• Language and Information
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• v.14 no.1
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• pp.145-163
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• 2010

This paper aims to propose that Benford's Law, non-uniform distribution of the leading digits in lists of numbers from many real-life sources, also appears in linguistic texts. The first digits in the frequency lists of morphemes from Sejong Morphologically Analyzed Corpora represent non-uniform distribution following Benford's Law, but showing complexity of numerical sources from complex systems like earthquakes. Benford's Law in texts is a principle reflecting regular distribution of low-frequency linguistic types, called LNRE(large number of rare events), and governing texts, corpora, or sample texts relatively independent of text sizes and the number of types. Although texts share a similar distribution pattern by Benford's Law, we can investigate non-uniform distribution slightly varied from text to text that provides useful applications to evaluate randomness of texts distribution focused on low-frequency types.

• The Journal of Industrial Distribution & Business
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• v.6 no.2
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• pp.13-16
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• 2015

Purpose - Benford's Law is a simple and effective auditor tool that detects fraud. This paper's purpose is to audit the efficiency of Benford's law, which uses a set of strange observations, certain numbers repeated over other numbers in the data set. Research design, data, and methodology - Benford's law was applied in numerical analysis. We can say that in addition to reducing the duration of the audit, the capacities of the audit were more robust. Results - Sample auditse valuated the ability of auditors to prove fraud and expand the use of analytical procedures in planning the audit. Additionally, the use of the analyses as part of the computer's internal controls helped to further improve the effectiveness of internal controls and reinforce them. Conclusions - Benford analysis should be carried out as appropriate. In subsequent studies, it can also be examined as a tool to reveal doubtful accounts. Numerical analysis of the data and a computer are necessary. Programs for data analysis in various applications such as auditing (SAS) and (ACL) and (Case Ware) and (IDEA) are available.

• The Korean Journal of Applied Statistics
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• v.22 no.3
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• pp.553-568
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• 2009

Using the information about the frequency of occurrence of numbers in WWW, we can find properties of the array of numbers and validate whether this array satisfies the several laws(Power law, Zipf's law, Benford's law).

• Proceedings of the National Institute of Ecology of the Republic of Korea
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• v.5 no.2
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• pp.43-49
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• 2024

Ecological monitoring provides indispensable data for biodiversity conservation and sustainable resource management. However, the complexity and variability inherent in ecological monitoring data necessitate robust verification processes to ensure data integrity. This study employed Benford's Law, a statistical principle traditionally used in fields such as finance and health sciences, to evaluate the authenticity of ecological monitoring data related to the abundance of migratory bird species across various locations in South Korea. Benford's Law anticipates a specific logarithmic distribution of leading digits in naturally occurring numerical datasets. Our investigation involved two stages of analysis: a first-order analysis considering the leading digit and a second-order analysis examining the first two digits of bird population counts. While the first-order analysis displayed moderate conformity to Benford's Law that suggested overall data integrity, the second-order analysis revealed more pronounced deviations, indicating potential inconsistencies or inaccuracies in certain subsets of the data. Although our data did not perfectly align with Benford's Law, these deviations underscore the complex nature of ecological research, which is influenced by a multitude of environmental, methodological, and human factors.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.1055-1075
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• 2010

In presented paper there were studied some properties of Benford's law. The existence of this law in not necessary large sets of numbers is a very interesting example that can show how the complex phenomena can appear in the positional number systems. Such systems seem to be very simple and intuitive and help us proceed with numbers. However, their simplicity in the case of usage in our lifetime is not necessary connected with the simplicity in the case of laws that govern them. Even if this laws indicate the existence of self-similar properties.

• The Korean Journal of Applied Statistics
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• v.22 no.5
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• pp.1103-1113
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• 2009

We know that the first digits sequence of fibonacci numbers obey Benford's law. For the sequence in which the first two numbers are the arbitrary integers and the recurrence relation $a_{n+2}=a_{n+1}+a_n$ is satisfied, we can find that the first digits sequence of this sequence obey Benford's law. Also, we can find the stucture of the first digits sequence of this sequence with the exploratory data analysis tools.

• Journal of the Institute of Electronics and Information Engineers
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• v.51 no.5
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• pp.160-167
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• 2014

This paper presents a spliced color image detection method using Benford' Law and color difference. For a suspicious image, after color conversion, the discrete wavelet transform and the discrete cosine transform are performed. We extract the difference between the ideal Benford distribution and the empirical Benford distribution of the suspicious image as features. The difference between Benford distributions for each color component were also used as features. Our method shows superior splicing detection performance using only 13 features. After training the extracted feature vector using SVM classifier, we determine whether the presence of the image splicing forgery. Experimental results show that the proposed method outperforms the existing methods with smaller number of features in terms of splicing detection accuracy.

• Proceedings of the Korea Water Resources Association Conference
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• 2023.05a
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• pp.102-102
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• 2023

벤포드 법칙(Benford's Law)은 실생활에서 관찰되는 수치 데이터를 첫 자리 숫자에 따라 분류할 때 첫 자리의 숫자가 커질수록 그 분포가 점차 감소되는 현상을 말한다. 이러한 벤포드 법칙은 일반식으로 도출하여 다양한 자릿수로 확장하여 적용할 수 있는 연구결과가 제시되었으며, 회계학, 사회과학, 물리학, 컴퓨터과학, 생물학 등 다방면의 수치 자료에서 그 유효성이 확인되고 있다. 자릿수의 관찰빈도를 분석하는 것만으로 많은 양의 실생활 데이터에서 빠르고 쉽게 데이터 조작여부를 탐지하거나 1차적인 데이터 품질검사에 효과적으로 활용되고 있다. 본 연구에서는 다학제적 연구의 측면에서 수학·물리적 법칙인 벤포드 법칙을 일유량 등 다양한 수문학 측정자료에 적용하여 그 적용가능성을 확인하고 자료의 불균질성과 신뢰성을 빠르게 탐지할 수 있는 방법론을 제시하고자 한다. 수문자료는 공인심의를 통해 자료의 신뢰도를 확보하고 있으나 확정·배포까지 약 2년이 소요되어 활용기간 단축에 대한 사용자 요구가 지속되고 있는 실정이다. 따라서 본 연구에서는 분석대상 데이터의 자릿수 관찰빈도가 벤포드 법칙에 의한 예상자릿수 빈도를 따르는지 여부에 대한 가설을 설정하고 카이제곱 검정 또는 Kolmogorov-Smirnov(K-S) 검정 등을 통해 적합도에 대한 통계적 유의미함을 분석함으로써 대략적으로나마 빠르고 쉽게 측정자료의 신뢰성을 판단할 수 있다. 본 연구는 다양한 학문과의 결합을 통한 새로운 접근을 시도함으로써 빅데이터 시대에 효과적으로 수자원의 개발, 관리 및 운영의 의사결정을 하는데 도움이 될 수 있을 것으로 판단된다.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.3
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• pp.231-240
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• 2016

Recently, fake test data of power cables in nuclear power plants was a terrible shock to the citizens. Some cable companies manipulated the test data to make unfair profits. In addition, fake test data cases were found in military supplies. The fake test data cases focused on parts of army's tank, armored car. This paper propose a new method that can detect fake test data using known statistical methods. In addition, the method was implemented in Microsoft Excel to allow easy use. Lastly, a check sheet was proposed to check the validity of the test system of military suppliers. By detecting and checking the fake test data, it is expected that our new method will play an important role in quality assurance of military supplies.