'LIKELIHOOD AND MINIMIZATION' RooFit tutorial macro #602

Setting up a chi^2 fit to a binned dataset

**Author:** 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 10:07 AM.*

In [ ]:

```
from __future__ import print_function
import ROOT
```

Declare observable x

In [ ]:

```
x = ROOT.RooRealVar("x", "x", 0, 10)
```

Create two Gaussian PDFs g1(x,mean1,sigma) anf g2(x,mean2,sigma) and their parameters

In [ ]:

```
mean = ROOT.RooRealVar("mean", "mean of gaussians", 5)
sigma1 = ROOT.RooRealVar("sigma1", "width of gaussians", 0.5)
sigma2 = ROOT.RooRealVar("sigma2", "width of gaussians", 1)
sig1 = ROOT.RooGaussian("sig1", "Signal component 1", x, mean, sigma1)
sig2 = ROOT.RooGaussian("sig2", "Signal component 2", x, mean, sigma2)
```

Build Chebychev polynomial p.d.f.

In [ ]:

```
a0 = ROOT.RooRealVar("a0", "a0", 0.5, 0.0, 1.0)
a1 = ROOT.RooRealVar("a1", "a1", 0.2, 0.0, 1.0)
bkg = ROOT.RooChebychev("bkg", "Background", x, [a0, a1])
```

Sum the signal components into a composite signal p.d.f.

In [ ]:

```
sig1frac = ROOT.RooRealVar("sig1frac", "fraction of component 1 in signal", 0.8, 0.0, 1.0)
sig = ROOT.RooAddPdf("sig", "Signal", [sig1, sig2], [sig1frac])
```

Sum the composite signal and background

In [ ]:

```
bkgfrac = ROOT.RooRealVar("bkgfrac", "fraction of background", 0.5, 0.0, 1.0)
model = ROOT.RooAddPdf("model", "g1+g2+a", [bkg, sig], [bkgfrac])
```

In [ ]:

```
d = model.generate({x}, 10000)
dh = d.binnedClone()
```

Construct a chi^2 of the data and the model. When a p.d.f. is used in a chi^2 fit, probability density scaled by the number of events in the dataset to obtain the fit function If model is an extended p.d.f, expected number events is used instead of the observed number of events.

In [ ]:

```
ll = ROOT.RooLinkedList()
model.chi2FitTo(dh, ll)
```

NB: It is also possible to fit a ROOT.RooAbsReal function to a ROOT.RooDataHist using chi2FitTo().

Note that entries with zero bins are *not* allowed
for a proper chi^2 calculation and will give error
messages

In [ ]:

```
dsmall = d.reduce(ROOT.RooFit.EventRange(1, 100))
dhsmall = dsmall.binnedClone()
chi2_lowstat = ROOT.RooChi2Var("chi2_lowstat", "chi2", model, dhsmall)
print(chi2_lowstat.getVal())
```

Draw all canvases

In [ ]:

```
from ROOT import gROOT
gROOT.GetListOfCanvases().Draw()
```