A Method for Statistical Comparison of Histograms

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Abstract


The problem of the testing the hypothesis that two histograms are drawn from the same distribution is a very important problem in many scientific researches. There are several approaches to formalize and resolve this problem. Usually, one-dimensional test statistics is used for this purpose. We propose 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 “significance of deviation”, which has a distribution close to standard normal distribution if both histograms are drawn from the same distribution. This approach allows to estimate the statistical difference between two histograms using multi-dimensional test statistics. The distinguishability of histograms is estimated with the help of the construction a number of clones (rehistograms) of the observed histograms. The approach considered in the paper allows to perform the comparison of histograms with a test more powerful, in the cases considered, than those that use only one test statistic. Also, the probability of correct decision is used as an estimate of the quality of the decision about the distinguishability of histograms.

S I Bityukov

Institute for High Energy Physics

Email: Sergey.Bityukov@ihep.ru

N V Krasnikov

INR RAS

Email: krasniko@inr.ac.ru

A N Nikitenko

Imperial College Sci., Tech. & Med, London, UK S Joint Institute for Nuclear Research

Email: Alexandre.Nikitenko@cern.ch

V V Smirnova

Institute for High Energy Physics

Email: Vera.Smirnova@ihep.ru

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Copyright (c) 2014 Битюков С.И., Красников Н.В., Никитенко А.Н., Смирнова В.В.

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