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Topic · Statistics and Probability

Benford’s Law and Fraud Detection

Benford’s Law and Fraud Detection is a research topic within Statistics and Probability. Science Explorer counts 3.4k research works in it since 1950. 10.7% of them reached the world's top 10% most cited for their field and year.

This cluster of papers focuses on the statistical analysis and applications of Benford's Law, a phenomenon that describes the frequency distribution of leading digits in many real-life sets of numerical data. The papers cover topics such as fraud detection, election irregularities, data authenticity, financial data analysis, forensic accounting, and the application of Benford's Law to monitor and assess the quality of COVID-19 reporting.

  • Benford's Law
  • fraud detection
  • election irregularities
  • data authenticity
  • financial data
  • statistical analysis
  • forensic accounting
  • COVID-19 reporting
  • accounting data manipulation
  • data quality
Research works
3.4k
fractional, since 1950
In the world top 10%
359
per year above
Top-10% rate
10.7%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+41%
the tick is no change
Largest producer
United States
35% of the 10 largest, 2022-now
Benford’s Law and Fraud Detection

Which countries lead Benford’s Law and Fraud Detection research?

By volume, the United States and India publish the most (224 and 88 works in 2022-now).

By volume, 2022-now

  1. 1 United States 224 works
  2. 2 India 88 works
  3. 3 China 64 works
  4. 4 Türkiye 46 works
  5. 5 Brazil 44 works
  6. 6 Germany 43 works
  7. 7 United Kingdom 39 works
  8. 8 Russia 36 works
  9. 9 France 25 works
  10. 10 Italy 25 works

How concentrated that is

The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.

United States: 35.4%India: 13.8%China: 10.1%Türkiye: 7.3%6 others listed: 33.5%35%largest
United States224 · 35.4%India88 · 13.8%China64 · 10.1%Türkiye46 · 7.3%6 others listed213 · 33.5%

Shares of the rows listed above, not of the whole node.

Which institutions lead Benford’s Law and Fraud Detection research?

By volume in 2022-now, Russian Academy of Sciences publishes the most Benford’s Law and Fraud Detection research, followed by Centre National de la Recherche Scientifique and Eckerd College.

By volume, 2022-now

  1. 1 Russian Academy of SciencesRussia 9 works
  2. 2 Centre National de la Recherche ScientifiqueFrance 8 works
  3. 3 Eckerd CollegeUnited States 7 works
  4. 4 Universidad de San Carlos de GuatemalaGuatemala 6 works
  5. 5 Kazan Federal UniversityRussia 6 works
  6. 6 Universidade de São PauloBrazil 6 works
  7. 7 Universidad San CarlosParaguay 6 works
  8. 8 CHDI FoundationUnited States 5 works
  9. 9 NEC (China)China 5 works
  10. 10 University of California, Los AngelesUnited States 5 works

Who are the leading researchers in Benford’s Law and Fraud Detection?

The most-cited researchers publishing on Benford’s Law and Fraud Detection include Jürgen Schmidhuber, Edward H. Witten and Bradley Efron.

  1. 1 Jürgen Schmidhuber Switzerland 188k citations
  2. 2 Edward H. Witten United States 174k citations
  3. 3 Bradley Efron United States 140k citations
  4. 4 Claudiu Herţeliu Romania 135k citations
  5. 5 Marcel Ausloos Belgium 132k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Benford’s Law and Fraud Detection?

The most cited paper in Benford’s Law and Fraud Detection is "Computing Machinery and Intelligence (1950)" (Alan Mathison Turing, 2004), with 6,187 citations. Next come "Optical image encryption based on input plane and Fourier plane random encoding" (2,675) and "How to construct random functions" (2,133).

Most cited papers
#PaperReleasedCitations
1 Computing Machinery and Intelligence (1950) Alan Mathison Turing Book chapter 9 Sep 2004 6,187
2 Optical image encryption based on input plane and Fourier plane random encoding Philippe Réfrégier, Bahram Javidi · Optics Letters Apr 1995 2,675
3 How to construct random functions Oded Goldreich, Shafi Goldwasser, Silvio Micali · Journal of the ACM Open access 10 Aug 1986 2,133
4 How to Generate Cryptographically Strong Sequences of Pseudorandom Bits Manuel Blum, Silvio Micali · SIAM Journal on Computing Nov 1984 1,332
5 The definition of random sequences Per Martin-Löf · Information and Control Open access Dec 1966 1,237
All 100 most cited papers, with filters and sorting

Where is Benford’s Law and Fraud Detection research done?

The largest centres of Benford’s Law and Fraud Detection research in 2022-now are Beijing (China), New York (United States), Moscow (Russia) and Washington D.C. (United States).

Largest cities, 2022-now

  1. 1 BeijingChina 19 works
  2. 2 New YorkUnited States 14 works
  3. 3 MoscowRussia 14 works
  4. 4 Washington D.C.United States 12 works
  5. 5 LondonUnited Kingdom 10 works
  6. 6 IstanbulTürkiye 9 works
  7. 7 Los AngelesUnited States 9 works
  8. 8 ParisFrance 9 works
  9. 9 TokyoJapan 8 works
  10. 10 AnkaraTürkiye 8 works
See Benford’s Law and Fraud Detection on the map

Is Benford’s Law and Fraud Detection research growing?

Output in 2022-2025 was 41% higher than in 2018-2021, peaking in 2026. The fastest-growing topics are Benford’s Law and Fraud Detection.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Benford’s Law and Fraud Detection as a percentage of every work published that year, 0.0027% in 2024.

still counting0.0025%0.0050%0.0075%Benford’s Law and Fraud Detection0.0049% in 202519801990200020102020

Fractional works of Benford’s Law and Fraud Detection over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Benford’s Law and Fraud Detection11.6% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

Which topics inside it are moving

Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.

Discussion

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