Anomalies in cryptocurrencies trading volumes using Benford’s law
DOI: https://doi.org/10.3846/jbem.2026.27877Abstract
(1) Background: This research evaluates the efficacy of an expanded suite of Benford’s Law analyses—integrating highly sensitive Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) tests—across diverse cryptocurrencies and temporal scales. By examining both legitimate digital assets and a documented Ponzi scheme, the study identifies robust statistical methodologies for detecting manipulated trading-volume data in de-centralized markets; (2) Methods: The analytical framework assesses the conformity of first- and second-digit distributions with theoretical Benford expectations. The methodology employs a multi-test battery including Pearson Chi-square, Mean Absolute Deviation (MAD), Anderson-Darling, Kolmogorov-Smirnov, Kuiper and Cramérvon Mises tests to ensure sensitivity to both central and tail-end distributional anomalies; (3) Results: Empirical findings demonstrate that Dogecoin, Litecoin, and Luckycoin exhibit significant conformity with Benford’s distribution across the KS and AD metrics. Conversely, Bitconnect demonstrates systemic nonconformity across all applied statis-tical tests; (4) Conclusions: While Benford’s Law is an effective initial diagnostic, it is not a standalone solution for cryptocurrency fraud detection. Among the methods tested, the Anderson-Darling (A-D) and Kolmogorov-Smirnov (K-S) tests exhibited the highest sensitivity, providing a robust framework for identifying sophisticated data manipulation.
Keywords:
Benford’s law, cryptocurrency, trading volume, fraudulent activity, anomaly detection, manipulated datasetHow to Cite
Share
License
Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University.
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Arshadi, L., & Jahangir, A. H. (2014). Benford’s law behavior of internet traffic. Journal of Network and Computer Applications, 40, 194–205. https://doi.org/10.1016/j.jnca.2013.09.007
Ausloos, M., Castellano, R., & Cerqueti, R. (2016). Regularities and discrepancies of credit default swaps: A data science approach through Benford’s law. Chaos, Solitons & Fractals, 90, 8–17. https://doi.org/10.1016/j.chaos.2016.03.002
Badal-Valero, E., Alvarez-Jareño, A. Ignasi, & Pavía, J. M. (2018). Combining Benford’s Law and machine learning to detect money laundering. An actual Spanish court case. Forensic Science International, 282, 24–34. https://doi.org/10.1016/j.forsciint.2017.11.008
Baek, H., Oh, J., Kim, C. Y., & Lee, K. (2019). A model for detecting cryptocurrency transactions with discernible purpose. In 2019 Eleventh International Conference on Ubiquitous and Future Networks (ICUFN) (pp. 713–717). IEEE. https://doi.org/10.1109/ICUFN.2019.8806126
Bartoletti, M., Carta, S., Cimoli, T., & Saia, R. (2020). Dissecting Ponzi schemes on Ethereum: Identification, analysis, and impact. Future Generation Computer Systems, 102, 259–277. https://doi.org/10.1016/J.FUTURE.2019.08.014
Baum, S. C. (2018). Cryptocurrency fraud: A look into the frontier of fraud [Honors College Theses]. Georgia Southern University.
Benford, F. (1938). The law of anomalous numbers. Proceedings of the American Philosophical Society, 78(4), 551–572.
Berger, A., & Hill, T. P. (2011). A basic theory of Benford’s law. Probability Surveys, 8, 1–126. https://doi.org/10.1214/11-PS175
Bertin, M., & Lafouge, T. (2025). Categorization of scientometric data in a Benfordian context. Quantitative Science Studies, 6, 524–545. https://doi.org/10.1162/qss_a_00361
Bhattacharya, S., Xu, D., & Kumar, K. (2011). An ANN-based auditor decision support system using Benford’s law. Decision Support Systems, 50, 576–584. https://doi.org/10.1016/j.dss.2010.08.011
Bredl, S., Winker, P., & Kötschau, K. (2012). A statistical approach to detect interviewer falsification of survey data. Survey Methodology, 38, 1–10.
Buntinx, J. (2018). The BitConnect Ponzi scheme has finally collapsed as exit scam becomes evident. NewsBTC.
Carol, A., & Douglas, C. (2020). Corruption and fraud in financial markets: Malpractice, misconduct and manipulation. John Wiley & Sons.
