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Related papers: Discussion on Benford's Law and its Application

200 papers

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…

Methodology · Statistics 2025-07-14 Lucio Barabesi , Andrea Cerioli , Andrea Cerasa , Domenico Perrotta

According to Benford's Law, many data sets have a bias towards lower leading digits (about $30\%$ are $1$'s). The applications of Benford's Law vary: from detecting tax, voter and image fraud to determining the possibility of match-fixing…

This article presents a concise proof of the famous Benford's law when the distribution has a Riemann integrable probability density function and provides a criterion to judge whether a distribution obeys the law. The proof is intuitive and…

Statistics Theory · Mathematics 2024-08-07 Luohan Wang , Bo-Qiang Ma

We found that in transition arrays of complex atomic spectra, the strengths of electric-dipolar lines obey Benford's law, which means that their significant digits follow a logarithmic distribution favoring the smallest values. This…

Quantum Physics · Physics 2022-12-13 Jean-Christophe Pain

Benford's law states that the occurrence of significant digits in many data sets is not uniform but tends to follow a logarithmic distribution such that the smaller digits appear as first significant digits more frequently than the larger…

Data Analysis, Statistics and Probability · Physics 2011-11-07 Tariq Ahmad Mir

Benford's law states that in data sets from different phenomena leading digits tend to be distributed logarithmically such that the numbers beginning with smaller digits occur more often than those with larger ones. Particularly, the law is…

Physics and Society · Physics 2016-01-12 Tariq Ahmad Mir

The occurrence of digits one through nine as the leftmost nonzero digit of numbers from real world sources is often not uniformly distributed, but instead, is distributed according to a logarithmic law, known as Benford's law. Here, we…

Instrumentation and Methods for Astrophysics · Physics 2010-05-14 Lijing Shao , Bo-Qiang Ma

We show the leading digits of a variety of systems satisfying certain conditions follow Benford's Law. For each system proving this involves two main ingredients. One is a structure theorem of the limiting distribution, specific to the…

Number Theory · Mathematics 2015-06-26 Alex V. Kontorovich , Steven J. Miller

Kossovsky recently conjectured that the distribution of leading digits of a chain of probability distributions converges to Benford's law as the length of the chain grows. We prove his conjecture in many cases, and provide an interpretation…

Probability · Mathematics 2010-09-15 Dennis Jang , Jung Uk Kang , Alex Kruckman , Jun Kudo , Steven J. Miller

In many real life situations, it is observed that the first digits (i.e., $1,2,\ldots,9$) of a numerical data-set, which is expressed using decimal system, do not follow a random distribution. Instead, smaller numbers are favoured by nature…

Earth and Planetary Astrophysics · Physics 2022-06-10 Abhishek Shukla , Ankit Kumar Pandey , Anirban Pathak

The reproducibility of academic research has long been a persistent issue, contradicting one of the fundamental principles of science. What is even more concerning is the increasing number of false claims found in academic manuscripts…

Information Retrieval · Computer Science 2024-06-18 Teddy Lazebnik , Dan Gorlitsky

Benford's law is an empirical observation, first reported by Simon Newcomb in 1881 and then independently by Frank Benford in 1938: the first significant digits of numbers in large data are often distributed according to a logarithmically…

Digital Libraries · Computer Science 2018-02-13 Tariq Ahmad Mir , Marcel Ausloos

Researchers have observed that the frequencies of leading digits in many man-made and naturally occurring datasets follow a logarithmic curve, with digits that start with the number 1 accounting for $\sim 30\%$ of all numbers in the dataset…

Computation and Language · Computer Science 2022-12-22 Leo Hsu , Visar Berisha

A universal First-Letter Law (FLL) is derived and described. It predicts the percentages of first letters for words in novels. The FLL is akin to Benford's law (BL) of first digits, which predicts the percentages of first digits in a data…

Computation and Language · Computer Science 2018-08-21 Xiaoyong Yan , Seong-Gyu Yang , Beom Jun Kim , Petter Minnhagen

We show that the frequency distribution of the first significant digits of the numbers in the data sets generated from a large class of measures of quantum correlations, which are either entanglement measures, or belong to the…

Quantum Physics · Physics 2016-07-28 Titas Chanda , Tamoghna Das , Debasis Sadhukhan , Amit Kumar Pal , Aditi Sen De , Ujjwal Sen

Iafrate, Miller, and Strauch [Equipartition and a Distribution for Numbers: A Statistical Model for Benford's Law," arXiv:1503.08259] construct and test a statistical model for partitioning a conserved quantity. One consequence of their…

Data Analysis, Statistics and Probability · Physics 2016-04-20 Don S. Lemons

We study the individual digits for the absolute value of the characteristic polynomial for the Circular $\beta$-Ensemble. We show that, in the large $N$ limit, the first digits obey Benford's Law and the further digits become uniformly…

Probability · Mathematics 2023-12-19 Nedialko Bradinoff , Maurice Duits

Benford's law is often used as a support to critical decisions related to data quality or the presence of data manipulations or even fraud. However, many authors argue that conventional statistical tests will reject the null of data…

Methodology · Statistics 2022-06-16 Roy Cerqueti , Claudio Lupi

According to Benford's law, the most significant digit in many datasets is not uniformly distributed, but obeys a well defined power law distribution with smaller digits appearing more often. Among one of the myriad particle physics…

Physics and Society · Physics 2018-05-18 Aisha Dantuluri , Shantanu Desai

The goal of this note is to show that a widespread claim about Benford's Law, namely, that the range of every Benford distribution spans at least several orders of magnitude, is false. The proof is constructive and concrete examples are…

Probability · Mathematics 2020-11-30 Theodore P. Hill