Calculating effective sigma

[Tanvi_Wamorkar]

Dear experts,

Apologies if this is not the correct forum for my question.
I have a branch in a TTree containing the mass of a diphoton object. Is there a way to find the smallest interval which contains 68% of the events, without performing a fit (i.e not the value of the sigma parameter of the gaussian fit to the distribution)?

Thanks in advance.

[StephanH]

On first thought, nothing comes to mind that would do this for you. A first approach could be to calculate a 68% quantile by calculating the upper and lower 16% quantiles. This is not what you want, but a first step. Now you can start to optimise the lower quantile until you get the desired quantile.

[Tanvi_Wamorkar]

Thanks for the tip Stephan. Is there a function in ROOT to calculate the quantile? Could you point me to correct one?

Thanks again!

[Wile_E_Coyote]

Try:

grep -r -i quantile `root-config --incdir`
grep -r -i quantile ${ROOTSYS}/t[eu]*

If you create a histogram of the “mass of a diphoton object”, then maybe: TH1::GetQuantiles

Median of histogram

The “median” is just the “0.5 quantile”: { // create, fill and draw the histogram TF1 *f = new TF1("f", "TMath::Gaus(x, 5, 1)", 0, 10); TH1D *h = new TH1D("h", "h", 100, 0, 10); h->FillRandom("f"); h->Draw(); // calculate and print the "median" Double_t x, q; q = 0.5; // 0.5 for "median" h->ComputeIntegral(); // just a precaution h->GetQuantiles(1, &x, &q); std::cout << "median = " << x << std::endl; }