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Robust inference under Benford's law
Lucio Barabesi, Andrea Cerioli, Andrea Cerasa, Domenico Perrotta
https://arxiv.org/abs/2507.08650 https://

Robust inference under Benford's law
We address the task of identifying anomalous observations by analyzing digits under the lens of Benford's law. Motivated by the crucial objective of providing reliable statistical analysis of customs declarations, we answer one major and still open question: How can we detect the behavior of operators who are aware of the prevalence of the Benford's pattern in the digits of regular observations and try to manipulate their data in such a way that the same pattern also holds after data fabricatio…

How much is too much? Measuring divergence from Benford's Law with the Equivalent Contamination Proportion (ECP)
Manuel Cano-Rodriguez
https://arxiv.org/abs/2506.09915

How much is too much? Measuring divergence from Benford's Law with the Equivalent Contamination Proportion (ECP)
Conformity with Benford's Law is widely used to detect irregularities in numerical datasets, particularly in accounting, finance, and economics. However, the statistical tools commonly used for this purpose (such as Chi-squared, MAD, or KS) suffer from three key limitations: sensitivity to sample size, lack of interpretability of their scale, and the absence of a common metric that allows for comparison across different statistics. This paper introduces the Equivalent Contamination Proportion (…

Benford's Curse: Tracing Digit Bias to Numerical Hallucination in LLMs
Jiandong Shao, Yao Lu, Jianfei Yang
https://arxiv.org/abs/2506.01734 https://

Benford's Curse: Tracing Digit Bias to Numerical Hallucination in LLMs
Large Language Models (LLMs) exhibit impressive performance on complex reasoning tasks, yet they frequently fail on basic numerical problems, producing incorrect outputs. Inspired by Benford's Law -- a statistical pattern where lower digits occur more frequently as leading digits -- we hypothesize that the long-tailed digit distributions in web-collected corpora may be learned by LLMs during pretraining, leading to biased numerical generation. To investigate the hypothesis, we first examine whe…