Search Results (25)

Background and Objectives: Healthcare payment systems face challenges such as fraud and overbilling, which often require costly and resource-intensive detection tools. In response, the utility of simple statistical tests was explored in this study as a practical alternative for identifying irregularities in dermatology service payments within the Health Insurance Institute of Slovenia (HIIS). Materials and Methods: Ten-year-old anonymized billing data from 30 dermatology providers in Slovenia (with a population of 2 million) were analyzed to evaluate the effectiveness of the proposed methodology while aiming to avoid reputational harm to current providers. The dataset from 2014 included variables such as the “number of services charged”, “total number of points charged” (under Slovenia’s point-based tariff system at the time), “number of points per examination”, “average examination values (EUR)”, “number of first examinations”, and “total number of first/follow-up examinations”. Data credibility was assessed using Benford’s Law (for calculating χ² values and testing null hypothesis rejection at the 95% level), and Grubbs’ test, Hampel’s test, and T-test were used to identify outliers. Results: An analysis using Benford’s Law revealed significant deviations for the “number of services charged” (p < 0.005), “total number of points charged” (p < 0.01), “number of points per examination” (p < 0.0005), and “average examination values (EUR)” (p < 0.005), suggesting anomalies. Conversely, data on the numbers of “first” (p < 0.7) and “total first/follow-up examinations” (p < 0.3) were found to align with Benford’s Law, indicating authenticity. Outlier detection consistently identified two institutions with unusually high values for points per examination and average examination monetary value. Conclusions: Simple statistical tests can effectively identify potential irregularities in healthcare payment data, providing a cost-effective screening method for further investigation. Identifying outlier providers highlights areas needing detailed scrutiny to understand anomaly causes. Full article

Pre-taxation analysis plays a crucial role in ensuring the fairness of public revenue collection. It can also serve as a tool to reduce the risk of tax avoidance, one of the UK government’s concerns. Our report utilises pre-tax income ($PI$) and total assets ($TA$) data from 567 companies listed on the FTSE All-Share index, gathered from the Refinitiv EIKON database, covering 14 years, i.e., the period from 2009 to 2022. We also derive the $PI/TA$ ratio, and distinguish between positive and negative $PI$ cases. We test the conformity of such data to Benford’s Laws, specifically studying the first significant digit ($Fd$), the second significant digit ($Sd$), and the first and second significant digits ($FSd$). We use and justify two pertinent tests, the ${\chi }^2$ and the Mean Absolute Deviation (MAD). We find that both tests do not lead to conclusions in complete agreement with each other—in particular, the MAD test entirely rejects the Benford’s Laws conformity of the reported financial data. From the mere accounting point of view, we conclude that the findings not only cast some doubt on the reported financial data, but also suggest that many more investigations should be considered on closely related matters. On the other hand, the study of a ratio, like $PI/TA$, of variables that are (or are not) Benford’s Laws-compliant adds to the literature concerning whether such indirect variables should (or should not) be Benford’s Laws-compliant. Full article

This study systematically evaluates the reliability of PM2.5 monitoring data across major urban areas, utilizing a comprehensive dataset covering 283 cities in China over a seven-year period. By using Benford’s Law, robust regression analysis, and various machine learning methods, such as Gradient Boosting Trees and Random Forests, the overall reliability of China’s PM2.5 monitoring data is high. These models effectively captured complex patterns and detected anomalies related to both natural environmental and socioeconomic factors, as well as potential data manipulation. Based on the integrated models, the proportion of anomalies in PM2.5 concentration monitoring data across 283 cities in China from 2015 to 2022 was less than 2%, which strongly indicates the overall reliability of China’s PM2.5 concentration monitoring data. Additionally, machine learning models provided a ranking of the importance of different variables affecting PM2.5 concentrations, offering a scientific basis for understanding the driving factors behind the data. The three variables that have the greatest impact on PM2.5 concentrations are population density, average temperature, and relative humidity. By comparing with other related studies, we further validated our findings. Overall, this study provides new methods and perspectives for understanding and evaluating the reliability of PM2.5 data in China, laying a solid foundation for future research. Full article

