Steven J. Miller is associate professor of mathematics at Williams College. He is the coauthor of An Invitation to Modern Number Theory (Princeton).
Benford's law states that the leading digits of many data sets are not uniformly distributed from one through nine, but rather exhibit a profound bias. This bias is evident in everything from electricity bills and street addresses to stock prices, population numbers, mortality rates, and the lengths of rivers. Here, Steven Miller brings together many of the world's leading experts on Benford's law to demonstrate the many useful techniques that arise from the law, show how truly multidisciplinary it is, and encourage collaboration.Beginning with the general theory, the contributors explain the prevalence of the bias, highlighting explanations for when systems should and should not follow Benford's law and how quickly such behavior sets in. They go on to discuss important applications in disciplines ranging from accounting and economics to psychology and the natural sciences. The contributors describe how Benford's law has been successfully used to expose fraud in elections, medical tests, tax filings, and financial reports. Additionally, numerous problems, background materials, and technical details are available online to help instructors create courses around the book.Emphasizing common challenges and techniques across the disciplines, this accessible book shows how Benford's law can serve as a productive meeting ground for researchers and practitioners in diverse fields.
Steven J. Miller is associate professor of mathematics at Williams College. He is the coauthor of An Invitation to Modern Number Theory (Princeton).
| Erscheint lt. Verlag | 9.6.2015 |
|---|---|
| Zusatzinfo | 78 line illus. |
| Verlagsort | Princeton |
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre | |
| Technik | |
| Schlagworte | 1938 paper • 2009 presidential elections • Accounting • accounting programs • accounting students • Accuracy and precision • Addition • Almost surely • Antiderivative • Arbitrarily large • Auditing • Auditing (Scientology) • Auditor • authentic data sets • Azuma's inequality • Bayesian • Bayesian Statistics • behavioral approaches • Benford analysis • Benford classifier formulation • Benford distribution • Benford-good system • Benford property • Benford's Law • Benford's law geometry • Benford's law limit • Benford test • Bernoulli trial • beta distribution • Bias • Bibliography • Big O notation • Book • Bootstrap model • Bootstrapping (statistics) • Calculation • central limit theorem • Characteristic function (probability theory) • Chi-squared test • Closure (mathematics) • coefficient • complaint data sets • Computation • Computer systems • concentration of measure • Convolution Theorem • cumulative distribution • Cumulative distribution function • data-adaptive methods • data set • Data Sets • decision-making research • Degrees of freedom (statistics) • densities • Deterministic Processes • differential equation • digital camera • digit bias • direct applications • Division by zero • econometric regression • Economics • election fraud • Elections • electoral fraud • Empirical Bayes method • Empirical Economics • empirical economics research • empirical likelihood • Eric Poehlman • error • error detection • estimation • Euler's formula • European statistics • Eurostat • Exercises • existential quantification • expected value • Explanation • explicit error bounds • explicit error estimates • exponential distribution • exponential function • exponential Lvy processes • Exponential sum • Fair coin • Fibonacci Number • Finance • financial reports • Financial statement • financial statistics • first-digit analysis • first-digit frequency • first significant digits • fixed odds • For All Practical Purposes • Forecasts • fourier analysis • Fourier transform • Frank Benford • Fraud • fraud detection • fraudulent data sets • Free parameter • FSDs • Fubini's Theorem • Functions • Fundamental Equivalence • Gambling • gamma function • Gaussian (software) • Generalized method of moments • generic potential applications • Geometric Brownian motion • Geometric series • Geometry • gold standard • government deficit • Greek statistics • Heaviside step function • Heavy-tailed distribution • histogram • human visual system • Hypergeometric distribution • Hyperparameter • image capture devices • image forensics • Independence (probability theory) • Independent and identically distributed random variables • inference • Infimum and supremum • Infinite divisibility (probability) • Infinite product • Information-theoretic methods • Insulin • Integer • Iranian election • Iranian presidential elections • Jeffreys prior • Joint probability distribution • Kronecker delta • Lebesgue measure • length scale • linear regression • local boostrap model • Locally integrable function • logarithm • logarithmic distribution • logarithms • Log-normal Distribution • Loss Function • lottery • lucky number • Lvy processes • Lychrel number • macroeconomic data • Macroeconomics • Managing Risk • Martingale (probability theory) • mathematical problems • Mathematical Theory • Mathematics • Maxima and minima • Maximum entropy probability distribution • maximum likelihood estimation • meaningful numbers • Measurement • Medical Imaging • medical tests • misreporting • Monotonic Function • Mutual exclusivity • natural data • natural logarithm • Natural number • Natural Sciences • Nature • Newton's method • Nonparametric regression • non-uniformity • Normal distribution • normalized functionals • Normalizing constant • null hypothesis • number lottery games • Numbers Games • Order of magnitude • order statistic • Ordinary Least Squares • Origins • Parameter • parametric distributions • Parseval's theorem • Partial Volume effect • Partial volume (imaging) • payout • Pearson's chi-squared test • PET • PET-CT • Poisson Summation • Poisson summation formula • Positive real numbers • Positron Emission Tomography • power law • Prime number • prime number theorem • principle of maximum entropy • Probability • Probability density function • Probability Distribution • probability distributions • Probability mass function • probability measure • Proportionality (mathematics) • Psychology • Publication • Publishing • PV effect • Quantity • random processes • random sequence • Random Variable • Rate of Convergence • Receiver Operating Characteristic • Replication • Requirement • result • Riemann zeta function • Roth's theorem • Rounding • round-off error • Sample Size • Sampling (Statistics) • scale invariance • scientific data sets • Scientific Misconduct • second digits • Series expansion • significand • significant digits • Significant figures • Sign (mathematics) • Simon Newcomb • Sinc function • small number • Social Statistics • Special case • Standard Condition • standard deviation • Statistic • Statistical hypothesis testing • statistical relationship • Statistics • Statistics Education • stochastic • Subset • summary statistics • Summation • supplementary information • tampering • Tax • tax filing • Tax Fraud • test statistic • Theorem • total variation • Uniform distribution • Uniform distribution (discrete) • Upper and lower bounds • Value at risk • VaR • Variance • vote counts • Voting • voxel • Weibull distribution • Zipf's law |
| ISBN-10 | 1-4008-6659-6 / 1400866596 |
| ISBN-13 | 978-1-4008-6659-5 / 9781400866595 |
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