# Efficiency error calculation for an estimated process

Hello,

I have a certain distribution of data with the Poisson errors as a TGraphAsymmErrors graph. I also have a TH1 histo of the same distribution but the bin contents are measured estimates for a certain physics process. This process is believed to be presented in that data distribution. The errors from the measurement are symmetric (So, the histo can be replaced with an TGrapErrors object). Now, I want to measure an “efficiency” for each bin (the asymmetry graph and the histo have the same binning), which is the ratio of the process estimate over data in a given bin. My question would be how one calculates errors on this (binned) efficiency and how to do this in ROOT? Also, the related question is how one should treat the bins where, estimate>data due to statistical fluctuations? Many thanks in advance for any help/suggestions/comments.

Best regards,
Gia

Hi,

If I have understood you well you want to calculate the ratio of n1 / n2 where n1 is Poisson distributed and n2 is Gaussian. In ROOT using TH1::Divide you can compute the error on the ratio n1/n2 assuming that both n1 and n2 are Gaussian of using the class TEfficiency (or TGraphAsymmErrors::Divide) you can compute the error in case
of a binomial distributions for n1/n2. When n1/n2 are both Poisson, the Poisson ratio can be transformed in
the binomial case

Best Regards,

Lorenzo