Comparison of histograms in physical research

Abstract

Main approaches to the methods of comparison of histograms in physical studies are examined. The term “histogram” was originally introduced by Karl Pierson as the “generalized form of graphic representation” [1]. Histograms are very useful in this canonic application for visual data presentation. However, as of today histograms are often regarded as a purely mathematical object. Histograms became indispensable tool in different subject fields of science. Besides the scientific data analysis in experimental studies histograms play important role in data base maintenance and in computer “vision” [1]. Accordingly, the goals and methods of histogram processing vary depending on the specific field of application. Histograms are addressed in the resent paper as one of the elements of data processing system used in the analysis of the data collected in the studies conducted on experimental facilities. Certain methods of histogram comparison are presented and results of comparison are given for three methods (statistical histogram comparison method (SCH), Kolmogorov–Smirnov (KS) method and Anderson–Darling (AD) method) for determination of the possibility to compare histograms during assessment of distinguishability of data samples in the processing of which the histograms were generated.

Keywords

• A histogram
• The Monte Carlo method
• The flow of events
• The test statistic