The following are some Benford resources that I am posting here for the benefit of the community. This is a work in progress; in particular, it is meant to help some authors share data sets. For comments / questions / additions to this site, email sjm1 AT williams.edu.

• Theory and Application of Benford's Law (edited by S. J. Miller)
  • Homepage of book: https://web.williams.edu/Mathematics/sjmiller/public_html/benford/index.htm
  • My papers and talks are available on my homepage: https://web.williams.edu/Mathematics/sjmiller/public_html/
    • Benford's law, values of L-functions and the 3x+1 problem (with Alex Kontorovich), Acta Arithmetica. (120 (2005), no. 3, 269--297).  pdf.
    • Benford's Law applied to hydrology data - results and relevance to other geophysical data (with Mark Nigrini), Mathematical Geology (39 (2007), no. 5, 469--490).  pdf
    • The Modulo 1 Central Limit Theorem and Benford's Law for Products (with Mark Nigrini), International Journal of Algebra. (2 (2008), no. 3, 119--130). pdf
    • Order statistics and Benford's law (with Mark Nigrini), International Journal of Mathematics and Mathematical Sciences (Volume 2008 (2008), Article ID 382948, 19 pages, doi:10.1155/2008/382948)  pdf
    • Chains of distributions, hierarchical Bayesian models and Benford's Law (with D. Jang, J. U. Kang, A. Kruckman and J. Kudo), Journal of Algebra, Number Theory: Advances and Applications. (volume 1, number 1 (March 2009), 37--60)   pdf
    • Data diagnostics using second order tests of Benford's Law (with Mark Nigrini), Auditing: A Journal of Practice and Theory.  (28 (2009), no. 2, 305--324. doi: 10.2308/aud.2009.28.2.305)  MSWord file
    • Benford Behavior of Zeckendorf Decompositions (with A. Best, P. Dynes, X. Edelsbrunner, B. McDonald, C. Turnage-Butterbaugh and M. Weinstein),  Fibonacci Quarterly. (52 (2014), no. 5, 35--46)  pdf
    • Equipartitions and a Distribution for Numbers: A Statistical Model for Benford's Law (with Joe Iafrate and Frederick Strauch), Physical Review E (91 (2015), no. 6, 062138 (6 pages))   pdf
    • The Weibull distribution and Benford's Law (with Victoria Cuff and Allie Lewis), Involve (8-5 (2015), 859--874. DOI 10.2140/involve.2015.8.859).  pdf
    • Benford Behavior of Generalized Zeckendorf Decompositions  (with A. Best, P. Dynes, X. Edelsbrunner, B. McDonald C. Turnage-Butterbaugh and M. Weinstein), Combinatorial and Additive Number Theory II: CANT, New York, NY, USA, 2015 and 2016, Springer, New York, 2017. pdf
    • Benford's Law and Continuous Dependent Random Variables (with Thealexa Becker, David Burt, Taylor C. Corcoran, Alec Greaves-Tunnell, Joseph R. Iafrate, Joy Jing, Jaclyn D. Porfilio, Ryan Ronan, Jirapat Samranvedhya, Blaine Talbut and Frederick W. Strauch), (388 (2018), 350--381) Annals of Physics. pdf.
    • Benford's Law Beyond Independence: Tracking Benford Behavior in Copula Models (with Becky Durst). Involve (19 (2020), no. 7, 1193-1218) pdf
    •  The Inverse Gamma Distribution and Benford's Law (with Rebecca F. Durst, Chi Huynh, Adam Lott, Eyvindur A. Palsson, Wouter Touw, and Gert Vriend), The PUMP Journal of Undergraduate Research (3 (2020), 95-109).   pdf
    • Recurrence Relations and Benford's Law (with Madeleine Farris, Noal Luntzlara, Lily Shao and Mengxi Lang), submitted to Statistical Methods and Applications.  pdf
    • Note by Alex Kossovsky and Steven J. Miller on Benford's law and the 2020 presidential election
    • TALKS:  Benford's law, or, Why the IRS cares about Number Theory.
      • Brown University: https://www.youtube.com/watch?v=rCsavxidCZ4 (slides here, technical talk:  Benford good, Products, Chains)
      • Carnegie Mellon:  http://youtu.be/z2Rx1w5UDnk (slides here, technical talk: L-fns, 3x+1, Decompositions)
      • Williams College: http://youtu.be/JmBXZCbbwas (slides here, colloquium talk to all faculty, more general than the Brown / Carnegie Mellon)
      • More here: https://web.williams.edu/Mathematics/sjmiller/public_html/math/talks/talks.html

       

• Data sets from Alex Kossovsky
  • Time in seconds between the 19,451 Global Earthquakes during the year 2012.
  • The populations in USA of all its Cities and Towns in 2009 - 19509 Population Centers in total.
  • Canford PLC Price List, Oct 2013 - 15,194 items for sale (in catalog).
  • 48,111 Star Distances from the Solar System, NASA.
  • Biological Genetic Measure - DNA V230 Bone Marrow - 91,223 data points.
  • Oklahoma State 986,962 positive expenses below $1 million in the year 2011.
  • The list of 92 Atomic Weights in the Periodic Table, from Hydrogen to (and including) Uranium.
  • The list of Electric Conductivity Values (in 1,000,000 Siemens/meter) for 24 Common Metals.