Benford's Law Research Articles

Benford’s Law for Data Cleaning in Big Data

With the exponential increase in data, the need to authenticate the integrity accuracy of the data also increases. Regarded as a mysterious law, Benford's Law has seen many use cases over the centuries ranging from detecting fraud in accounting to checking for GAN generated images. This First digit law has helped finding anomalies in various data across many domains. This paper summarizes what this mysterious law is and implements the same to asteroid data to check for the pattern. This law has the potential to handle the growing need for authenticity for the big data revolution. Further research on this field includes not only the implementation here on earth but also for the data being generated by satellites and telescopes in deep space!

COVID-19 DATA RELIABILITY RANKING OF COUNTRIES WITH GREY RELATIONAL ANALYSIS AND BENFORD’S LAW / Gri İlişkisel Analiz Ve Benford Yasası Yardımıyla Ülkelerin Covid-19 Veri Güvenirliği Sıralaması

The covid-19 disease has become a pandemic that spreads at an unexpected pace around the world. There are more than 450 million cases and 6 million deaths worldwide at the start of March 2022. Benford's law is a statistical technique that serves to determine whether data fraud has been committed in a data structure that uses repetitive numbers. In this study, 18 countries with more than 5 million cases worldwide were ranked using grey relational analysis with the help of Benford's law, an effective method of data fraud. 18 countries are listed separately for 2 years of data with the help of the grey relational analysis method and Benford’s analysis results. According to the results of the study, it was determined that some countries showed changes in data reliability between 2020 and 2021. It has been determined that the data of Germany, France, and the Netherlands are the most reliable.

FORENSIC ACCOUNTING: THE USE OF BENFORD'S LAW TO EVALUATE INDICATIONS OF FRAUD

The sudden decline in profit at PII Corporation is an important issue that requires further discussion. This study aims to evince whether there are indications of fraud in the preparation of PII Corporation's profit and loss statements, which can be proven through Benford's Law. This study uses the Binomial Test, Sign Test, and Chi-Squared Test methods to test the alignment of data with Benford's Law. The sample in this study consists of PII Corporation's 2013-2019 profit and loss reports. The results have shown that 25 out of 28 tests expressed no indication of fraud, while 3 tests have indicated fraud, detected in the fourth digit of the company's expenses, in the first 2 digits of its expenses, and in the last 2 digits of other incomes and costs. After further investigation, it was found that the significant decrease in profit occurred because the company had paid interest on bonds with quite large values in 2019, so the statistical test results were considered false-positive. The recommendation that can be given is that PII Corporation regulates the imposition of the bond coupon value in stages.

Benford’s Law and County-Level Votes in US Presidential Elections

In the aftermath of the 2020 US Presidential election, the argument was raised that because Joseph Biden's county vote totals in Pennsylvania do not follow Benford's law but Donald Trump's do, Democratic voter fraud occurred in Pennsylvania. We use US recent presidential election data to investigate whether this argument holds water. We use statistical tools such as chi squared goodness-of-fit tests and hypothesis tests for proportions, which are commonly used in Benford settings.

Benford's law, small business financial reporting, and survival

Benford's law states that in collections of numbers, the leading digit is likely to be small. Drawing on this law, which is a widely used tool in forensic accounting, we ask whether small and medium‐sized enterprises (SMEs) that violate Benford's law on the reporting of key accounting items are more likely to fail. Using a sample of 220,583 Portuguese SMEs (2010–2018), those companies violating Benford's law in reporting cash had the highest odds of failure, followed by net income, current liabilities, assets, and sales. The findings indicate that myopic strategic manipulation in financial reporting may lead to SME failure.

Benford's law for integrity tests of high-volume databases: a case study of internal audit in a state-owned enterprise

