Annotations languages:

** 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

1. Brekht, B. (1998), “Trokhgroshovaya opera i drugiye p'yesy” [Threepenny opera and other plays], Azbuka, St. Petersburg, 328 p.

2. Demidovich, B.P. and Maron, I.A. (1996), “Osnovy vychislitel'noy matematiki” [Fundamentals of Computational Mathematics], Science, Moscow, 664 p.

3. Necomb, S. (1881), Note on the frequency of use of different digits in natural number, American Journal of Mathematics, Vol. 4, pp. 39-40.

4. Benford, F. (1938), The law of anomalous numbers, Proceedings of American Philosophical Society, Vol. 78, No. 4, pp. 551-572.

5. Nigrini, M.J. (1999), The peculiar patterns of first digits, IEE Potentials, No. 18, pp. 24-27.

6. Nigrini, M.J. (1999), I’ve Got Your Number, Journal of Accountancy, May, pp. 79-83.

7. Nigrini, M.J. (2002), Forensic Analytics, Methods and Techniques for Forensic Accounting Investigations, Wiley, Hoboken, NJ, 480 p.

8. Klimov, Yu.N. (2016), “Kvantitativnaya leksikologiya, korpusnaya lingvistika i kolichestvennaya informatika: monografíya” [Quantitative lexicology, corpus linguistics and quantitative informatics: monograph], OchU VO MMA, Moscow, 340 p.

9. Zenkov, A.V. (2015), “Otkloneniya ot zakona Benforda i raspoznavaniye avtorskikh osobennostey v tekstakh” [Deviations from Benford's Law and Recognition of Author's Features in Texts], Computer research and modeling, Vol. 7, No. 1, pp. 197-201.

10. Arnol'd, V. (1998), “Statistika pervykh tsifr stepeney dvoyki i peredel mira” [Statistics of the first degrees of powers of two and repartition of the world], Quant, No. 1, pp. 2-4.

11. Arnol'd, V.I. (2004), “Zhestkiye i myagkiye matematicheskiye modeli” [Hard and soft mathematical models], ICNMO, Moscow, 32 p.

12. Hill, T.P. (1998), The First Digit Phenomen, American Scientist, Vol. 86, July-August, pp. 358-363.

13. Pavlov, A.I. (1981), “O raspredelenii drobnykh doley i zakone Benforda” [On the distribution of fractional shares and the law of Benford], News of the Academy of Sciences of the USSR, Ser. Mat., Vol. 45, No. 4, pp. 760-774.

14. Balazh, V., Nagasaka, K. and Strauch, O. (2010), “Zakon Benforda i funktsii raspredeleniya na (0,1)” [Benford's law and distribution functions on (0,1)], Mathematical Notes, Vol. 88, No. 4, pp. 485-501.

15. Alekseyev, M.A. (2016), “Primenimost' zakona Benforda dlya opredeleniya dostovernosti finansovoy otchotnosti” [The applicability of Benford's law to determine the reliability of financial statements], Bulletin of the Novosibirsk State. Un. economics and management, No. 4, pp. 114-128.

16. Ivakhnenkov, S.V. and Ivakhnenkova, V.V. “Zakon Benforda v audyti finansovoyi zvitnosti” [Benford Law on Financial Reporting Audit], available at: https://conferences.vntu.edu.ua/index.php/pmovc/pmovc/paper/viewFile/5579/4733, (accessed 07.03.2019).

17. Kellerman, L. (2014), Evaluating the effectiveness of Benford’s Law as an invtstigative tool for forensic accountants, Northwest University, 129 p.

18. Adrien, Jamain (2014), Benford’s Law, Imperial College of London, Department of Mathematics, 69 p.

19. CaseWare IDEA Inc. (2007), A Guide to Benford’s Law, Toronto, 31 p.

20. Yang, Lu (2014), Benford’s Law AND Fraud Detection, Williams College, Massaschuesetts, 145p.

21. Ivakhnenkov, S.V. (2010), “Informatsiyni tekhnolohiyi audytu ta vnutrishnʹohospodarsʹkoho kontrolyu v konteksti svitovoyi intehratsiyi” [Information technologies of audit and internal control in the context of world integration], PE “Ruta”, Zhytomyr, 432 p.

22. Byelova, I.V. and Nilova, N.M. (2016), “Metodychni zasady optymizatsiyi protsesu zboru danykh pro operatsiyni vtraty banku” [Methodical principles of optimizing the process of data collection on operational losses of the bank], Bulletin of Khmelnytsky National University, Vol. 1, No. 2, pp. 135-141.

23. Bityukov, S.I., Maksimushkina, A.V. and Smirnova, V.V. (2016), “Sravneniye gistogramm v fizicheskikh issledovaniyakh” [Comparison of histograms in physical research], Izv.vuzov. Nuclear energy, No. 1, pp. 81-88.

24. Kul'bak, S. (1967), “Teoriya informatsii i statistika” [Information Theory and Statistics], Science, Moscow, 408 p.

25. Kolmogorov, A.N. (1967), “Predisloviye redaktora perevoda k knige: Kul'bak S. Teoriya informatsii i statistika” [Preface of the translation editor to the book: Kulbak S. Information Theory and Statistics], Science, Moscow, pp. 2-3.

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],