IDEAS home Printed from https://ideas.repec.org/p/cep/cepdps/dp1291.html
   My bibliography  Save this paper

Benford's Law, Families of Distributions and a Test Basis

Author

Listed:
  • John Morrow

Abstract

Benford's Law is used to test for data irregularities. While novel, there are two weaknesses in the current methodology. First, test values used in practice are too conservative and the test values of this paper are more powerful and hold for fairly small samples. Second, testing requires Benford's Law to hold, which it often does not. I present a simple method to transform distributions to satisfy the Law with arbitrary precision and induce scale invariance, freeing tests from the choice of units. I additionally derive a rate of convergence to Benford's Law. Finally, the results are applied to common distributions.

Suggested Citation

  • John Morrow, 2014. "Benford's Law, Families of Distributions and a Test Basis," CEP Discussion Papers dp1291, Centre for Economic Performance, LSE.
    • Handle: RePEc:cep:cepdps:dp1291
    as

    Download full text from publisher

    File URL: https://cep.lse.ac.uk/pubs/download/dp1291.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    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. G. Noether, 1963. "Note on the kolmogorov statistic in the discrete case," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 7(1), pages 115-116, December.
    3. Grendar, Marian & Judge, George & Schechter, Laura, 2007. "An empirical non-parametric likelihood family of data-based Benford-like distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 429-438.
    4. Scott Marchi & James Hamilton, 2006. "Assessing the Accuracy of Self-Reported Data: an Evaluation of the Toxics Release Inventory," Journal of Risk and Uncertainty, Springer, vol. 32(1), pages 57-76, January.
    5. Rodriguez R.J., 2004. "First Significant Digit Patterns From Mixtures of Uniform Distributions," The American Statistician, American Statistical Association, vol. 58, pages 64-71, February.
    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. Rabeea Sadaf, 2017. "Advanced Statistical Techniques For Testing Benford'S Law," Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 1(2), pages 229-238, December.
    2. Bernhard Rauch & Max Göttsche & Gernot Brähler & Stefan Engel, 2011. "Fact and Fiction in EU‐Governmental Economic Data," German Economic Review, Verein für Socialpolitik, vol. 12(3), pages 243-255, August.
    3. Ronelle Burger & Canh Thien Dang & Trudy Owens, 2017. "Better performing NGOs do report more accurately: Evidence from investigating Ugandan NGO financial accounts," Discussion Papers 2017-10, University of Nottingham, CREDIT.
    4. 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.
    5. Holz, Carsten A., 2014. "The quality of China's GDP statistics," China Economic Review, Elsevier, vol. 30(C), pages 309-338.
    6. Kalaichelvan, Mohandass & Lim Kai Jie, Shawn, 2012. "A Critical Evaluation of the Significance of Round Numbers in European Equity Markets in Light of the Predictions from Benford’s Law," MPRA Paper 40960, University Library of Munich, Germany.
    7. Eutsler, Jared & Kathleen Harris, M. & Tyler Williams, L. & Cornejo, Omar E., 2023. "Accounting for partisanship and politicization: Employing Benford's Law to examine misreporting of COVID-19 infection cases and deaths in the United States," Accounting, Organizations and Society, Elsevier, vol. 108(C).
    8. George Judge & Laura Schechter, 2009. "Detecting Problems in Survey Data Using Benford’s Law," Journal of Human Resources, University of Wisconsin Press, vol. 44(1).
    9. Hürlimann, Werner, 2015. "On the uniform random upper bound family of first significant digit distributions," Journal of Informetrics, Elsevier, vol. 9(2), pages 349-358.
    10. Pankaj C. Patel & Mike G. Tsionas & Maria João Guedes, 2022. "Benford's law, small business financial reporting, and survival," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(8), pages 3301-3315, December.
    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. Thomas Stoerk, 2015. "Statistical corruption in Beijing’s air quality data has likely ended in 2012," GRI Working Papers 194, Grantham Research Institute on Climate Change and the Environment.

    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. 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.
    2. Matthew A. Cole & David J. Maddison & Liyun Zhang, 2020. "Testing the emission reduction claims of CDM projects using the Benford’s Law," Climatic Change, Springer, vol. 160(3), pages 407-426, June.
    3. Lee, Kang-Bok & Han, Sumin & Jeong, Yeasung, 2020. "COVID-19, flattening the curve, and Benford’s law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    4. Kishore Singh & Peter Best, 2020. "Implementing Benford’s Law in Continuous Monitoring Applications," Journal of Accounting and Management Information Systems, Faculty of Accounting and Management Information Systems, The Bucharest University of Economic Studies, vol. 19(2), pages 379-404, June.
    5. 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.
    6. Ronelle Burger & Canh Thien Dang & Trudy Owens, 2017. "Better performing NGOs do report more accurately: Evidence from investigating Ugandan NGO financial accounts," Discussion Papers 2017-10, University of Nottingham, CREDIT.
    7. 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.
    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. Fraas, Art & Egorenkov, Alex, 2015. "A Retrospective Study of EPA’s Air Toxics Program under the Revised Section 112 Requirements of the Clean Air Act," RFF Working Paper Series dp-15-23, Resources for the Future.
    10. Louie Rivers & Tamara Dempsey & Jade Mitchell & Carole Gibbs, 2015. "Environmental Regulation and Enforcement: Structures, Processes and the Use of Data for Fraud Detection," Journal of Environmental Assessment Policy and Management (JEAPM), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-29, December.
    11. Brice Corgnet & Roberto Hernán-González, 2011. "Don't Ask Me If You Will Not Listen: The Dilemma of Participative Decision Making," Working Papers 11-04, Chapman University, Economic Science Institute.
    12. Jeremy G. Moulton & Nicholas J. Sanders & Scott A. Wentland, 2024. "Toxic Assets: How the Housing Market Responds to Environmental Information Shocks," Land Economics, University of Wisconsin Press, vol. 100(1), pages 66-88.
    13. Bauckloh, Michael Tobias & Beyer, Victor & Klein, Christian, 2022. "Does it pay to invest in dirty industries? New insights on the shunned-stock hypothesis," CFR Working Papers 22-07, University of Cologne, Centre for Financial Research (CFR).
    14. Auffhammer, Maximilian & Carson, Richard T., 2006. "Forecasting the Path of China's CO2 Emissions: Offsetting Kyoto - and Then Some," CUDARE Working Papers 7197, University of California, Berkeley, Department of Agricultural and Resource Economics.
    15. George Judge & Laura Schechter, 2009. "Detecting Problems in Survey Data Using Benford’s Law," Journal of Human Resources, University of Wisconsin Press, vol. 44(1).
    16. Alex Hollingsworth & Ivan Rudik, 2021. "The Effect of Leaded Gasoline on Elderly Mortality: Evidence from Regulatory Exemptions," American Economic Journal: Economic Policy, American Economic Association, vol. 13(3), pages 345-373, August.
    17. J. Scott Holladay & Lawrence D. LaPlue, 2021. "Decomposing changes in establishment‐level emissions with entry and exit," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 54(3), pages 1046-1071, November.
    18. 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.
    19. Farrelly, Trisia & Tucker, Corrina, 2014. "Action research and residential waste minimisation in Palmerston North, New Zealand," Resources, Conservation & Recycling, Elsevier, vol. 91(C), pages 11-26.
    20. 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.

    More about this item

    Keywords

    Benfords Law; data quality; fraud detection;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:cep:cepdps:dp1291. 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: the person in charge (email available below). General contact details of provider: https://cep.lse.ac.uk/_new/publications/discussion-papers/ .

    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.