Cerqueti, R., & Provenzano, D. (2023). Benford’s Law for economic data reliability: The case of tourism flows in Sicily. Chaos, Solitons & Fractals, 173, Article 113635. https://doi.org/10.1016/j.chaos.2023.113635
Chemin, M., & Mbiekop, F. (2015). Addressing child sex tourism: The Indian case. European Journal of Political Economy, 38, 169–180. https://doi.org/10.1016/j.ejpoleco.2015.02.005
Cleary, R., & Thibodeau, J. C. (2005). Applying digital analysis using Benford’s Law to detect fraud: The dangers of type I errors. Auditing, 24, 77–81. https://doi.org/10.2308/aud.2005.24.1.77
Clippe, P., & Ausloos, M. (2012). Benford’s law and Theil transform of financial data. Physica A: Statistical Mechanics and its Applications, 391, 6556–6567. https://doi.org/10.1016/j.physa.2012.07.063
Coderre, D. (1999). Computer-assisted techniques for fraud detection. CPA Journal, 69(8), 57–59.
Diekmann, A. (2007). Not the first digit! Using Benford’s Law to detect fraudulent scientific data. Journal of Applied Statistics, 34, 321–329. https://doi.org/10.1080/02664760601004940
Diekmann, A., & Jann, B. (2010). Benford’s law and fraud detection: Facts and legends. German Economic Review, 11, 397–401. https://doi.org/10.1111/j.1468-0475.2010.00510.x
Drake, P. D., & Nigrini, M. J. (2000). Computer assisted analytical procedures using Benford’s Law. Journal of Accounting Education, 18, 127–146. https://doi.org/10.1016/S0748-5751(00)00008-7
Druică, E., Oancea, B., & Vâlsan, C. (2018). Benford’s law and the limits of digit analysis. International Journal of Accounting Information Systems, 31, 75–82. https://doi.org/10.1016/j.accinf.2018.09.004
Durtschi, C., Hillison, W., & Pacini, C. (2004). The effective use of Benford’s law to assist in detecting fraud in accounting data. Journal of Forensic Accounting, 5, 17–43.
Eckhartt, G. M., & Ruxton, G. D. (2023). Investigating and preventing scientific misconduct using Benford’s Law. Research Integrity and Peer Review, 8, 1–10. https://doi.org/10.1186/s41073-022-00126-w
Efrem, N. (2021). Benford’s law applied to sale prices on the Swedish housing market [Thesis]. Stockholms Universitet.
Farrugia, S., Ellul, J., & Azzopardi, G. (2020). Detection of illicit accounts over the Ethereum blockchain. Expert Systems with Applications, 150, Article 113318. https://doi.org/10.1016/j.eswa.2020.113318
Feng, X., Shi, Q., Li, X., Liu, H., & Wang, L. (2024). IDPonzi: An interpretable detection model for identifying smart Ponzi schemes. Engineering Applications of Artificial Intelligence, 136, Article 108868. https://doi.org/10.1016/j.engappai.2024.108868
Gao, B., Wang, H., Xia, P., Wu, S., Zhou, Y., Luo, X., & Tyson, G. (2021). Tracking counterfeit cryptocurrency end-to-end. ACM SIGMETRICS Performance Evaluation Review, 49(1), 33–34. https://doi.org/10.1145/3543516.3456282
Giles, D. E. (2007). Benford’s law and naturally occurring prices in certain eBay auctions. Applied Economics Letters, 14, 157–161. https://doi.org/10.1080/13504850500425667
Giudici, G., Milne, A., & Vinogradov, D. (2020). Cryptocurrencies: Market analysis and perspectives. Journal of Industrial and Business Economics, 47, 1–18. https://doi.org/10.1007/s40812-019-00138-6
Goernitz, N., Kloft, M., Rieck, K., & Brefeld, U. (2013). Toward supervised anomaly detection. Journal of Artificial Intelligence Research, 46, 235–262. https://doi.org/10.1613/jair.3623
Goldstein, M., & Uchida, S. (2016). A comparative evaluation of unsupervised anomaly detection algorithms for multivariate data. PLoS ONE, 11, Article e0152173. https://doi.org/10.1371/journal.pone.0152173
Grigorescu, P.-C., & Amza, A. (2025). Cryptocurrency trading pairs and Benford’s law: Investigating market irregularities. Proceedings of the International Conference on Business Excellence, 19, 506–513. https://doi.org/10.2478/picbe-2025-0041
Hassler, U., & Hosseinkouchack, M. (2019). Testing the Newcomb-Benford Law: Experimental evidence. Applied Economics Letters, 26, 1762–1769. https://doi.org/10.1080/13504851.2019.1597248
Holz, C. A. (2014). The quality of China’s GDP statistics. China Economic Review, 30, 309–338. https://doi.org/10.1016/j.chieco.2014.06.009
Ivan, L., & Bădele, C. S. (2021). Cryptocurrencies–The modality of payment of the future. Risks and vulnerabilities. The Journal Contemporary Economy, 6(4), 130–141.
