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Application of Benford’s law (first-digit law, anomalous numbers law) in financial audit

S. Gadetska, V. Dubnitskiy, V. Lukin, A. Khodyrev
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Description: A separate group among documentary control instruments are calculation analytical methods, among them Benford’s law analysis of financial reports has recently acquired wide application. This law postulates that distribution of digits in numbers may be not random, but meeting a certain regularity. This regularity is just what is used in audit practice. Benford’s law is an empirical principle. It application enables inspection of financial reports for eventual forgery. It does not ensure unambiguous conclusion as regards actual violation of rules, but indicates eventual possibility of such violations. This work dwells on peculiarities of Benford’s law application in audit practice. It includes statistical checking of the model for appearance of sequences meeting Benford’s law; comparison between pairs of histograms generated by data of different model observations; statistical checking of Benford’s law correspondence to the data of actual financial documents. In order to check correspondence of obtained data to Benford’s law classical criterion and information measure of deviation were used. It was shown the models existing as per today are based on logarithmic transformation of random numbers evenly distributed along section actually cause appearance of sequences meeting Benford’s law. It6 was shown that sample size, beginning from 100 observations, does not affect modeling result. In the course of numerical modeling some cases happened when distribution of first digits in pairs of histograms did not meet Benford’s law, despite the fact that models of their obtaining were substantially different. For statistical checking of Benford’s law correspondence to data of actual financial documents data were used from balance sheet items of one of the largest Ukrainian companies for three time periods. In the course of data preparation to ensure correct comparisons a method of their preparation was developed with due consideration of the peculiarities of existing accounting regulations. Results of the analysis showed that in only one out of three actual balance sheets first digit distribution met Benford’s law. Nevertheless, a conclusion was made that suitability of Benford’s law application to financial audit may be determined only after subsequent research under ea special program.


Keywords: Benford’s law, financial audit, compliance of histograms

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Reference:
 Hadetska, S.V., Dubnytskyi, V.Yu., Lukin, V.O. and Khodyriev, O.I. (2019), “Vykorystannia zakonu Benforda (zakonu pershoi tsyfry, zakonu anomalnykh vidkhylen) pid chas provedennia finansovoho audytu” [Application of Benford’s law (first-digit law, anomalous numbers law) in financial audit], Information Processing Systems, Vol. 2(157), pp. 22-32. https://doi.org/10.30748/soi.2019.157.03.