The year 2022 was marked by a significant increase in electricity prices in Germany, with prices reaching extreme levels due to various geopolitical and climatic factors. This research analyzes the evolution of electricity prices in Germany from 2015 to 2024 and applies Benford’s Law to examine the distribution of the first digits of these prices. Historical electricity price data from Germany, obtained from publicly available sources, were used for the analysis. We applied Benford’s Law to determine the frequency of occurrence of the first digits of electricity prices and compared the results with the expected distribution according to Benford’s Law. We also considered the impact of negative electricity prices. The results suggest that external factors, such as geopolitical events and climatic conditions, have a significant impact on the volatility of electricity prices. Benford’s Law can be a useful tool for analyzing electricity prices, although its application to this market shows certain deviations. Full article

We survey the literature on the use of Benford’s distribution digit analysis applied to COVID-19 case data reporting. We combine a bibliometric analysis of 32 articles with a survey of their content and findings. In spite of combined efforts from teams of researchers across multiple countries and universities, using large data samples from a multitude of sources, there is no emerging consensus on data misreporting. We believe we are nevertheless able to discern a faint pattern in the segregation of findings. The evidence suggests that studies using very large, aggregate samples and a methodology based on hypothesis testing are marginally more likely to identify significant deviations from Benford’s distribution and to attribute this deviation to data tampering. Our results are far from conclusive and should be taken with a very healthy dose of skepticism. Academics and policymakers alike should remain mindful that the misreporting controversy is still far from being settled. Full article

The increasing proliferation of cyber-attacks threatening the security of computer networks has driven the development of more effective methods for identifying malicious network flows. The inclusion of statistical laws, such as Benford’s Law, and distance functions, applied to the first digits of network flow metadata, such as IP addresses or packet sizes, facilitates the detection of abnormal patterns in the digits. These techniques also allow for quantifying discrepancies between expected and suspicious flows, significantly enhancing the accuracy and speed of threat detection. This paper introduces a novel method for identifying and analyzing anomalies within computer networks. It integrates Benford’s Law into the analysis process and incorporates a range of distance functions, namely the Mean Absolute Deviation (MAD), the Kolmogorov–Smirnov test (KS), and the Kullback–Leibler divergence (KL), which serve as dispersion measures for quantifying the extent of anomalies detected in network flows. Benford’s Law is recognized for its effectiveness in identifying anomalous patterns, especially in detecting irregularities in the first digit of the data. In addition, Bayes’ Theorem was implemented in conjunction with the distance functions to enhance the detection of malicious traffic flows. Bayes’ Theorem provides a probabilistic perspective on whether a traffic flow is malicious or benign. This approach is characterized by its flexibility in incorporating new evidence, allowing the model to adapt to emerging malicious behavior patterns as they arise. Meanwhile, the distance functions offer a quantitative assessment, measuring specific differences between traffic flows, such as frequency, packet size, time between packets, and other relevant metadata. Integrating these techniques has increased the model’s sensitivity in detecting malicious flows, reducing the number of false positives and negatives, and enhancing the resolution and effectiveness of traffic analysis. Furthermore, these techniques expedite decisions regarding the nature of traffic flows based on a solid statistical foundation and provide a better understanding of the characteristics that define these flows, contributing to the comprehension of attack vectors and aiding in preventing future intrusions. The effectiveness and applicability of this joint method have been demonstrated through experiments with the CICIDS2017 public dataset, which was explicitly designed to simulate real scenarios and provide valuable information to security professionals when analyzing computer networks. The proposed methodology opens up new perspectives in investigating and detecting anomalies and intrusions in computer networks, which are often attributed to cyber-attacks. This development culminates in creating a promising model that stands out for its effectiveness and speed, accurately identifying possible intrusions with an F1 of nearly $80\%$, a recall of $99.42\%$, and an accuracy of $65.84\%$. Full article

