# Best function for fiting the trigger efficiency turn-on curve with Roofit

Can anyone please suggest the best function to fit the trigger efficiency turn-on curve with Roofit?

That depends on the trigger, the objects you trigger on, etc. It’s impossible to answer that in a general way.

Here I have plotting efficiency for HLT_DiPFJetAve(60,80,140,200…500) as a function of HT2(average of two leading Jet). Already, I have the turn-on histogram which I want to fit with a suitable function for calculate the turn-on value for each trigger.

That question cannot be answered in a general way. When I said “that depends on the trigger, the objects you trigger on” what I really meant is that this is specific to the detector, the algorithms, the trigger parameter values, etc - that’s why we won’t be able to give you “the trigger efficiency turn-on curve”.

You probably want to talk to other people from your experiment having done similar fits.

yes, Something like that.
Trigger_efficiency.pdf (44.8 KB)
I like to fit those histograms. I have found some example like https://root.cern.ch/doc/master/rf703__effpdfprod_8C.html.

That’s why I have put those queries here.

Cheers,

Well - that usually just works for toys like in the tutorial, but in there we use: `RooFormulaVar eff("eff", "0.5*(TMath::Erf((t-1)/0.5)+1)", t);`

You can try different available “continuous probability distributions”. e.g.:

``````{
new TCanvas("c", "distributions");
c->Divide(1, 2);
c->cd(1);
// https://en.wikipedia.org/wiki/Cauchy_distribution
TF1 *f_cauchy = new TF1("f_cauchy", "TMath::ATan((x - ) / ) / TMath::Pi() + 0.5", 0., 200.); // CDF
f_cauchy->SetParNames("median", "gamma");
f_cauchy->SetParameters(85., 4.);
f_cauchy->Draw();
c->cd(2);