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Extended likelihood PDFs

//  extended likelihood use
intro7()
{
  // Build regular Gaussian PDF
  RooRealVar x("x","x",-10,10) ;
  RooRealVar mean("mean","mean of gaussian",-3,-10,10) ;
  RooRealVar sigma("sigma","width of gaussian",1,0.1,5) ;
  RooGaussian gauss("gauss","gaussian PDF",x,mean,sigma) ;  
    
  // Make extended PDF based on gauss. n will be the expected number of events
  RooRealVar n("n","number of events",10000,0,20000) ;
  RooExtendPdf egauss("egauss","extended gaussian PDF",gauss,n) ;

  // Generate events from extended PDF
  // The default number of events to generate is taken from gauss.expectedEvents()
  // but can be overrided using a second argument
  RooDataSet* data = egauss.generate(x)  ;

  // Fit PDF to dataset in extended mode (selected by fit option "e")
  egauss.fitTo(*data,"mhe") ;
 
  // Plot both on a frame ;
  RooPlot* xframe = x.frame() ;
  data->plotOn(xframe) ;
  egauss->plotOn(xframe,Normalization(1.0,RooAbsReal::RelativeExpected)) ; // select intrinsic normalization
  xframe->Draw() ;  

  // Make an extended gaussian PDF where the number of expected events
  // is counted in a limited region of the dependent range
  x.setRange("cut",-4,2) ;
  RooRealVar mean2("mean2","mean of gaussian",-3) ;
  RooRealVar sigma2("sigma2","width of gaussian",1) ;
  RooGaussian gauss2("gauss2","gaussian PDF 2",x,mean2,sigma2) ;  
  
  RooRealVar n2("n2","number of events",10000,0,20000) ;
  RooExtendPdf egauss2("egauss2","extended gaussian PDF w limited range",gauss2,n2,"cut") ;

  egauss2.fitTo(*data,"mhe");
  cout << "fitted number of events in data in range (-6,0) = " << n2.getVal() << endl ; 

  // Adding two extended PDFs gives an extended sum PDF

  mean = 3.0 ;  sigma = 2.0 ;

  // Note that we omit coefficients when adding extended PDFS
  RooAddPdf sumgauss("sumgauss","sum of two extended gauss PDFs",RooArgList(egauss,egauss2)) ;
  sumgauss->plotOn(xframe,Normalization(1.0,RooAbsReal::RelativeExpected),LineColor(kRed)) ; // select intrinsic normalization
  xframe->Draw() ;  

  // Note that in the plot sumgauss does not follow the normalization of the data
  // because its expected number was intentionally chosen not to match the number of events in the data

  // If no special 'cut normalizations' are needed (as done in egauss2), there is a shorthand 
  // way to construct an extended sumpdf:

  RooAddPdf sumgauss2("sumgauss2","extended sum of two gaussian PDFs",
		      RooArgList(gauss,gauss2),RooArgList(n,n2)) ;
  sumgauss2->plotOn(xframe,Normalization(1.0,RooAbsReal::RelativeExpected),LineColor(kGreen)) ; // select intrinsic normalization
  xframe->Draw() ;  

  // Note that sumgauss2 looks different from sumgauss because for gauss2 the expected number
  // of event parameter n2 now applies to the entire gauss2 area, whereas in egauss2 it was
  // constructed to represent the number of events in the range (-4,-2). If we would use a separate
  // parameter n3, set to 10000, to represent the number of events for gauss2 in sumgauss2, then
  // sumgauss and sumgauss2 would be indentical.

}

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