PurposeThe technical feasibility of using Benford's law to assist internal auditors in reviewing the integrity of high-volume data sets is analysed. This study explores whether Benford's distribution applies to the set of numbers represented by the quantity of records (size) that comprise the different tables that make up a state-owned enterprise's (SOE) enterprise resource planning (ERP) relational database. The use of Benford's law streamlines the search for possible abnormalities within the ERP system's data set, increasing the ability of the internal audit functions (IAFs) to detect anomalies within the database. In the SOEs of emerging economies, where groups compete for power and resources, internal auditors are better off employing analytical tests to discharge their duties without getting involved in power struggles.Design/methodology/approachRecords of eight databases of an SOE in Argentina are used to analyse the number of records of each table in periods of three to 12 years. The case develops step-by-step Benford's law application to test each ERP module records using Chi-squared (χ²) and mean absolute deviation (MAD) goodness-of-fit tests.FindingsBenford's law is an adequate tool for performing integrity tests of high-volume databases. A minimum of 350 tables within each database are required for the MAD test to be effective; this threshold is higher than the 67 reported by earlier researches. Robust results are obtained for the complete ERP system and for large modules; modules with less than 350 tables show low conformity with Benford's law.Research limitations/implicationsThis study is not about detecting fraud; it aims to help internal auditors red flag databases that will need further attention, making the most out of available limited resources in SOEs. The contribution is a simple, cheap and useful quantitative tool that can be employed by internal auditors in emerging economies to perform the first scan of the data contained in relational databases.Practical implicationsThis paper provides a tool to test whether large amounts of data behave as expected, and if not, they can be pinpointed for future investigation. It offers tests and explanations on the tool's application so that internal auditors of SOEs in emerging economies can use it, particularly those that face divergent expectations from antagonist powerful interest groups.Originality/valueThis study demonstrates that even in the context of limited information technology tools available for internal auditors, there are simple and inexpensive tests to review the integrity of high-volume databases. It also extends the literature on high-volume database integrity tests and our knowledge of the IAF in Civil law countries, particularly emerging economies in Latin America.

Dirichlet, Sierpiński, and Benford

Sixty years ago, Sierpiński observed that for any positive integers A and B, and any g≥2, there are infinitely many primes whose base g-expansion begins with the digits of A and ends with those of B. Sierpiński's short proof rests on the prime number theorem for arithmetic progressions (PNT for APs). We explain how his result can be viewed as a natural intermediary between Dirichlet's theorem on primes in progressions and the PNT for APs. In addition to being of pedagogical interest, this perspective quickly yields a generalization of Sierpiński's result where the initial and terminal digits of p are prescribed in two coprime bases simultaneously; moreover, the proportion (Dirichlet density) of the corresponding primes is determined explicitly. The same quasielementary method shows that the arithmetic functions φ(n), σ(n), and d(n) obey “Benford's law” in a suitable sense.

Is conditional conservatism a source of deviations of financial statements from Benford's Law?

PurposeIn this paper, the authors examine the association between conditional conservatism and deviations of the first digits of financial statement items from what are expected by Benford's Law.Design/methodology/approachThis research uses data of companies listed on the London Stock Exchange. The authors measure deviations of first digits from Benford's Law following Amiram et al. (2015) and firm-year conditional conservatism following previous studies (Basu, 1997; Khan and Watts, 2009; García Lara et al., 2016). The authors use multiple regressions to provide evidence for their hypothesis.FindingsThe results show that conditional conservatism is positively associated with deviations from Benford's Law. The findings are robust across different measures of deviations and conditional conservatism. Also, the authors find that the relationship between deviations from Benford's Law and conditional conservatism is more pronounced for firms with debt issuance, and for leveraged firms facing financial distress. Next, the authors’ analyses confirm previous evidence by showing that the first digits of financial statement items of UK listed companies conform to Benford's Law at the firm-specific level and the market level, and deviations of income statements are larger than those of balance sheets and cash flow statements.Research limitations/implicationsThe research makes significant contributions to the literature. First, this is the first study that provides empirical evidence suggesting that conditional conservatism may be a source of deviations from Benford’s Law. Second, the authors provide evidence confirming previous US findings (e.g. Amiram et al., 2015) showing that the distributions of first digits of financial statement items of UK listed companies also conform to Benford's Law.Practical implicationsThe authors’ findings have implications for auditors. Auditors should be aware of “false positive” for material misstatements when using Benford's Law as a risk assessment procedure. While both conditional conservatism and earnings management are related to deviations from Benford's Law, conservatism-related biases could indicate less audit risks.Originality/valueThe authors provide new and original evidence suggesting that conditional conservatism is related to deviations from Benford's Law.

A Novel Image Splicing Detection Algorithm Based on Generalized and Traditional Benford’s Law

Due to the ease of access to platforms that can be used by forgers to tamper digital documents, providing automatic tools for identifying forged images is now a hot research field in image processing. This paper presents a novel forgery detection algorithm based on variants of Benford's law. In the proposed method, Mean Absolute Deviation (MAD) feature is extracted using traditional Benford's law. Also, generalized Benford's law is used for mantissa distribution feature vector. In addition to Benford's law-based features, other statistical features are used to construct the final feature vector. Finally, support vector machine (SVM) with three different kernel functions is used to classify original and forged images. The method has been tested on two common image datasets (CASIA V1.0 and V2.0). The experimental results show that 0.27% and 0.21% improvements on CASIA V1.0 and CASIA V2.0 datasets were achieved, respectively in detection accuracy by the proposed method in comparison to best state-of-the-art methods. The proposed efficient algorithm has a simple implementation. Moreover, on the basis of Benford’s law rich features are extracted from images so that classification process is efficiently performed by a simple SVM classifier in a short time.

