# Uncertainty on ratio of integrals

This is more of a pure statistical question rather than related to any tool, but maybe this is a good place anyway in case there is some standard facilities for these things.

I want to estimate the uncertainty on the following ratio:

``` r = int_sub / int_full ```
where int_sub the integral over a subrange of a histogram, int_full is the full range integral of the same histogram. The numerator and denominator both have Poisson errors, but what is the uncertainty on the ratio? (The numerator and the denominator are obviously correlated… I recall hearing the ratio can be approximated with a binomial distribution?)

Hi,

Yes the distribution in this ratio is binomial. You can use for getting the uncertainty the TEfficiency class.
See its reference doc, root.cern.ch/root/html/TEfficiency.html

Lorenzo

Hi all–

I know that a ratio of independent, normally distributed variates is a Cauchy distribution, but when you consider correlated errors, it gets messier, as pointed out here:

Can someone lend an explanation (or point to a source) as to why this ratio is said to be a binomial distribution?

Also, how does the binomial option “b” in the “Divide” command –
https://root.cern.ch/doc/master/TH1_8cxx_source.html#l02793
affect the histogram errors if ‘Sumw2’ was called for them already?

Also, how is this related to the TEfficiency class?

Thanks,
Andrew