How to add 2 PDFs?

[DIKSHA_GARG]

Hi,
I want to add 2 PDFs. One is gaussian and the other is Landau function. How to do it ?

-Diksha

[Graipher]

If you are using RooFit, you can just use RooAddPdf:

auto mass = new RooRealVar("mass", ...);
auto mu = new RooRealVar("mu", ...);
auto sigma = new RooRealVar("sigma", ...);
auto gauss = new RooGaussian("signal", "Peak", mass, mu, sigma);
...
auto landau = new RooLandau(...);

auto n_gauss = new RooRealVar("n_gauss", "N_{gauss}", ...);
auto n_landau = new RooRealVar("n_landau", "N_{landau}", ...);
auto combined = new RooAddPdf("combined_model", "Gauss + Landau", RooArgList(gauss, landau), RooArgList(n_gauss, n_landau));

combined is then an extended PDF which is the sum of the two PDFs. If you don’t want an extended PDF, just give it only one variable in the second RooArgList, which will then be the fraction of the first PDF of the total PDF.

[DIKSHA_GARG]

I am actually new to root. I have defined my gaussian function and landau function separately using TF1 command.
Now I want to add these two. Can you please tell me in this direction.

[Graipher]

If you have defined them something like this, it is quite easy as well:

auto gaus = new TF1("g", "gaus", -10, 10);
gaus->SetParameters(1, 0, 1);
auto landau = new TF1("l", "landau", -10, 10);
landau->SetParameters(1, 4, 0.5);

auto f = new TF1("s", "g + l", -10, 10);
f->Draw("l");

Or, just define the combined function right away:

auto f = new TF1("f", "gaus(0) + landau(3)", -10, 10);
f->SetParameters(1, 0, 1, 1, 4, 0.5);
f->Draw("l");

[DIKSHA_GARG]

Alright I have to fit this landau+gaus curve to my values present in a root file. So, I did my fitting in this way :

{
TFile func(“test1GeVmum_theta18.19_reco.root”); /*loading root file */

TH1F *h= new TH1F(“h”,“trkmm gaus+landau fit”,30,0,2.5); /*creating empty
histogram */

T1-> Project (“h”,“abs(trkmm)”); /*projecting the values of trkmm present in root file on the empty histogram, h */

auto gaus = new TF1(“g”, “gaus”, -10, 10);

gaus-> SetParameters(1, 0, 1);

auto landau = new TF1 (“l”,“landau”,-10,10);

landau-> SetParameters(1, 0, 1);

auto f = new TF1 (“s”,“g+l”,-10,10);

h->Fit(“s”);
h->Draw(“e1”);

}

Now I also want to now the area under the curve. How to do that?
And this AddPdf function is only present in RooFit ?

[DIKSHA_GARG]

Now I also want to *know

[Graipher]

Yes, AddPdf only works in RooFit. However, using RooFit might be a good idea anyway, at least as soon as you are doing somewhat complicated fits.

To get the integral of a TF1, you can simply do:

f->Integral(0., 100.);

where the two numbers are the boundaries of the integral.

[DIKSHA_GARG]

Alright. Thanks a lot !