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Article
A Basic Theory of Benford’s Law
Probability Surveys
  • Arno Berger, University of Alberta
  • Theodore P. Hill, Georgia Institute of Technology - Main Campus
Publication Date
1-1-2011
Abstract

Drawing from a large, diverse body of work, this survey presents a comprehensive and unified introduction to the mathematics underlying the prevalent logarithmic distribution of significant digits and significands, often referred to as Benford’s Law (BL) or, in a special case, as the First Digit Law. The invariance properties that characterize BL are developed in detail. Special attention is given to the emergence of BL in a wide variety of deterministic and random processes. Though mainly expository in nature, the article also provides strengthened versions of, and simplified proofs for, many key results in the literature. Numerous intriguing problems for future research arise naturally.

Citation Information
Arno Berger and Theodore P. Hill. "A Basic Theory of Benford’s Law" Probability Surveys Vol. 8 (2011) p. 1 - 126
Available at: http://works.bepress.com/tphill/78/