Compute +/-1 and +/-2 sigma bands around the expected limit

ROOT
1

I hope this is the right forum for my question:
I am using a binned LikelihoodMethod to compute an (“observed”) upper limit on the Zprime (to ttbar) prduction cross section, as function of a physical parameter ( Zprime mass).
Using the sum of (Standard Model) background processes, I also compute an expected upper limit as function of the physical parameter.

I would like to compute +/-1 and +/-2 sigma bands around the expected limit, in order to provide an estimate of how compatible a certain observed upper limit with the expected value of the limit.

I am wondering if there is a recommended way to compute the +/-1 and +/-2 sigma bands ?

so the code is attached

Thank you very much,
Wael
BinnedLikelihood.C (4.67 KB)
MC_Sig_500GeV_Bck.root (5.17 KB)

2

I’m not sure if that’s what you want … but … see … http://root.cern.ch/root/html/TH1.html#TH1:GetQuantiles

Edit your “BinnedLikelihood.C” and set:
const double maxsig = 15.0;
then in a root interactive session do:
.L BinnedLikelihood.C
DoMe();
Double_t q[4], probSum[4] = {0.5, 0.6827, 0.90, 0.9545};
L->GetQuantiles(4, q, probSum);
cout << "50% : " << q[0] << endl << "1 sigma : " << q[1] << endl;
cout << "90% : " << q[2] << endl << "2 sigma : " << q[3] << endl;

3

Thank you Pepe Le Pew,
this calculte the limit at different confidence levels. But i want to calculate the statistical uncertainties to this limit with +/- 1 sigma and +/-2 sigma (sigma=standard deviation) bands around this expected limit.
To be clear i want to compute the bands as the yellow and the the green bands in the attached plots.

thank you very much
Limit.pdf (34.7 KB)