The rapid growth in multimedia, storage systems, and digital computers has resulted in huge repositories of multimedia content and large image datasets in recent years. For instance, biometric databases, which can be used to identify individuals based on fingerprints, facial features, or iris patterns, have gained a lot of attention both from academia and industry. Specifically, face image quality assessment (FIQA) has become a very important part of face recognition systems, since the performance of such systems strongly depends on the quality of input data, such as blur, focus, compression, pose, or illumination. The main contribution of this paper is an analysis of Benford’s law-inspired first digit distribution and perceptual features for FIQA. To be more specific, I investigate the first digit distributions in different domains, such as wavelet or singular values, as quality-aware features for FIQA. My analysis revealed that first digit distributions with perceptual features are able to reach a high performance in the task of FIQA. Full article

The reproducibility of academic research has long been a persistent issue, contradicting one of the fundamental principles of science. Recently, there has been an increasing number of false claims found in academic manuscripts, casting doubt on the validity of reported results. In this paper, we utilize an adapted version of Benford’s law, a statistical phenomenon that describes the distribution of leading digits in naturally occurring datasets, to identify the potential manipulation of results in research manuscripts, solely using the aggregated data presented in those manuscripts rather than the commonly unavailable raw datasets. Our methodology applies the principles of Benford’s law to commonly employed analyses in academic manuscripts, thus reducing the need for the raw data itself. To validate our approach, we employed 100 open-source datasets and successfully predicted $79\%$ of them accurately using our rules. Moreover, we tested the proposed method on known retracted manuscripts, showing that around half (48.6%) can be detected using the proposed method. Additionally, we analyzed 100 manuscripts published in the last two years across ten prominent economic journals, with 10 manuscripts randomly sampled from each journal. Our analysis predicted a $3\%$ occurrence of results manipulation with a $96\%$ confidence level. Our findings show that Benford’s law adapted for aggregated data, can be an initial tool for identifying data manipulation; however, it is not a silver bullet, requiring further investigation for each flagged manuscript due to the relatively low prediction accuracy. Full article

Recently, we demonstrated the validity of the anomalous numbers law, known as Newcomb–Benford’s law, in mammalian neuromuscular transmission, considering different extracellular calcium. The present work continues to examine how changes in extracellular physiological artificial solution can modulate the first digit law in the context of spontaneous acetylcholine release at the neuromuscular junction. Using intracellular measurements, we investigated if the intervals of miniature potentials collected at the neuromuscular junction obey the law in a hyperkalemic environment. When bathed in standard Ringer’s solution, the experiments provided 22,582 intervals extracted from 14 recordings. On the other hand, 690,385 intervals were obtained from 12 experiments in a modified Ringer’s solution containing a high potassium concentration. The analysis showed that the intervals, harvested from recordings at high potassium, satisfactorily obeyed Newcomb–Benford’s law. Furthermore, our data allowed us to uncover a conformity fluctuation as a function of the number of intervals of the miniature potentials. Finally, we discuss the biophysical implications of the present findings. Full article

