Entropy Principle in Direct Derivation of Benford's Law

2009/01/20 by Oded Kafri, Kafri, Oded · 2 citations
Computer Science · Mathematics · #Benford’s Law and Fraud Detection #Computability, Logic, AI Algorithms #Data Analysis #Digital Media Forensic Detection #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Physical sciences #Statistics and Probability (physics.data-an)

paper · pdf · doi:10.48550/arxiv.0901.3047

openalex publication_date 2009/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The uneven distribution of digits in numerical data, known as Benford's law, was discovered in 1881. Since then, this law has been shown to be correct in copious numerical data relating to economics, physics and even prime numbers. Although it attracts considerable attention, there is no a priori probabilistic criterion when a data set should or should not obey the law. Here a general criterion is suggested, namely that any file of digits in the Shannon limit (namely, having maximum entropy) has a Benford's law distribution of digits.

Citations

• Note on the Frequency of Use of the Different Digits in Natural Numbers

Cited by

• Lagrangians, Renormalization, and Quantization in Prefix Coding
• Random Consolidations and Fragmentations Cycles Lead to Benford' Law

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