IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v32y2023i4d10.1007_s11749-023-00881-y.html
   My bibliography  Save this article

Statistical models and the Benford hypothesis: a unified framework

Author

Listed:
  • Lucio Barabesi

    (University of Siena)

  • Andrea Cerioli

    (University of Parma)

  • Marco Marzio

    (“G. D’Annunzio” University)

Abstract

The Benford hypothesis is the statement that a random sample is made of realizations of an absolutely continuous random variable distributed according to Benford’s law. Its potential interest spans over many domains such as detection of financial frauds, verification of electoral processes and investigation of scientific measurements. Our aim is to provide a principled framework for the statistical evaluation of this statement. First, we study the probabilistic structure of many classical univariate models when they are framed in the space of the significand and we measure the closeness of each model to the Benford hypothesis. We then obtain two asymptotically equivalent and powerful tests. We show that the proposed test statistics are invariant under scale transformation of the data, a crucial requirement when compliance to the Benford hypothesis is used to corroborate scientific theories. The empirical advantage of the proposed tests is shown through an extensive simulation study. Applications to astrophysical and hydrological data also motivate the methodology.

Suggested Citation

  • Lucio Barabesi & Andrea Cerioli & Marco Marzio, 2023. "Statistical models and the Benford hypothesis: a unified framework," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(4), pages 1479-1507, December.
    • Handle: RePEc:spr:testjl:v:32:y:2023:i:4:d:10.1007_s11749-023-00881-y
    DOI: 10.1007/s11749-023-00881-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-023-00881-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11749-023-00881-y?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. Shao, Lijing & Ma, Bo-Qiang, 2010. "The significant digit law in statistical physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3109-3116.
    2. Roy Cerqueti & Claudio Lupi, 2023. "Severe testing of Benford’s law," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 677-694, June.
    3. Lucas Lacasa, 2019. "Newcomb–Benford law helps customs officers to detect fraud in international trade," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 116(1), pages 11-13, January.
    4. Barabesi, Lucio & Pratelli, Luca, 2020. "On the Generalized Benford law," Statistics & Probability Letters, Elsevier, vol. 160(C).
    5. E. Barrio & H. Inouzhe & C. Matrán, 2020. "On approximate validation of models: a Kolmogorov–Smirnov-based approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 938-965, December.
    6. Lucio Barabesi & Andrea Cerasa & Andrea Cerioli & Domenico Perrotta, 2022. "On Characterizations and Tests of Benford’s Law," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(540), pages 1887-1903, October.
    7. Juan Fernández-Gracia & Lucas Lacasa, 2018. "Bipartisanship Breakdown, Functional Networks, and Forensic Analysis in Spanish 2015 and 2016 National Elections," Complexity, Hindawi, vol. 2018, pages 1-23, January.
    8. Engel, Hans-Andreas & Leuenberger, Christoph, 2003. "Benford's law for exponential random variables," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 361-365, July.
    9. Steven J. Miller, 2015. "Benford's Law: Theory and Applications," Economics Books, Princeton University Press, edition 1, number 10527.
    10. Lucio Barabesi & Andrea Cerasa & Andrea Cerioli & Domenico Perrotta, 2018. "Goodness-of-Fit Testing for the Newcomb-Benford Law With Application to the Detection of Customs Fraud," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(2), pages 346-358, April.
    11. Lucio Barabesi & Andrea Cerioli & Domenico Perrotta, 2021. "Forum on Benford’s law and statistical methods for the detection of frauds," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 767-778, September.
    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. Lucio Barabesi & Andrea Cerioli & Domenico Perrotta, 2021. "Forum on Benford’s law and statistical methods for the detection of frauds," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 767-778, September.
    2. Di Marzio, Marco & Fensore, Stefania & Passamonti, Chiara, 2024. "Validating Benfordness on contaminated data," Socio-Economic Planning Sciences, Elsevier, vol. 95(C).
    3. Katherine M. Anderson & Kevin Dayaratna & Drew Gonshorowski & Steven J. Miller, 2022. "A New Benford Test for Clustered Data with Applications to American Elections," Stats, MDPI, vol. 5(3), pages 1-15, August.
    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. Don Lemons & Nathan Lemons & William Peter, 2021. "First Digit Oscillations," Stats, MDPI, vol. 4(3), pages 1-7, July.
    6. Barabesi, Lucio & Pratelli, Luca, 2020. "On the Generalized Benford law," Statistics & Probability Letters, Elsevier, vol. 160(C).
    7. Huang, Yasheng & Niu, Zhiyong & Yang, Clair, 2020. "Testing firm-level data quality in China against Benford’s Law," Economics Letters, Elsevier, vol. 192(C).
    8. Villas-Boas, Sofia B. & Fu, Qiuzi & Judge, George, 2017. "Benford’s law and the FSD distribution of economic behavioral micro data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 711-719.
    9. Liu, Renliang & Sheng, Liugang & Wang, Jian, 2023. "Faking trade for capital control evasion: Evidence from dual exchange rate arbitrage in China," Journal of International Money and Finance, Elsevier, vol. 138(C).
    10. 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).
    11. 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.
    12. Arno Berger & Theodore P. Hill, 2021. "The mathematics of Benford’s law: a primer," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 779-795, September.
    13. Schräpler Jörg-Peter, 2011. "Benford’s Law as an Instrument for Fraud Detection in Surveys Using the Data of the Socio-Economic Panel (SOEP)," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 231(5-6), pages 685-718, October.
    14. repec:hal:spmain:info:hdl:2441/3tk4fhvbi18ndq2n4gs2e9pp6j is not listed on IDEAS
    15. 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).
    16. Dlugosz, Stephan & Müller-Funk, Ulrich, 2012. "Ziffernanalyse zur Betrugserkennung in Finanzverwaltungen: Prüfung von Kassenbelegen," Arbeitsberichte des Instituts für Wirtschaftsinformatik 133, University of Münster, Department of Information Systems.
    17. Gueron, Eduardo & Pellegrini, Jerônimo, 2022. "Application of Benford–Newcomb law with base change to electoral fraud detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    18. Cerqueti, Roy & Maggi, Mario, 2021. "Data validity and statistical conformity with Benford’s Law," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    19. Gamermann, Daniel & Antunes, Felipe Leite, 2018. "Statistical analysis of Brazilian electoral campaigns via Benford’s law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 171-188.
    20. Madeleine Farris & Noah Luntzlara & Steven J. Miller & Lily Shao & Mengxi Wang, 2021. "Recurrence relations and Benford’s law," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 797-817, September.
    21. Arno Berger & Chuang Xu, 2019. "Best Finite Approximations of Benford’s Law," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1525-1553, September.

    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:spr:testjl:v:32:y:2023:i:4:d:10.1007_s11749-023-00881-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.