Data are produced every single instant in the modern era of technological breakthroughs we live in today and is correctly termed as the lifeblood of today’s world; whether it is Google or Meta, everyone depends on data to survive. But, with the immense surge in technological boom comes several backlashes that tend to pull it down; one similar instance is the data morphing or modification of the data unethically. In many jurisdictions, the phenomenon of data morphing is considered a severe offense, subject to lifelong imprisonment. There are several cases where data are altered to encrypt reliable details. Recently, in March 2023, Silicon Valley Bank collapsed following unrest prompted by increasing rates. Silicon Valley Bank ran out of money as entrepreneurial investors pulled investments to maintain their businesses afloat in a frigid backdrop for IPOs and individual financing. The bank’s collapse was the biggest since the financial meltdown of 2008 and the second-largest commercial catastrophe in American history. By confirming the “Silicon Valley Bank” stock price data, we will delve further into the actual condition of whether there has been any data morphing in the data put forward by the Silicon Valley Bank. To accomplish the very same, we applied a very well-known statistical paradigm, Benford’s Law and have cross-validated the results using comparable statistics, like Zipf’s Law, to corroborate the findings. Benford’s Law has several temporal proximities, known as conformal ranges, which provide a closer examination of the extent of data morphing that has occurred in the data presented by the various organizations. In this research for validating the stock price data, we have considered the opening, closing, and highest prices of stocks for a time frame of 36 years, between 1987 and 2023. Though it is worth mentioning that the data used for this research are coarse-grained, still since the validation is subjected to a larger time horizon of 36 years; Benford’s Law and the similar statistics used in this article can point out any irregularities, which can result in some insight into the situation and into whether there has been any data morphing in the Stock Price data presented by SVB or not. This research has clearly shown that the stock price variations of the SVB diverge much from the permissible ranges, which can give a conclusive direction on further investigations in this issue by the responsible authorities. In addition, readers of this article must note that the conclusion formed about the topic discussed in this article is objective and entirely based on statistical analysis and factual figures presented by the Silicon Valley Bank Group. Full article

The Benford law applied within complex networks is an interesting area of research. This paper proposes a new algorithm for the generation of a Benford network based on priority rank, and further specifies the formal definition. The condition to be taken into account is the probability density of the node degree. In addition to this first algorithm, an iterative algorithm is proposed based on rewiring. Its development requires the introduction of an ad hoc measure for understanding how far an arbitrary network is from a Benford network. The definition is a semi-distance and does not lead to a distance in mathematical terms, instead serving to identify the Benford network as a class. The semi-distance is a function of the network; it is computationally less expensive than the degree of conformity and serves to set a descent condition for the rewiring. The algorithm stops when it meets the condition that either the network is Benford or the maximum number of iterations is reached. The second condition is needed because only a limited set of densities allow for a Benford network. Another important topic is assortativity and the extremes which can be achieved by constraining the network topology; for this reason, we ran simulations on artificial networks and explored further theoretical settings as preliminary work on models of preferential attachment. Based on our extensive analysis, the first proposed algorithm remains the best one from a computational point of view. Full article

A frequent problem with classic first digit applications of Benford’s law is the law’s inapplicability to clustered data, which becomes especially problematic for analyzing election data. This study offers a novel adaptation of Benford’s law by performing a first digit analysis after converting vote counts from election data to base 3 (referred to throughout the paper as 1-BL 3), spreading out the data and thus rendering the law significantly more useful. We test the efficacy of our approach on synthetic election data using discrete Weibull modeling, finding in many cases that election data often conforms to 1-BL 3. Lastly, we apply 1-BL 3 analysis to selected states from the 2004 US Presidential election to detect potential statistical anomalies. Full article

The first coronavirus disease 2019 (COVID-19) case was detected in Singapore on 23 January 2020. Over the two years, Singapore witnessed tightening and easing of policies in response to and in anticipation of new variants, stress on the healthcare sector, and new waves of infection. Upon confirming the reliability of the data using Benford’s analysis, the collated COVID-19 data and trends were analyzed alongside the policies between 2020 and 2021 in Singapore. Due to the proactive nature of these policies, Singapore was largely successful in reducing the imported cases that would spill over and result in community waves of infection and death. The government has taken necessary steps to support the citizens and reduce the impact of the pandemic on the economy of the country. Furthermore, there were policies that were more responsive and there are lessons to be learned from neighboring countries on their management of the pandemic. Given the endemic approach the government has adopted, the efficacy of these policies comes down to its sustainability. Since the pandemic requires frequent revisiting of these policies, Singapore’s long-term management of the pandemic (or endemic) and its impact comes down to the ability of the government to introduce sustainable policies and update these according to new developments in treatments, variants, and vaccines, bearing in mind the socioeconomic condition of the country. Full article