Jawabreh, O., Bader, A., Saleh, M., & Alrabie, A. M. A. (2018). Fraud inference investigation within tourism sector in Jordan. Journal of Economic & Management Perspectives, 12, 5–20.
Kamišalić, A., Kramberger, R., & Fister, I. (2021). Synergy of blockchain technology and data mining techniques for anomaly detection. Applied Sciences, 11, Article 7987. https://doi.org/10.3390/app11177987
Kauko, K. (2024). How to detect what drives deviations from Benford’s law? An application to bank deposit data. Empirical Economics, 67, 1045–1061. https://doi.org/10.1007/s00181-024-02576-1
Keller, G., & Warrack, B. (2003). Statistics for management and economics. Thomson/Brooks/Cole.
Kenny, D. A. (2024). Measuring model fit. http://davidakenny.net/cm/fit.htm
Kharpal, A. (2018, March 9). Mysterious cryptocurrency scammers ran off with more than $2 million after ditching their investors. CNBC. http://www.cnbc.com/2018/03/09/cryptocurrency-scammers-of-giza-make-off-with-2-million-after-ico.html
Kolar, I., & Horvat, R. (2026). Benford’s Law as an investigative tool: Application to the financial statements of Slovenian micro and small enterprises and sole proprietors. Revija za kriminalistiko in kriminologijo, 77.
Kolias, P. (2022). Applying Benford’s law to COVID-19 data: The case of the European Union. Journal of Public Health, 44, e221–e226. https://doi.org/10.1093/pubmed/fdac005
Leemis, L. M., Schmeiser, B. W., & Evans, D. L. (2000). Survival distributions satisfying Benford’s Law. The American Statistician, 54(4), 236–241. https://doi.org/10.2307/2685773
Levine, M. (2017). SEC halts a silly Initial Coin Offering. Bloomberg. https://www.bloomberg.com/opinion/articles/2017-12-05/sec-halts-a-silly-initial-coin-offering
Licer, A., Cano-rodríguez, M., & Nú, M. (2025). Divergence from Benford’s law fails to measure financial statement accuracy. International Journal of Accounting Information Systems, 56, Article 100745. https://doi.org/10.1016/j.accinf.2025.100745
Marsaglia, G., & Marsaglia, J. (2004). Evaluating the Anderson-Darling distribution. Journal of Statistical Software, 9(2), 1–5. https://doi.org/10.18637/jss.v009.i02
Martineau, P. (2018, January 23). Inside the group chats where people pump and dump cryptocurrency. Future. https://theoutline.com/post/3074/inside-the-group-chats-where-people-pump-and-dump-cryptocurrency
Matakovic, H. (2021). Tourism data in Croatia assessed by Benford’s Law. Journal of Public Administration, Finance and Law, 19, 166–184. https://doi.org/10.47743/jopafl-2021-19-13
Michalski, T., & Stoltz, G. (2013). Do countries falsify economic data strategically? Some evidence that they might. The Review of Economics and Statistics, 95(2), 591–616. https://doi.org/10.1162/REST_a_00274
Mir, T. A., & Ausloos, M. (2018). Benford’s law: A “sleeping beauty” sleeping in the dirty pages of logarithmic tables. Journal of the Association for Information Science and Technology, 69, 349–358. https://doi.org/10.1002/asi.23845
Neves, G. A., Nunes, C. S., & Fernandes, P. O. (2021). Application of Benford’s Law to the tourism demand: The case of the Island of Sal, Cape Verde. Springer International Publishing. https://doi.org/10.1007/978-3-030-91885-9_43
Newcomb, S. (1881). Note on the frequency of use of the different digits in natural numbers. American Journal of Mathematics, 4(1), 39–40. https://doi.org/10.2307/2369148
Nica, O., Piotrowska, K., & Schenk-Hoppé, K. R. (2017). Cryptocurrencies: Economic benefits and risks. SSRN. https://doi.org/10.2139/ssrn.3059856
Nigrini, M. J., Wells, J. T., Almeida, C. S. de, et al. (2012). Benford’s Law: Applications for forensic accounting, auditing, and fraud detection. Wiley. https://doi.org/10.1002/9781119203094
Nye, J., & Moul, C. (2007). The political economy of numbers: On the application of Benford’s Law to international macroeconomic statistics. The BE Journal of Macroeconomics, 7(1). https://doi.org/10.2202/1935-1690.1449
