A basic theory of Benford's law

DOI10.1214/11-PS175zbMath1245.60016OpenAlexW1649927443MaRDI QIDQ431507

Arno Berger, Theodore P. Hill

Publication date: 28 June 2012

Published in: Probability Surveys (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ps/1311860830

zbMATH Keywords

difference equationmixture of distributionsBenford's lawshadowinguniform distribution mod 1random probability measurebase-invariancescale-invariancesignificant digitssum-invariance

Mathematics Subject Classification ID

Related Items (20)

Quantization-unaware double JPEG compression detection ⋮ Data validity and statistical conformity with Benford's law ⋮ A characterization of Benford's law in discrete-time linear systems ⋮ Modulo 1 limit theorems for autoregressive random variables and their sums ⋮ Leading digit laws on linear Lie groups ⋮ A general framework for constructing distributions satisfying Benford’s law ⋮ Quantifying non-stationarity effects on organization of atmospheric turbulent eddy motion by Benford's law ⋮ Benford's law and continuous dependent random variables ⋮ How fast increasing powers of a continuous random variable converge to Benford's law ⋮ A characterization of Benford's law through generalized scale-invariance ⋮ A local Benford Law for a class of arithmetic sequences ⋮ A LIMIT THEOREM FOR OCCUPATION MEASURES OF LÉVY PROCESSES IN COMPACT GROUPS ⋮ Products of random variables and the first digit phenomenon ⋮ \(n\)-digit Benford converges to Benford ⋮ Leading Digits of Mersenne Numbers ⋮ Ubiquity of Benford's law and emergence of the reciprocal distribution ⋮ Benford's law and distractors in multiple choice exams ⋮ Forum on Benford's law and statistical methods for the detection of frauds ⋮ A multivariate test for detecting fraud based on Benford's law, with application to music streaming data ⋮ Benford’s Law for Mixtures

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Benford's law strikes back: no simple explanation in sight for mathematical gem
• Multidimensional dynamical systems and Benford's law
• Sequences, discrepancies and applications
• On roundoff error distributions in floating point and logarithmic arithmetic
• Extensions of Black-Scholes processes and Benford's law
• Order statistics and Benford's law
• On a law of the iterated logarithm for sums mod 1 with application to Benford's law
• The distribution of leading digits and uniform distribution mod 1
• Seventy years of Rajchman measures
• Benford's law for exponential random variables.
• A statistical derivation of the significant-digit law
• Some dynamical properties of Benford sequences
• The Multiplication Game
• Finite-state Markov Chains Obey Benford’s Law
• On the Distribution of First Significant Digits
• Benford's law, values of L-functions and the 3x+1 problem
• BENFORD'S LAW FOR THE $3x+1$ FUNCTION
• Overflow, Underflow, and Severe Loss of Significance in Floating-Point Addition and Subtraction
• The First Digit Problem
• Base-Invariance Implies Benford's Law
• An invariant-sum characterization of Benford's law
• Foundations of Modern Probability
• One-dimensional dynamical systems and Benford’s law
• On the distribution of mantissae in nonautonomous difference equations
• Newton's Method Obeys Benford's Law
• On the Probability that a Random Integer has Initial Digit A
• On the Distribution of Numbers
• Initial Digits for the Sequence of Primes
• Regular sets and conditional density: an extension of Benford's law
• BENFORD'S LAW IN POWER-LIKE DYNAMICAL SYSTEMS
• On the Equidistribution of Sums of Independent Random Variables

This page was built for publication: A basic theory of Benford's law