Rf 7 0 3_Effpdfprod¶

Special pdf's: using a product of an (acceptance) efficiency and a pdf as pdf

Author: Clemens Lange, Wouter Verkerke (C++ version)
This notebook tutorial was automatically generated with ROOTBOOK-izer from the macro found in the ROOT repository on Monday, January 17, 2022 at 10:16 AM.

In [ ]:
import ROOT

Define observables and decay pdf¶

Declare observables

In [ ]:
t = ROOT.RooRealVar("t", "t", 0, 5)

Make pdf

In [ ]:
tau = ROOT.RooRealVar("tau", "tau", -1.54, -4, -0.1)
model = ROOT.RooExponential("model", "model", t, tau)

Define efficiency function¶

Use error function to simulate turn-on slope

In [ ]:
eff = ROOT.RooFormulaVar("eff", "0.5*(TMath::Erf((t-1)/0.5)+1)", [t])

Define decay pdf with efficiency¶

Multiply pdf(t) with efficiency in t

In [ ]:
modelEff = ROOT.RooEffProd("modelEff", "model with efficiency", model, eff)

Plot efficiency, pdf¶

In [ ]:
frame1 = t.frame(Title="Efficiency")
eff.plotOn(frame1, LineColor="r")

frame2 = t.frame(Title="Pdf with and without efficiency")

model.plotOn(frame2, LineStyle="--")
modelEff.plotOn(frame2)

Generate toy data, fit model eff to data¶

Generate events. If the input pdf has an internal generator, internal generator is used and an accept/reject sampling on the efficiency is applied.

In [ ]:
data = modelEff.generate({t}, 10000)

Fit pdf. The normalization integral is calculated numerically.

In [ ]:
modelEff.fitTo(data)

Plot generated data and overlay fitted pdf

In [ ]:
frame3 = t.frame(Title="Fitted pdf with efficiency")
data.plotOn(frame3)
modelEff.plotOn(frame3)

c = ROOT.TCanvas("rf703_effpdfprod", "rf703_effpdfprod", 1200, 400)
c.Divide(3)
c.cd(1)
frame1.GetYaxis().SetTitleOffset(1.4)
frame1.Draw()
c.cd(2)
frame2.GetYaxis().SetTitleOffset(1.6)
frame2.Draw()
c.cd(3)