Relative error and Chi-Squared-Test

Hi ROOT experts,

I have a histogram A that holds a distribution describing kinematics. Now I want to approximate that distribution by other distributions that were made under simplified assumptions. Then I want to quantify which estimation gave the smallest relative error when compared to the true one. Let’s consider one of these simplified distributions and call it histogram B.

Two questions:

  1. I assume the relative error that I make when using histogram B would simply be, for bin i:
    \text{rel. err}_{i} = \text{Abs}(\text{bincontent}_\text{A,i}-\text{bincontent}_\text{B,i})/\text{bincontent}_\text{A,i}
    Is that correct?

  2. How would I quantify which assumption (histo B, C or D) has the lowest relative error when considering all of the bins, some of which being wider than others? Taking the mean of the relative errors over all bins is not accurate due to the different bin sizes. Would I have to use a \chi^2-test and then compare the \chi^2/\text{DOF} of histos B, C and D? Or would I better compare the p-value? Or is there another way?

Thank you very much in advance!

ROOT Version: 6.24/06
Platform: Debian GNU/Linux 11
Compiler: I’m not sure

Dear RootFruit,

Maybe better to put such a general analysis question at the appropriate forum on StackExchange ?