2021/01/31 by Andrea Burgos, Andrés Santos · 12 citations
Mathematics · Physics and Astronomy · #Analogy #Benford’s Law and Fraud Detection #Invariance principle #Markov chain #Markov process #Markov property #Probability distribution #Random Matrices and Applications #Scale (ratio) #Scale invariance #Simple (philosophy) #Statistical Mechanics and Entropy #cond-mat.stat-mech #math.PR #physics.pop-ph #physics.soc-ph
paper · pdf · open access · doi:10.1119/10.0004957
published in American Journal of Physics 89(9), 851-861 (American Institute of Physics) · 12 pages, 10 figures; v2: substantial changes, including title and structure; v3: final version published as open access
openalex created_date 2021/04/13 · openalex publication_date 2021/08/19 · arxiv created 2021/08/20 · arxiv updated 2021/08/25 · openalex updated_date 2026/08/05
The Newcomb-Benford law, also known as the first-digit law, gives the probability distribution associated with the first digit of a dataset, so that, for example, the first significant digit has a probability of 30.1 % of being 1 and 4.58 % of being 9. This law can be extended to the second and next significant digits. This article presents an introduction to the discovery of the law, its derivation from the scale invariance property, as well as some applications and examples, are presented. Additionally, a simple model of a Markov process inspired by scale invariance is proposed. Within this model, it is proved that the probability distribution irreversibly converges to the Newcomb-Benford law, in analogy to the irreversible evolution toward equilibrium of physical systems in thermodynamics and statistical mechanics.