IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v144y2021ics096007792100093x.html
   My bibliography  Save this article

Data validity and statistical conformity with Benford’s Law

Author

Listed:
  • Cerqueti, Roy
  • Maggi, Mario

Abstract

Benford’s Law is a statistical regularity of a large number of datasets; assessing the compliance of a large dataset with the Benford’s Law is a theme of remarkable relevance, mainly for its practical consequences. Such a task can be faced by introducing a statistical distance concept between the empirical distribution of the data and the random variable associated with Benford’s Law. This paper deals with the problem of measuring the compliance of a random variable – which can be seen as describing the empirical distribution of a collection of data – with the Benford’s Law. It proposes a statistical methodology for detecting the critical values related to conformity/nonconformity with Benford’s Law in some well-established cases of statistical distance. The followed approach is grounded on the proper selection of a family of parametric random variables – the lognormal distribution, in our case – and of a reference statistical distance concept – mean absolute deviation. A discussion of the obtained results is carried out on the ground of the existing literature. Moreover, some open problems are also presented.

Suggested Citation

  • Cerqueti, Roy & Maggi, Mario, 2021. "Data validity and statistical conformity with Benford’s Law," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
  • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s096007792100093x
    DOI: 10.1016/j.chaos.2021.110740
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792100093X
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2021.110740?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. T. A. 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.
    2. Deckert, Joseph & Myagkov, Mikhail & Ordeshook, Peter C., 2011. "Benford's Law and the Detection of Election Fraud," Political Analysis, Cambridge University Press, vol. 19(3), pages 245-268, July.
    3. Marcel Ausloos & Rosella Castellano & Roy Cerqueti, 2016. "Regularities and Discrepancies of Credit Default Swaps: a Data Science approach through Benford's Law," Papers 1603.01103, arXiv.org.
    4. Karl-Heinz Tödter, 2009. "Benford's Law as an Indicator of Fraud in Economics," German Economic Review, Verein für Socialpolitik, vol. 10, pages 339-351, August.
    5. De Ceuster, Marc J. K. & Dhaene, Geert & Schatteman, Tom, 1998. "On the hypothesis of psychological barriers in stock markets and Benford's Law," Journal of Empirical Finance, Elsevier, vol. 5(3), pages 263-279, September.
    6. Nye John & Moul Charles, 2007. "The Political Economy of Numbers: On the Application of Benford's Law to International Macroeconomic Statistics," The B.E. Journal of Macroeconomics, De Gruyter, vol. 7(1), pages 1-14, July.
    7. 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.
    8. Ausloos, M. & Herteliu, C. & Ileanu, B., 2015. "Breakdown of Benford’s law for birth data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 736-745.
    9. 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.
    10. 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.
    11. Broniatowski, M. & Leorato, S., 2006. "An estimation method for the Neyman chi-square divergence with application to test of hypotheses," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1409-1436, July.
    12. 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.
    13. Tariq Ahmad Mir & Marcel Ausloos & Roy Cerqueti, 2014. "Benford's law predicted digit distribution of aggregated income taxes: the surprising conformity of Italian cities and regions," Papers 1410.2890, arXiv.org.
    14. Aaron D Slepkov & Kevin B Ironside & David DiBattista, 2015. "Benford’s Law: Textbook Exercises and Multiple-Choice Testbanks," PLOS ONE, Public Library of Science, vol. 10(2), pages 1-13, February.
    15. Karl‐Heinz Tödter, 2009. "Benford's Law as an Indicator of Fraud in Economics," German Economic Review, Verein für Socialpolitik, vol. 10(3), pages 339-351, August.
    16. 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.
    17. Fang, Guojun & Chen, Qihong, 2020. "Several common probability distributions obey Benford’s law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    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. 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.
    2. 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.
    3. 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).
    4. 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.
    5. 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).
    6. 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.
    7. 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.
    8. 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.
    9. Marcel Ausloos & Rosella Castellano & Roy Cerqueti, 2016. "Regularities and Discrepancies of Credit Default Swaps: a Data Science approach through Benford's Law," Papers 1603.01103, arXiv.org.
    10. 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.
    11. Tariq Ahmad Mir & Marcel Ausloos & Roy Cerqueti, 2014. "Benford's law predicted digit distribution of aggregated income taxes: the surprising conformity of Italian cities and regions," Papers 1410.2890, arXiv.org.
    12. T. A. 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.
    13. 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.
    14. 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).
    15. 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.
    16. 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.
    17. Alexandre Donizeti Alves & Horacio Hideki Yanasse & Nei Yoshihiro Soma, 2016. "An analysis of bibliometric indicators to JCR according to Benford’s law," Scientometrics, Springer;Akadémiai Kiadó, vol. 107(3), pages 1489-1499, June.
    18. Ausloos, Marcel & Jovanovic, Franck & Schinckus, Christophe, 2016. "On the “usual” misunderstandings between econophysics and finance: Some clarifications on modelling approaches and efficient market hypothesis," International Review of Financial Analysis, Elsevier, vol. 47(C), pages 7-14.
    19. Ausloos, M. & Herteliu, C. & Ileanu, B., 2015. "Breakdown of Benford’s law for birth data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 736-745.
    20. Carrera, César, 2015. "Tracking exchange rate management in Latin America," Review of Financial Economics, Elsevier, vol. 25(C), pages 35-41.

    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:144:y:2021:i:c:s096007792100093x. See general information about how to correct material in RePEc.

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

    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 hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.