Benford's Law: What Does it Say on Adversarial Images?

Convolutional neural networks (CNNs) are fragile to small perturbations in the input images. These networks are thus prone to malicious attacks that perturb the inputs to force a misclassification. Such slightly manipulated images aimed at deceiving the classifier are known as adversarial images. In this work, we investigate statistical differences between natural images and adversarial ones. More precisely, we show that employing a proper image transformation and for a class of adversarial attacks, the distribution of the leading digit of the pixels in adversarial images deviates from Benford's law. The stronger the attack, the more distant the resulting distribution is from Benford's law. Our analysis provides a detailed investigation of this new approach that can serve as a basis for alternative adversarial example detection methods that do not need to modify the original CNN classifier neither work on the raw high-dimensional pixels as features to defend against attacks.

Integrated application of Benford's Law tests to detect corporate fraud

The paper assesses the possibility of an integrated application of tests based on a statistical tool for detecting data distortions, known as Benford's Law, to detect corporate fraud. The approach has been applied as part of a forensic examination of a construction company's bona fides as a borrower. Implementation of the method allowed a fraudulent scheme associated with high tax risk activities to be exposed, while significantly reducing the workload of the audit. The effectiveness of an integrated application of Benford's Law tests has been confirmed.

Detecting Financial Fraud using Two Types of Benford Factors: Evidence from China

Financial fraud of listed companies can lead to anomalies in the distribution of financial data, which can be detected by Benford's Law. This study takes financial data of Chinese listed companies to construct two types of Benford factors for detecting financial fraud. The empirical results show that as the deviation of financial data distribution from Benford's law increases, the probability of financial fraud increases significantly. Furthermore, compared with rustically using traditional financial indicators, the addition of the Benford factors can effectively reduce the Type I or Type II error using the logistic regression model. Finally, we show that the identification indicators selected in this study contributes to the detection of financial fraud with the help of digital distribution laws.

Injuries and fatalities in Colombian mining emergencies (2005-2018): a retrospective ecological study.

Mining injuries have decreased in a number of developed countries in recent decades. Although mining has become a very important sector of Colombia's economy, no analyses of mining injuries and fatalities have been conducted. This study describes the occurrence of mining emergencies in Colombia between 2005 and 2018 and their principal characteristics. This retrospective ecological study analyzed mining emergencies registered by the National Mining Agency between 2005 and 2018. The study described the place, event type, legal status, mine type, extracted mineral, and number of injuries and fatalities. Benford's law was used to explore data quality. A total of 1,235 emergencies occurred, with 751 injured workers and 1,364 fatalities. The majority of emergencies were from collapses, polluted air, and explosions, most of which occurred in coal (77.41%), gold (18.06%), and emerald (1.38%) mines. Many emergencies occurred in illegal mines (27.21%), most of which were for gold, construction materials, emeralds, and coal. Illegal mines had a higher relative proportion of injuries and fatalities than legal mines (p < 0.05). Mining disasters are likely to be underreported given that Benford's Law was not satisfied. As mining increases in Colombia, so are mining emergencies, injuries, and fatalities. This is the first full description of mining emergencies in Colombia based on the few available data.

The forensics of fraud: Evidence from the 2018 Brazilian presidential election

ObjectiveThis paper studies the integrity of the vote counting system in Brazil. MethodWe analyze data from the Superior Electoral Court (TSE) for the 2018 Brazilian presidential election to assess suspicious vote count patterns deploying five techniques commonly used to detect fraud: a) the second-digit Benford's law test; b) the last digit mean; c) frequency analysis of last digits 0 and 5; d) correlation between the percentage of votes and the turnout rate; and e) resampled Kernel density of the proportion of votes. ResultsThe results show that the second-digit distributions for the three most voted candidates – Jair Messias Bolsonaro (PSL), Fernando Haddad (PT), and Ciro Gomes (PDT) – conform to Benford's law. We also find that last digit means and last digit frequency are within normal parameters, indicating no irregularities. Similarly, the fingerprint plot indicates a correlation coefficient that is consistent with the theoretical expectation of a fair election. The resampled Kernel density suggests that the vote count was performed without statistically significant distortions. These results are robust at different levels of data aggregation (polling station and municipality). ConclusionThe joint application of digit-focused tests, regression-based techniques, and patterns in the distribution of vote-shares provide a more reliable method for detecting anomalous cases. Relying on this unified framework, we find no evidence of electoral fraud in the 2018 Brazilian presidential election. These results advance our current understanding of statistical forensics tools and may be easily replicated to examine electoral integrity in other countries.