Osborne, C. (2018, February 13). LoopX pulls exit scam, walks away with $4.5m in investor cryptocurrency. ZDnet. https://www.zdnet.com/article/loopx-pulls-exit-scam-walks-away-with-4-5m-in-investor-funds/
Pietronero, L., Tosatti, E., Tosatti, V., & Vespignani, A. (2001). Explaining the uneven distribution of numbers in nature: The laws of Benford and Zipf. Physica A: Statistical Mechanics and its Applications, 293(1-2), 297–304. https://doi.org/10.1016/S0378-4371(00)00633-6
Prasad, N. R., Almanza-Garcia, S., & Lu, T. T. (2009). Anomaly detection: A survey. Computers, Materials, & Continua, 14, 1–22. https://doi.org/10.3970/cmc.2009.014.001
Sambridge, M., Tkalčić, H., & Jackson, A. (2010). Benford’s law in the natural sciences. Geophysical Research Letters, 37(22), L22301. https://doi.org/10.1029/2010GL044830
Sarkar, B. P. (1973). An observation on the significant digits of the binomial coefficients and factorials. Sankhyā: The Indian Journal of Statistics, Series B, 35, 363–364.
Sayadi, S., Ben Rejeb, S., & Choukair, Z. (2019). Anomaly detection model over blockchain electronic transactions. In 2019 15th International Wireless Communications & Mobile Computing Conference (IWCMC) (pp. 895–900). IEEE. https://doi.org/10.1109/IWCMC.2019.8766765
Shi, J., Ausloos, M., & Zhu, T. (2018). Benford’s law first significant digit and distribution distances for testing the reliability of financial reports in developing countries. Physica A: Statistical Mechanics and its Applications, 492, 878–888. https://doi.org/10.1016/j.physa.2017.11.017
Shobhit, S. (2018). $9 Million lost each day in cryptocurrency scams. Investopedia. https://www.investopedia.com/news/beware-9m-are-lost-each-day-crypto-scams/
Singleton, T. W. (2011). IT audit basics: Understanding and applying Benford’s Law. Isaca Journal, 3.
Slosar, D. J. (2026). Analysis of Benford’s Law conformity with Web of Science citations of documents. Acta Informatica Pragensia, 15, 22–35. https://doi.org/10.18267/j.aip.281
Stoerk, T. (2016). Statistical corruption in Beijing’s air quality data has likely ended in 2012. Atmospheric Environment, 127, 365–371. https://doi.org/10.1016/j.atmosenv.2015.12.055
Gorard, S. (2013). Revisiting a 90-Year-Old debate: The advantages of the mean deviation. British Journal of Educational Studies, 53, 417–430. https://doi.org/10.1111/j.1467-8527.2005.00304.x
Tam Cho, W. K., & Gaines, B. J. (2007). Breaking the (Benford) Law: Statistical fraud detection in campaign finance. The American Statistician, 61(3), 218–223. https://doi.org/10.1198/000313007X223496
Tsai, C.-F., & Yen, C.-C. (2007). Unsupervised anomaly detection using HDG-Clustering algorithm. in M. Ishikawa, K. Doya, H. Miyamoto, & T. Yamakawa (Eds.), Lecture notes in computer science: Vol. 4985. Neural information processing. ICONIP 2007 (pp. 356–365). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-69162-4_37
Vičič, J., & Tošić, A. (2022). Application of Benford’s Law on cryptocurrencies. Journal of Theoretical and Applied Electronic Commerce Research, 17, 313–326. https://doi.org/10.3390/jtaer17010016
Wallace, W. A. (2002). Assessing the quality of data used for benchmarking and decision-making. The Journal of Government Financial Management, 51(3), 16–22.
Wlodarski, J. (1971). Fibonacci an Luca numbers tend to obey Benford’s Law. The Fibonacci Quarterly, 9, 87–88. https://doi.org/10.1080/00150517.1971.12431041
Wong, S. C. Y. (2010). Testing Benford’s Law with the first two significant digits [MSc Thesis, University of Victoria].
Zuckoff, M. (2006). Ponzi’s scheme: The true story of a financial legend. Random House Incorporated.
View article in other formats
CrossMark check
Published
Issue
Section
Copyright
Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University.
License
This work is licensed under a Creative Commons Attribution 4.0 International License.