Error of self-normalized histogram

ROOT
1

Dear experts,

Probably my problem can be trivially solved, but I don’t find the solution:

I have a histogram with error bars which I want to normalize to unity.
When normalizing the histogram to unity, I would like the error bars to be correlated bin-by-bin, taking into account that a fluctuation in one bin changes also all the other bins due to the normalization.

This is not what I get with the default error propagation in ROOT. Is there a standard way in ROOT to get the uncertainty I am looking for?

Best,
Rudiger

2

Different ways of normalizing histograms

3

Thanks, I already found this topic, but I cannot find the solution there.

It’s not an issue of bin sizes or calling Sumw2. What I’m searching for is that ROOT handles the error calculation differently, ensuring that my normalization is also fixed.

Maybe I am missing something from the linked topic?

4

You will need to manually modify all values (bin by bin) the way you want, if you don’t like what ROOT does.

5

Hi,

The bin by bin correlations are generally not considered in the ROOT histograms. If you just want the bin standard error, you need to correct by the factor (1. - N_i/N) where N_i is the number of observed events in the bin. This is obtained assuming a multinomial distributions for the bin content.

Lorenzo

6

Thanks!

I thought there maybe was a built-in ROOT function for this cases. I solved it now by calculating the uncertainties on my own with a toy.

Rudiger

7

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