IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v540y2020ics0378437119317649.html
   My bibliography  Save this article

Several common probability distributions obey Benford’s law

Author

Listed:
  • Fang, Guojun
  • Chen, Qihong

Abstract

Benford’s law states that the frequency of lower first significant digits(FSD) is higher than that of upper FSD in many naturally produced numbers. The law can be applied to many various fields, so it is important to know which common probability distributions obey Benford’s law. We revisit whether the Log-normal probability distribution obeys the law by using the method of Fourier analysis and numerical simulation. Moreover, we use simulation method to judge whether the Weibull distribution and the Inverse Gamma distribution are close to Benford’s law under some conditions. Our work give some reasons to support why Benford’s law is universal in real world.

Suggested Citation

  • Fang, Guojun & Chen, Qihong, 2020. "Several common probability distributions obey Benford’s law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    • Handle: RePEc:eee:phsmap:v:540:y:2020:i:c:s0378437119317649
    DOI: 10.1016/j.physa.2019.123129
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119317649
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.123129?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. Tam Cho, Wendy K. & Gaines, Brian J., 2007. "Breaking the (Benford) Law: Statistical Fraud Detection in Campaign Finance," The American Statistician, American Statistical Association, vol. 61, pages 218-223, August.
    2. Mebane, Walter R., 2011. "Comment on “Benford's Law and the Detection of Election Fraudâ€," Political Analysis, Cambridge University Press, vol. 19(3), pages 269-272, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cerqueti, Roy & Maggi, Mario, 2021. "Data validity and statistical conformity with Benford’s Law," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

    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. Montag, Josef, 2017. "Identifying odometer fraud in used car market data," Transport Policy, Elsevier, vol. 60(C), pages 10-23.
    2. Sitsofe Tsagbey & Miguel de Carvalho & Garritt L. Page, 2017. "All Data are Wrong, but Some are Useful? Advocating the Need for Data Auditing," The American Statistician, Taylor & Francis Journals, vol. 71(3), pages 231-235, July.
    3. Dang, Canh Thien & Owens, Trudy, 2020. "Does transparency come at the cost of charitable services? Evidence from investigating British charities," Journal of Economic Behavior & Organization, Elsevier, vol. 172(C), pages 314-343.
    4. Edward J. Lusk & Michael Halperin, 2014. "Detecting Newcomb-Benford Digital Frequency Anomalies in the Audit Context: Suggested Chi2 Test Possibilities," Accounting and Finance Research, Sciedu Press, vol. 3(2), pages 191-191, May.
    5. Lee, Joanne & Cho, Wendy K. Tam & Judge, George G., 2010. "Stigler's approach to recovering the distribution of first significant digits in natural data sets," Statistics & Probability Letters, Elsevier, vol. 80(2), pages 82-88, January.
    6. Wójcik, Michał Ryszard, 2014. "A characterization of Benford’s law through generalized scale-invariance," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 1-5.
    7. 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).
    8. Montag, Josef, 2015. "Identifying Odometer Fraud: Evidence from the Used Car Market in the Czech Republic," MPRA Paper 65182, University Library of Munich, Germany.
    9. Frank Heilig & Edward J. Lusk, 2017. "A Robust Newcomb-Benford Account Screening Profiler: An Audit Decision Support System," International Journal of Financial Research, International Journal of Financial Research, Sciedu Press, vol. 8(3), pages 27-39, July.
    10. Jalan, Akanksha & Matkovskyy, Roman & Yarovaya, Larisa, 2021. "“Shiny” crypto assets: A systemic look at gold-backed cryptocurrencies during the COVID-19 pandemic," International Review of Financial Analysis, Elsevier, vol. 78(C).
    11. Druică, Elena & Oancea, Bogdan & Vâlsan, Călin, 2018. "Benford's law and the limits of digit analysis," International Journal of Accounting Information Systems, Elsevier, vol. 31(C), pages 75-82.
    12. Morrow, John, 2014. "Benford's Law, families of distributions and a test basis," LSE Research Online Documents on Economics 60364, London School of Economics and Political Science, LSE Library.
    13. Mir, T.A., 2014. "The Benford law behavior of the religious activity data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 408(C), pages 1-9.
    14. 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).
    15. Rosa Abrantes-Metz & Sofia Villas-Boas & George Judge, 2011. "Tracking the Libor rate," Applied Economics Letters, Taylor & Francis Journals, vol. 18(10), pages 893-899.
    16. 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.
    17. Shi, Jing & Ausloos, Marcel & Zhu, Tingting, 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, Elsevier, vol. 492(C), pages 878-888.
    18. Etienne Harb & Nohade Nasrallah & Rim El Khoury & Khaled Hussainey, 2022. "Applying Benford’s Law to detect accounting data manipulation in the pre-and post-financial engineering periods: Evidence from Lebanon," Working Papers of LaRGE Research Center 2022-10, Laboratoire de Recherche en Gestion et Economie (LaRGE), Université de Strasbourg.
    19. Vadim S. Balashov & Yuxing Yan & Xiaodi Zhu, 2020. "Who Manipulates Data During Pandemics? Evidence from Newcomb-Benford Law," Papers 2007.14841, arXiv.org, revised Jan 2021.
    20. Haenschen, Katherine & Wolf, Jordan, 2019. "Disclaiming responsibility: How platforms deadlocked the Federal Election Commission's efforts to regulate digital political advertising," Telecommunications Policy, Elsevier, vol. 43(8), pages 1-1.

    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:phsmap:v:540:y:2020:i:c:s0378437119317649. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.