Fitting a function in the form of an integral with variable limits to a data set with Roofit

Roofit and RooStats
4

Hello Hageboeck,

Thanks for the reply!

I tried to do p.setRange(min, max) followed by not specifying the range in the createIntegral() method.

 RooAbsReal* pdfMB = fmb.createIntegral(p,p);
 RooAbsReal* pdfBE = fbe.createIntegral(p,p);

But the integration gives curve with strange and unexpected shape.
The log is as follows

[#1] INFO:NumericIntegration -- RooRealIntegral::init(fmb_Int[p]) using numeric integrator RooIntegrator1D to calculate Int(p)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(fbe_Int[p]) using numeric integrator RooIntegrator1D to calculate Int(p)
[#0] ERROR:Plotting -- RooRealIntegral::fbe_Int[p]_Norm[p]:createPlotProjection: "c" is not a dependent and will be ignored.
[#1] INFO:NumericIntegration -- RooRealIntegral::init(fbe_Int[p]_Norm[p]) using numeric integrator RooIntegrator1D to calculate Int(p)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(fbe_Int[p]) using numeric integrator RooIntegrator1D to calculate Int(p)
[#0] ERROR:Plotting -- RooRealIntegral::fmb_Int[p]_Norm[p]:createPlotProjection: "c" is not a dependent and will be ignored.
[#1] INFO:NumericIntegration -- RooRealIntegral::init(fmb_Int[p]_Norm[p]) using numeric integrator RooIntegrator1D to calculate Int(p)
[#1] INFO:NumericIntegration -- RooRealIntegral::init(fmb_Int[p]) using numeric integrator RooIntegrator1D to calculate Int(p)

Before fitting, I wanted to confirm that the integration is done correctly. Basically, what I want to do is three integrals.

  1. Integral [range: 0 to Pt_Square(max) ] (E f(E) dPt^2 ) with Pt_Square(max) = function ( x axis variable of the histogram which I want to fit it with, which ranges from 0, 4)

PS: The code I made for this is pasted below

void Integrate()
{

//setup our variables
    RooRealVar E("E","E",0.0,0.0,22.4);
    RooRealVar z("z","z",0.01,2.0,4.0);// Decides the Integration limits && The X axis variable of the histogram to fit the integrated results with
    RooConstVar mass("mass","mass",0.139);
    
    RooConstVar Tmb("Tmb","Tmb",0.119);
    RooConstVar Tbe("Tbe","Tbe",0.134);

    RooRealVar ptSq; // .. 

//Create pdf
    RooGenericPdf fmb("fmb","fmb","E*exp(-E/Tmb) ",RooArgList(E,Tmb));
    RooGenericPdf fbe("fbe","fbe","E/(exp(E/Tbe) - 1)",RooArgList(E,Tbe));

//Create Limit Function
    RooFormulaVar max("max","max","pow((exp(-z)*22.4),2)-pow(mass,2)",RooArgList(z,mass));
    RooRealVar    min("min","min",0.);
   
    //Set Range  For integration
    ptSq.setRange("range",min,max);// Integration variable

//Do the integration
    RooAbsReal* pdfMB = fmb.createIntegral(ptSq,"range");
    RooAbsReal* pdfBE = fbe.createIntegral(ptSq,"range");

//Create a frame and plot
    RooPlot* frame = z.frame(Name("frame"),Title("Mass = 0.139"));
    pdfBE->plotOn(frame,LineColor(kRed));
    pdfMB->plotOn(frame,LineColor(kBlack));
   
    TCanvas* MB = new TCanvas("CMB","CMB");
    frame->Draw();
}

  1. Integral[range: [range: 0 to Pz_(max) ] ( f(E) dPz^2) with Pz_(max) = function (Pt^2), which is the x axis of the distribution which i want to fit with

  2. Integral [range: 0 to p(max) ] (f(E)p^2dp) with pmax = a function of ‘c’, which is the x axis of the distribution I want to fit it with( c ranges from 0,1).

I made the first code in the thread for the third case.

I got this idea of setting the range in the createIntegral() from this post: https://root-forum.cern.ch/t/intergration-with-variable-limits/11741

Also I was referring to this old post in root forum: https://root-forum.cern.ch/t/fitting-an-integral-function/8517/6

I am a bit confused with why the integration is not working at all now. If possible could you please suggest me some clear and correct way of doing it with root or roofit?

Regards
Rahul