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Explaining the uneven distribution of numbers in nature: the laws of Benford and Zipf

Citations

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Cited by:

  1. Ferrer i Cancho, Ramon, 2005. "Decoding least effort and scaling in signal frequency distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(1), pages 275-284.
  2. 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.
  3. Shao, Zhi-Gang & Jian-Ping Sang, & Zou, Xian-Wu & Tan, Zhi-Jie & Jin, Zhun-Zhi, 2005. "Blackmail propagation on small-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(2), pages 662-670.
  4. 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.
  5. David Giles, 2007. "Benford's law and naturally occurring prices in certain ebaY auctions," Applied Economics Letters, Taylor & Francis Journals, vol. 14(3), pages 157-161.
  6. 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.
  7. David B. Skillicorn, 2011. "Computational approaches to suspicion in adversarial settings," Information Systems Frontiers, Springer, vol. 13(1), pages 21-31, March.
  8. 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.
  9. 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.
  10. Štefančić, Hrvoje & Zlatić, Vinko, 2005. "Preferential attachment with information filtering—node degree probability distribution properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 657-670.
  11. Lasse Pröger & Paul Griesberger & Klaus Hackländer & Norbert Brunner & Manfred Kühleitner, 2021. "Benford’s Law for Telemetry Data of Wildlife," Stats, MDPI, vol. 4(4), pages 1-7, November.
  12. Barabesi, Lucio & Pratelli, Luca, 2020. "On the Generalized Benford law," Statistics & Probability Letters, Elsevier, vol. 160(C).
  13. 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.
  14. Hsiang-chi Tseng & Wei-neng Huang & Ding-wei Huang, 2017. "Modified Benford’s law for two-exponent distributions," Scientometrics, Springer;Akadémiai Kiadó, vol. 110(3), pages 1403-1413, March.
  15. 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.
  16. 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.
  17. Maurizio Marchi & Francesco Chianucci & Carlotta Ferrara & Giorgio Pontuale & Elisa Pontuale & Anastasios Mavrakis & Nathan Morrow & Fabrizio Rossi & Luca Salvati, 2018. "Sustainable Land-Use, Wildfires, and Evolving Local Contexts in a Mediterranean Country, 2000–2015," Sustainability, MDPI, vol. 10(11), pages 1-13, October.
  18. Biau, Damien, 2015. "The first-digit frequencies in data of turbulent flows," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 440(C), pages 147-154.
  19. 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).
  20. 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.
  21. Carlos Velarde & Alberto Robledo, 2017. "Rank distributions: Frequency vs. magnitude," PLOS ONE, Public Library of Science, vol. 12(10), pages 1-13, October.
  22. 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.
  23. 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.
  24. Parnes, Dror, 2022. "Banks' off-balance sheet manipulations," The Quarterly Review of Economics and Finance, Elsevier, vol. 86(C), pages 314-331.
  25. Gottwald, Georg A. & Nicol, Matthew, 2002. "On the nature of Benford's Law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 303(3), pages 387-396.
  26. 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).
  27. Phillips, J.C., 2015. "Phase transitions in the web of science," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 173-177.
  28. 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).
  29. Egghe, L., 2013. "The functional relation between the impact factor and the uncitedness factor revisited," Journal of Informetrics, Elsevier, vol. 7(1), pages 183-189.
  30. 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.
  31. Dorogovtsev, S.N. & Mendes, J.F.F. & Oliveira, J.G., 2006. "Frequency of occurrence of numbers in the World Wide Web," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(2), pages 548-556.
  32. Yan, Xiaoyong & Yang, Seong-Gyu & Kim, Beom Jun & Minnhagen, Petter, 2018. "Benford’s law and first letter of words," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 305-315.
  33. Jaroslav Petráš & Marek Pavlík & Ján Zbojovský & Ardian Hyseni & Jozef Dudiak, 2023. "Benford’s Law in Electric Distribution Network," Mathematics, MDPI, vol. 11(18), pages 1-27, September.
  34. Tariq Ahmad Mir, 2012. "The leading digit distribution of the worldwide Illicit Financial Flows," Papers 1201.3432, arXiv.org, revised Nov 2012.
  35. Lee, Joanne & Judge, George G, 2008. "Identifying falsified clinical data," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt8x00h1c1, Department of Agricultural & Resource Economics, UC Berkeley.
  36. da Silva, A.J. & Floquet, S. & Santos, D.O.C. & Lima, R.F., 2020. "On the validation of the Newcomb−Benford Law and the Weibull distribution in neuromuscular transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
  37. Carlos Velarde & Alberto Robledo, 2019. "Dynamical analogues of rank distributions," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-15, February.
  38. 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.
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