
//   sum4 = fA*A + (1-fA)*(fB*B + (1-fB)*(fC*C + (1-fC)*D))

// P l o t   r e c u r s i v e   a d d i t i o n   m o d e l
// ---------------------------------------------------------
model2.plotOn(xframe,LineColor(kRed),LineStyle(kDashed)) ;
model2.plotOn(xframe,Components(RooArgSet(bkg,sig2)),LineColor(kRed),LineStyle(kDashed)) ;
model2.Print("t") ;

// Draw the frame on the canvas
new TCanvas("rf201_composite","rf201_composite",600,600) ;
gPad->SetLeftMargin(0.15) ; xframe->GetYaxis()->SetTitleOffset(1.4) ; xframe->Draw() ;

}

```
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