IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v194y2025ics0960077925002668.html
   My bibliography  Save this article

Benford and power law distributions: Representation and simulation

Author

Listed:
  • Lupi, Claudio

Abstract

Some implications of the strong form of Benford’s law are analysed. It is shown that there is a close relationship between Benford’s law and power laws, which explains why the scope of these laws is often very similar. Furthermore, it is shown how to simulate Benford random variables with the desired characteristics.

Suggested Citation

  • Lupi, Claudio, 2025. "Benford and power law distributions: Representation and simulation," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925002668
    DOI: 10.1016/j.chaos.2025.116253
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077925002668
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2025.116253?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ausloos, Marcel & Castellano, Rosella & Cerqueti, Roy, 2016. "Regularities and discrepancies of credit default swaps: a data science approach through Benford's law," Chaos, Solitons & Fractals, Elsevier, vol. 90(C), pages 8-17.
    2. Mir, T.A., 2012. "The law of the leading digits and the world religions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 792-798.
    3. Rocha Filho, T.M. & Mendes, J.F.F. & Lucio, M.L. & Moret, M.A., 2023. "COVID-19 data, mitigation policies and Newcomb–Benford law," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    4. Ausloos, Marcel & Cerqueti, Roy & Mir, Tariq A., 2017. "Data science for assessing possible tax income manipulation: The case of Italy," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 238-256.
    5. Riccioni, Jessica & Cerqueti, Roy, 2018. "Regular paths in financial markets: Investigating the Benford's law," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 186-194.
    6. 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, Elsevier, vol. 293(1), pages 297-304.
    7. Cerqueti, Roy & Maggi, Mario, 2021. "Data validity and statistical conformity with Benford’s Law," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    8. Micha Kaiser, 2019. "Benford'S Law As An Indicator Of Survey Reliability—Can We Trust Our Data?," Journal of Economic Surveys, Wiley Blackwell, vol. 33(5), pages 1602-1618, December.
    9. Horton, Joanne & Krishna Kumar, Dhanya & Wood, Anthony, 2020. "Detecting academic fraud using Benford law: The case of Professor James Hunton," Research Policy, Elsevier, vol. 49(8).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Roy Cerqueti & Claudio Lupi, 2021. "Some New Tests of Conformity with Benford’s Law," Stats, MDPI, vol. 4(3), pages 1-17, September.
    2. Roy Cerqueti & Mario Maggi & Jessica Riccioni, 2024. "Statistical methods for decision support systems in finance: how Benford’s law predicts financial risk," Annals of Operations Research, Springer, vol. 342(3), pages 1445-1469, November.
    3. Solanki Gupta & Vivek Kumar Singh & Sumit Kumar Banshal, 2024. "Altmetric data quality analysis using Benford’s law," Scientometrics, Springer;Akadémiai Kiadó, vol. 129(7), pages 4597-4621, July.
    4. Arezzo, Maria Felice & Cerqueti, Roy, 2023. "A Benford’s Law view of inspections’ reasonability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).
    5. Wang, Delu & Chen, Fan & Mao, Jinqi & Liu, Nannan & Rong, Fangyu, 2022. "Are the official national data credible? Empirical evidence from statistics quality evaluation of China's coal and its downstream industries," Energy Economics, Elsevier, vol. 114(C).
    6. Cerqueti, Roy & Maggi, Mario, 2021. "Data validity and statistical conformity with Benford’s Law," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    7. Roy Cerqueti & Mario Maggi, 2025. "Classes of probability measures built on the properties of Benford’s law," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 109(1), pages 197-216, March.
    8. Azevedo, Caio da Silva & Gonçalves, Rodrigo Franco & Gava, Vagner Luiz & Spinola, Mauro de Mesquita, 2021. "A Benford’s Law based methodology for fraud detection in social welfare programs: Bolsa Familia analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    9. Bogdan Vasile Ileanu & Marcel Ausloos & Claudiu Herteliu & Marian Pompiliu Cristescu, 2019. "Intriguing behavior when testing the impact of quotation marks usage in Google search results," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(5), pages 2507-2519, September.
    10. Herteliu, Claudiu & Jianu, Ionel & Dragan, Irina Maria & Apostu, Simona & Luchian, Iuliana, 2021. "Testing Benford’s Laws (non)conformity within disclosed companies’ financial statements among hospitality industry in Romania," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 582(C).
    11. Riccioni, Jessica & Cerqueti, Roy, 2018. "Regular paths in financial markets: Investigating the Benford's law," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 186-194.
    12. Ausloos, Marcel & Cerqueti, Roy & Bartolacci, Francesca & Castellano, Nicola G., 2018. "SME investment best strategies. Outliers for assessing how to optimize performance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 754-765.
    13. Clippe, Paulette & Ausloos, Marcel, 2012. "Benford’s law and Theil transform of financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6556-6567.
    14. Bormashenko, Ed. & Shulzinger, E. & Whyman, G. & Bormashenko, Ye., 2016. "Benford’s law, its applicability and breakdown in the IR spectra of polymers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 524-529.
    15. Whyman, G. & Ohtori, N. & Shulzinger, E. & Bormashenko, Ed., 2016. "Revisiting the Benford law: When the Benford-like distribution of leading digits in sets of numerical data is expectable?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 595-601.
    16. Ausloos, Marcel & Ficcadenti, Valerio & Dhesi, Gurjeet & Shakeel, Muhammad, 2021. "Benford’s laws tests on S&P500 daily closing values and the corresponding daily log-returns both point to huge non-conformity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    17. T. Mir, 2016. "The leading digit distribution of the worldwide illicit financial flows," Quality & Quantity: International Journal of Methodology, Springer, vol. 50(1), pages 271-281, January.
    18. Adriano Silva & Sergio Floquet & Ricardo Lima, 2023. "Newcomb–Benford’s Law in Neuromuscular Transmission: Validation in Hyperkalemic Conditions," Stats, MDPI, vol. 6(4), pages 1-19, October.
    19. Ausloos, Marcel & Cerqueti, Roy & Lupi, Claudio, 2017. "Long-range properties and data validity for hydrogeological time series: The case of the Paglia river," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 39-50.
    20. Ausloos, Marcel & Cerqueti, Roy & Mir, Tariq A., 2017. "Data science for assessing possible tax income manipulation: The case of Italy," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 238-256.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925002668. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.