rekordy: Benford's law

Evidence: 100 • authority: 72

Benford's law, also known as the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation that in many real-life sets of numerical data, the leading digit is likely to be small. In sets that obey the law, the number 1 appears as the leading significant digit about 30% of the time, while 9 appears as the leading significant digit less than 5% of the time. Uniformly distributed digits would each occur about 11.1% of the time. Benford's law also makes predictions about the distribution of second digits, third digits, digit combinations, and so on. Benford's law may be derived by assuming the dataset values are uniformly distributed on a logarithmic scale. Th…

Evidence: 52 • authority: 88

Benford-Weighted Digit Sums and Second-Order Asymptotics for Exponential Sequences. <p>Let b >= 2 be an integer base, and let M_L denote the L-digit integer significand induced by the logarithmic, or Benford, mantissa measure. Starting from the classical prefix law P(M_L = m) = log_b((m + 1)/m), we derive an exact finite evaluation for the Benford-weighted base-b digit sum E[s_b(M_L)]. This yields an exact finite formula for the cumulative signed deviation of significant-digit expectations from the uniform digit mean and, in the limit,<span></span></p> <p>c_b = b/2 - ((b - 1)/2) log_b(2*pi).</p> <p>We also obtain a two-term finite-length expansion with an explicit Stirling-remainder bound.…

Evidence: 44 • authority: 92

Enhancing Healthcare Integrity Using Simple Statistical Methods: Detecting Irregularities in Historical Dermatology Services Payments.. 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 ef…

Evidence: 36 • authority: 92

Global Benford Deviation Clustering (GBDC): A Spatial Framework for Unsupervised Radiometric Anomaly Detection in Multispectral Imagery. Abstract Unsupervised anomaly detection in Earth observation data remains constrained by the reliance on labeled training samples and site-specific threshold calibration. This study investigates the empirical feasibility of Benford's Law, a statistical principle describing the logarithmic distribution of leading digits in natural datasets, as a generalized, threshold-free radiometric filter. We introduce the Global Benford Deviation Clustering (GBDC) framework, which projects a global first-digit deviation signal back onto each pixel via its leading digit,…

Evidence: 32 • authority: 80

Revisiting the Benford law: When the Benford-like distribution of leading digits in sets of numerical data is expectable?

Evidence: 24 • authority: 80

Does china income FSDs follow Benford? A comparison between Chinese income first significant digit distribution with Benford distribution

Evidence: 24 • authority: 80

Evidence: 24 • authority: 92

Validating self-reported Toxic Release Inventory data using Benford's Law: investigating toxic chemical release hazards in floodplains.. Introduction Acute and long-term health impacts from flooding related toxic chemical releases are a significant local health concern and can disproportionately impact communities with vulnerable populations; reliable release data are needed to quantify this hazard. Methods In this paper, we analyze US Federal Emergency Management Agency designated floodplain data and US Environmental Protection Agency Toxic Release Inventory (TRI) data to determine if geographically manipulated databases adhere to Benford's Law. Results We investigated multiple variants an…