The Newcomb–Benford law states that in a set of natural numbers, the leading digit has a probability distribution that decays logarithmically. One of its major applications is the JPEG compression of ...images, a field of great interest for domains such as image forensics. In this article, we study JPEG compression from the point of view of Benford’s law. The article focuses on ways to detect fraudulent images and JPEG quality factors. Moreover, using the image’s luminance channel and JPEG coefficients, we describe a technique for determining the quality factor with which a JPEG image is compressed. The algorithm’s results are described in considerably more depth in the article’s final sections. Furthermore, the proposed idea is applicable to any procedure that involves the analysis of digital images and in which it is strongly suggested that the image authenticity be verified prior to beginning the analyzing process.
The RNA-seq technique is applied for the investigation of transcriptional behaviour. The reduction in sequencing costs has led to an unprecedented trove of gene expression data from diverse ...biological systems. Subsequently, principles from other disciplines such as the Benford law, which can be properly judged only in data-rich systems, can now be examined on this high-throughput transcriptomic information. The Benford law, states that in many count-rich datasets the distribution of the first significant digit is not uniform but rather logarithmic.
All tested digital gene expression datasets showed a Benford-like distribution when observing an entire gene set. This phenomenon was conserved in development and does not demonstrate tissue specificity. However, when obedience to the Benford law is calculated for individual expressed genes across thousands of cells, genes that best and least adhere to the Benford law are enriched with tissue specific or cell maintenance descriptors, respectively. Surprisingly, a positive correlation was found between the obedience a gene exhibits to the Benford law and its expression level, despite the former being calculated solely according to first digit frequency while totally ignoring the expression value itself. Nevertheless, genes with low expression that exhibit Benford behavior demonstrate tissue specific associations. These observations were extended to predict the likelihood of tissue specificity based on Benford behaviour in a supervised learning approach.
These results demonstrate the applicability and potential predictability of the Benford law for gleaning biological insight from simple count data.
This study examines the rounding up/down behavior of selected key accounting figures in BRICS countries. It also examines the role of global financial crisis (GFC) on this rounding up or down of such ...key numbers. Five key financial figures (Revenue, Operating Income, Net Income, and Earnings per share (EPS), Dividend per share (DPS)) are studied during year 2000 to 2015. Results show rounding up/down is more prevalent in two markets, China and India, for positive as well as for negative profit firms during both periods. Brazilian, Russian, and South African markets are showing less rounding up/down of earnings figures during pre-GFC and also for post-GFC period.
Benford's law is the study of the frequency of the principal digits contained in numerical data. It is also commonly used in predicting the occurrence of numbers in numerical data, including auditing ...financial statements. When an Auditor chooses a method of detecting fraud / material misstatement of data, he should first consider which types of accounts that may be analyzed by the Benford method are expected to be effective or not, While most of the accounting data sets related to the Benford distribution are in accordance with the Benford distribution because digital analysis is only effective when applied to the appropriate data set. Auditors need to consider in advance the expectations for the use of the Benford method distribution before conducting digital analysis. The purpose of this study is that we want to demonstrate the effectiveness of the Benford Law method in assisting the auditing process.
Registries are indispensable in medical studies and provide the basis for reliable study results for research questions. Depending on the purpose of use, a high quality of data is a prerequisite. ...However, with increasing registry quality, costs also increase accordingly. Considering these time and cost factors, this work is an attempt to estimate the cost advantages of applying statistical tools to existing registry data, including quality evaluation. Results for quality analysis showed that there are unquestionable savings of millions in study costs by reducing the time horizon and saving on average € 523,126 for every reduced year. Replacing additionally the over 25 % missing data in some variables, data quality was immensely improved. To conclude, our findings showed dearly the importance of data quality and statistical input in avoiding biased conclusions due to incomplete data.
Processing massive transcriptomic datasets in a meaningful manner requires novel, possibly interdisciplinary, approaches. One principle that can address this challenge is the Benford law (BL), which ...posits that the occurrence probability of a leading digit in a large numerical dataset decreases as its value increases. Here, we analyzed large single-cell and bulk RNA-seq datasets to test whether cell types and tissue origins can be differentiated based on the adherence of specific genes to the BL. Then, we used the Benford adherence scores of these genes as inputs to machine-learning algorithms and tested their separation accuracy. We found that genes selected based on their first-digit distributions can distinguish between cell types and tissue origins. Moreover, despite the simplicity of this novel feature-selection method, its separation accuracy is higher than that of the mean-expression level approach and is similar to that of the differential expression approach. Thus, the BL can be used to obtain biological insights from massive amounts of numerical genomics data-a capability that could be utilized in various biomedical applications, e.g., to resolve samples of unknown primary origin, identify possible sample contaminations, and provide insights into the molecular basis of cancer subtypes.
In this paper, we analyze the importance of internal audit against banking fraud in order to ensure banking stability, using mathematic approach. We explain the steps involved in setting up an ...anti-fraud plan. Then, we implement two phases of this plan, namely the evaluation of the degree of exposure to the risk of fraud in a large private bank in Algeria, and then we propose a tool for detecting fraudulent acts, the Benford law. The result confirms that internal audit is an indispensable function. It enables the bank to have a solid assurance that the risks, to which it is exposed, including the risk of fraud, are under control.
Accurate and reliable data are vital for effective disease surveillance and control. This study examined the application of the Newcomb-Benford Law (NBL) as a tool for assessing the quality of dengue ...cases data in the Philippines. Large-scale datasets from the Epidemiology and Disease Control Surveillance (EDCS) and Philippine Integrated Disease Surveillance and Response (PIDSR) reports were analyzed to determine if the observed leading digit distributions deviate significantly from the expected NBL distribution. The statistical tests employed include the chi-squared test, Mantissa Arc Test, Mean Absolute Deviation (MAD), and distortion factor. The results reveal notable deviations from the expected NBL distribution, particularly in digits 1, 3, 4, 6, and 8, indicating potential irregularities and inconsistencies in the reported data. Factors contributing to these deviations may include data manipulation, measurement errors, and sampling biases. Improving data quality and integrity is crucial to ensure accurate disease surveillance.
First order digits in data sets of natural and social data often follow a distribution called Benford’s law. We studied the number of articles published, citations received and impact factors of all ...journals indexed in the Science Citation Index from 1998 to 2007. We tested their compliance with Benford’s law. Citations data followed Benford’s law remarkably well in all years studied. However, for the data on the numbers of articles, the differences between the values predicted by Benford’s law and the observed values were always statistically significant. This was also the case for most data for impact factors.
Each country has been racing to contain the spread of COVID-19. The published data of daily infection and death cases can be used to measure the effectiveness of the control interventions. We focus ...our study in two Southeast Asia countries: Indonesia and Malaysia during period between March and November 2020. Newcomb-Benford law has been commonly used to analyze the probabilities of the first significant digits in natural occurrences since the late 19th century. It is a prominent statistical tool for its capability to detect frauds in datasets. A chi-squared test was recruited to quantify the closeness of the data and Newcomb-Benford law distributions. The results revealed that the distributions of daily infection and death cases in Indonesia followed Newcomb-Benford law while the opposite results were obtained for Malaysia. We have done the analysis of verifying the daily COVID-19 infection and death cases in Indonesia and Malaysia using Newcomb-Benford law. It can be inferred that, between March and November 2020, the control interventions in Indonesia was less effective compared to Malaysia.
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