TH1 and RooDataHist asymmetric uncertainties differ

Hello everyone,

When asking to display asymmetric error bars, TH1 and RooDataHist give the same intervals except for a bin with 0 event.

The frequentist approach states that there is 68% coverage and 32% in the upper and lower tails (16% each). For the case n=0 there is no lower bound, so the upper bound could correspond to 32%. RooDataHist makes this distinction, while TH1 does not.

For RooDataHist, it returns the one-sided upper limit [0, 1.35].

For TH1, it returns the double-sided upper limit [0, 1.84]. As you can see in the link, the one-sided upper limit is also present l.9160 , but it is commented out without any explanations.

I wanted to know the reason behind this decision for TH1, why the RooDataHist uses another definition, and which one we should choose when using asymmetric uncertainties for empty bins?

I’m sure @jonas can give an explanation

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