Pore Properties, Power Laws and Benford's Law

Pore Properties, Power Laws and Benford's Law

The awareness of judicial accounting techniques towards the expectations of the external auditor in detecting fraud and its impact on the performance

Judicial accounting outputs are reports that guide judges in conflicting parties over financial litigation, supporting judicial cases, and settling and resolving disputes. As a discipline, judicial accounting applies the science and knowledge of accounting, such as finance, taxation and auditing in the form in which the judicial accountant can provide his expert opinion, through the availability of a set of techniques in the field of fraud investigation and support of lawsuits, to investigate the allegations alleged by the relevant parties, especially those allegations related to the existence of fraud, as the objective of the judicial accountant will depend on the purpose of his assignment, including investigating the presence of fraud. The external auditor's reliance on the sampling method when checking financial disclosure and his lack of responsibility for detecting fraud highlights the importance of judicial accounting in detecting fraud by employing a set of techniques, to assist him in detecting fraud. The achievement of its objectives by the judicial accountant also requires set of characteristics such as education, training, diverse experience in the field of accounting, auditing and law, oral and written communication skills, and the ability to work in a team environment. Judicial accounting is based on a range of techniques, for instance, including Benford's law, computer-based audit tools, data mining and analysis to show the role of judicial accounting techniques in the judicial accountant’s awareness of his duties towards the external auditor in detecting fraud and its impact on developing his performance.

Application of Benford's law in detecting fraudulent activities in a company

В статье исследуются способы выявления мошенничества с финансовой отчетностью, в том числе с помощью закона Бенфорда, приводятся точки зрения российских экономистов на применение данного метода на практике.

Financial reporting quality of private and public banks in India

The present study compares the earnings management practices amongst the Indian private and public sector banks using the second digit test, one of the primary Benford law tests. The sample consists of data on five variables: interest income, other income, interest expenses, deposits, and loans and advances from 14 private and 17 public sector banks for Q1 2005-Q4 2018. Deposit turns out to be the most misreported financial figure for the private banks while public sector banks misrepresented loans and advances the most. Overall, the public sector banks seem to be more into rounding up behaviour as compared to the private banks. We also explored possible linkages between financial manipulations and a CEO's tenure approaching its completion and observed evidence in support of this argument.

Benford's Law Test Method in Tax Audit Planning

The purpose of this research is to test whether the Benford’s Law test method can be used in tax audit planning. This research uses data on tax invoices of periodic VAT Tax Return registered in local tax office. The research was carried out by going through the identification and extraction stages of the first and second digits. The results show that Benford's Law can be used as an alternative method to indicate an improper periodic tax invoice. In addition, Benford's Law can also provide an assessment of which sectors and areas have indications of improper periodic tax invoice compared to other sectors and areas. Indications from this assessment can be used as a focus in planning tax invoice audit.

The Implementation of Benford's Law to Detect Indications of Corruption Patterns in Government Institutions

Disclosure of corruption cases requires a collaboration of experts in law, accounting, and auditing. In Indonesia's context, corruption patterns in government institutions can be identified based on the types of expenditure and the timing of cash disbursements. This study aims to reveal the indications and patterns of corruption in Indonesian government institutions. This study uses data on cash disbursements to detect indications and patterns of corruption. The first-digit, second-digits and first-two-digits digital analysis methods based on Benford's law were employed to analyze the data. This study found differences in cash disbursement transactions data value and Benford's law value. Furthermore, this study also discovers that corruption in government institutions follows a pattern in which corruptions often occur in the procurement of goods/services, purchases of food and beverage, and miscellaneous payments. The indications of corruption transpire throughout the year and show an increase at the end of the year (i.e., October to December), suggesting a 'year-end rush' and a phenomenon of 'hurry-up spending' in government institutions. Another pattern is related to digit groups of 30, 50, 60, and 90 committing corruption through cash disbursement transactions deliberately.