Chapter 1: A Quick Introduction to Benford’s Law (Miller)

• Additional Reading:
  • A. Berger and T. Hill: Benford Online Bibliography.
  • F. Benford, The Law of Anomalous Numbers, Proceedings of the American Philosophical Society 78 (1938), 551--572. Available through JStor.
  • T. Hill, The first-digit phenomenon, American Scientist 86 (1996), 358--363. Available online here.
  • T. Hill, A statistical derivation of the significant-digit law Statistical Science 10 (1996), 354--363. Available online here.
  • L. M. Leemis and colleagues, Univariate Distribution Relationships. Available online here.
  • L. M. Leemis, B. W. Schmeiser and D. L. Evans, Survival Distributions Satisfying Benford's Law, The American Statistician 54 (2000), no. 4, 236--241. Available online here.
  • S. Newcomb, Note on the Frequency of Use of the Different Digits in Natural Numbers, Amer. J. Math. 4 (1881), 39--40. Available online here.
  • R. A. Raimi, The first digit problem, Amer. Math. Monthly 83 (1976), no. 7, 521--538. Available through JStor.
• Homework Problems:
  • Click here for all homework problems.
• Programs:
  • Benford Tester: Excel program to test for Benfordness.
  • In Mathematica, if you define the following function you can then use it to find the first digit: firstdigit[x_] := Floor[10^Mod[Log[10,x],1]]
• Videos:
  • Benford's Law, or: Why the IRS cares about Number Theory (this is a talk I gave in an introductory probability class at Williams College and an introductory statistics class at Brown University)

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