Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8386Research ArticleA Method for Statistical Comparison of HistogramsBityukovS ISergey.Bityukov@ihep.ruKrasnikovN Vkrasniko@inr.ac.ruNikitenkoA NAlexandre.Nikitenko@cern.chSmirnovaV VVera.Smirnova@ihep.ruInstitute for High Energy PhysicsINR RASImperial College Sci., Tech. & Med, London, UK S Joint Institute for Nuclear Research15022014232433008092016Copyright © 2014,2014The 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.distribution theory and Monte Carlo studiesdata managementMeasurement and error theoryData analysis: algorithms and implementationestimation of parametersflow of eventshypotheses testingтеория распределенийметод Монте-Карлотеория ошибоканализ данныхобработка событийоценивание параметров распределенийпоток событийпроверка гипотез[Porter F. Testing Consistency of Two Histograms. - 2008.][Gagunashvili N.D. Chi-Square Tests for Comparing Weighted Histograms // Nucl. Instrum. Meth. - 2010. - Vol. 614, No 2. - Pp. 287-296.][Bityukov S.I., Krasnikov N.V., Nikitenko A.N., Smirnova V.V. A Method for Statistical Comparison of Histograms. - 2013.][Two Approaches to Combining Significances / S.I. Bityukov, N.V. Krasnikov, A.N. Nikitenko, V.V. Smirnova // PoS (ACAT08). - 2008. - P. 118.][Frodesen A.G., Skjeggestad O., Toft H. Probability and Statistics in Particle Physics. - Bergen-Oslo-Tromso: Universitetsforlaget, 1979.][Efron B. Bootstrap Methods: Another Look at the Jackknife // Annals of Statistics. - 1979. - Vol. 7, No 1. - Pp. 1-26.][Bityukov S.I., Krasnikov N.V. Distinguishability of Hypotheses // Nucl. Instrum. Meth. - 2004. - Vol. 534, No 1-2. - Pp. 152-155.][Brun R., Rademaker F. ROOT - an Object Oriented Data Analysis Framework // Nucl.Instrum.Meth. - 1997. - Vol. 389, No 1-2. - Pp. 81-86.]