Benford's Law. History, mathematical justification and applications

Newcomb-Benford’s Law, also known as “the first significant -digit Law “ or “the Law of Anomalous Numbers ”, is based on an observation from which a law was formalized about the distribution of the first significant digits in positive numerical data, where the probabilities of the most significant figures are not uniformly distributed, as might be expected. In addition, it receives these other names because it shows how the lower digits occur in nature more-often than the higher ones, indicating the absence of this event a possible risk of abnormal duplications and anomalies in certain datasets, and this is why it is a key tool in fields like fraud detection. In this sense, the issue of this project is to summarize bibliography with the purpose of showing the mathematical, statistical and empirical frameworks concerning this Law. We will study the distribution of the first significant digits, point out how to apply the formulas and we will interpret and check its effectiveness with the results obtained using two different datasets. Finally, we will also review the applications of this law in our day-to-day.La ley de Newcomb-Benford , también llamada “la ley del primer dígito” o “ley de los números anómalos”, está basada en una observación a partir de la cual se formalizó una ley sobre la distribución de los primeros dígitos significativos en conjuntos de datos numéricos positivos, donde las probabilidades de las cifras más significativas no están distribuidas de manera uniforme, como cabría esperar. Además, recibe estos otros nombres ya que muestra cómo los primeros dígitos ocurren en la naturaleza con mayor frecuencia que los últimos, indicando la ausencia de este suceso en ciertos conjuntos de datos un alto riesgo de que este contenga anomalías, y es por eso que es una herramienta clave en campos tales como la detección de fraude. En este sentido, este proyecto se basará en la recopilación de bibliografía acerca de la ley de Newcomb-Benford con el objeto de mostrar su marco matemático, estadístico y empírico. Estudiaremos la distribución de los primeros dígitos significativos y lo aplicaremos a dos conjuntos de datos reales . Por último, revisaremos también las aplicaciones de dicha ley en nuestro día a día.Grado en Estadístic

Digital analysis and the reduction of auditor litigation risk

https://egrove.olemiss.edu/dl_proceedings/1113/thumbnail.jp

Detection of debris-flow events from seismic signals using Benford’s law

The first step in building an early warning system using seismic signals is to automatically identify events of interest. Here, the first digit distribution of seismic signals generated by debris flows and other surface processes was calculated to validate compliance with Benford's law (BL). A detector model for debris flow events was introduced based on amplitude range and goodness of fit of BL. We show that seismic signals generated by debris flows, landslides, and bedload transport follow the BL. These events release more energy and last longer than rockfalls, which do not follow BL. In the test dataset with 1224 samples, the accuracy of the detector model in identifying debris flow events was 0.75

CSM-349 - Benford's Law: An Empirical Investigation and a Novel Explanation

This report describes an investigation into Benford?s Law for the distribution of leading digits in real data sets. A large number of such data sets have been examined and it was found that only a small fraction of them conform to the law. Three classes of mathematical model of processes that might account for such a leading digit distribution have also been investigated. We found that based on the notion of taking the product of many random factors the most credible. This led to the identification of a class of lognormal distributions, those whose shape parameter exceeds 1, which satisfy Benford?s Law. This in turn led us to a novel explanation for the law: that it is fundamentally a consequence of the fact that many physical quantities cannot meaningfully take negative values. This enabled us to develop a simple set of rules for determining whether a given data set is likely to conform to Benford?s Law. Our explanation has an important advantage over previous attempts to account for the law: it also explains which data sets will not have logarithmically distributed leading digits. Some techniques for generating data that satisfy Benford?s law are described and the report concludes with a summary and a discussion of the practical implications

Auditing Symposium XIII: Proceedings of the 1996 Deloitte & Touche/University of Kansas Symposium on Auditing Problems

Meeting the challenge of technological change -- A standard setter\u27s perspective / James M. Sylph, Gregory P. Shields; Technological change -- A glass half empty or a glass half full: Discussion of Meeting the challenge of technological change, and Business and auditing impacts of new technologies / Urton Anderson; Opportunities for assurance services in the 21st century: A progress report of the Special Committee on Assurance Services / Richard Lea; Model of errors and irregularities as a general framework for risk-based audit planning / Jere R. Francis, Richard A. Grimlund; Discussion of A Model of errors and irregularities as a general framework for risk-based audit planning / Timothy B. Bell; Framing effects and output interference in a concurring partner review context: Theory and exploratory analysis / Karla M. Johnstone, Stanley F. Biggs, Jean C. Bedard; Discussant\u27s comments on Framing effects and output interference in a concurring partner review context: Theory and exploratory analysis / David Plumlee; Implementation and acceptance of expert systems by auditors / Maureen McGowan; Discussion of Opportunities for assurance services in the 21st century: A progress report of the Special Committee on Assurance Services / Katherine Schipper; CPAS/CCM experiences: Perspectives for AI/ES research in accounting / Miklos A. Vasarhelyi; Discussant comments on The CPAS/CCM experiences: Perspectives for AI/ES research in accounting / Eric Denna; Digital analysis and the reduction of auditor litigation risk / Mark Nigrini; Discussion of Digital analysis and the reduction of auditor litigation risk / James E. Searing; Institute of Internal Auditors: Business and auditing impacts of new technologies / Charles H. Le Grandhttps://egrove.olemiss.edu/dl_proceedings/1012/thumbnail.jp

PATTERN SEEKING AND SERVICE SYSTEM DESIGN DRIVEN BY FACT-BASED DECISION-MAKING

Ph.DDOCTOR OF PHILOSOPH