On the distinguishability of histograms

We consider an approach for testing the hypothesis that two realizations of the random variables in the form of histograms are taken from the same statistical population (i.e. two histograms are drawn from the same distribution). The approach is based on the notion of “significance of deviation”. This approach allows to estimate the statistical difference between two histograms using multi-dimensional test statistics. The distinguishability of the histograms is estimated by constructing a number of clones (rehistograms) of the observed histograms.