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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.

Distribution (Probability theory) --- Probability measures. --- 1938 paper. --- 2009 presidential elections. --- Benford analysis. --- Benford distribution. --- Benford property. --- Benford test. --- Benford's law geometry. --- Benford's law limit. --- Benford's law. --- Benford-good system. --- Eric Poehlman. --- European statistics. --- FSDs. --- Fourier analysis. --- Frank Benford. --- Fundamental Equivalence. --- Greek statistics. --- Iranian election. --- Iranian presidential elections. --- Lvy processes. --- PV effect. --- Partial Volume effect. --- Poisson Summation Formula. --- Poisson Summation. --- Simon Newcomb. --- Standard Condition. --- VAR. --- Value at Risk. --- accounting programs. --- accounting students. --- accounting. --- auditing. --- authentic data sets. --- behavioral approaches. --- bias. --- complaint data sets. --- computer systems. --- cumulative distribution. --- data sets. --- data-adaptive methods. --- decision-making research. --- densities. --- deterministic processes. --- digit bias. --- direct applications. --- econometric regression. --- economics. --- election fraud. --- elections. --- empirical economics research. --- empirical economics. --- error detection. --- explicit error bounds. --- explicit error estimates. --- exponential Lvy processes. --- finance. --- financial reports. --- financial statistics. --- first significant digits. --- first-digit analysis. --- first-digit frequency. --- fixed odds. --- forecasts. --- fraud detection. --- fraud. --- fraudulent data sets. --- functions. --- gambling. --- generic potential applications. --- geometry. --- government deficit. --- information-theoretic methods. --- local boostrap model. --- logarithms. --- lottery. --- macroeconomic data. --- managing risk. --- mathematical theory. --- meaningful numbers. --- medical tests. --- misreporting. --- natural data. --- natural sciences. --- non-uniformity. --- normalized functionals. --- number lottery games. --- numbers games. --- origins. --- parametric distributions. --- probability distributions. --- psychology. --- random processes. --- replication. --- scale invariance. --- scientific data sets. --- scientific misconduct. --- second digits. --- significand. --- significant digits. --- small number. --- social statistics. --- statistical relationship. --- statistics education. --- statistics. --- tampering. --- tax filing. --- tax fraud. --- total variation. --- uniform distribution. --- vote counts. --- voting. --- 1938 paper. --- 2009 presidential elections. --- Benford analysis. --- Benford distribution. --- Benford property. --- Benford test. --- Benford's law geometry. --- Benford's law limit. --- Benford's law. --- Benford-good system. --- Eric Poehlman. --- European statistics. --- FSDs. --- Fourier analysis. --- Frank Benford. --- Fundamental Equivalence. --- Greek statistics. --- Iranian election. --- Iranian presidential elections. --- Lvy processes. --- PV effect. --- Partial Volume effect. --- Poisson Summation Formula. --- Poisson Summation. --- Simon Newcomb. --- Standard Condition. --- VAR. --- Value at Risk. --- accounting programs. --- accounting students. --- accounting. --- auditing. --- authentic data sets. --- behavioral approaches. --- bias. --- complaint data sets. --- computer systems. --- cumulative distribution. --- data sets. --- data-adaptive methods. --- decision-making research. --- densities. --- deterministic processes. --- digit bias. --- direct applications. --- econometric regression. --- economics. --- election fraud. --- elections. --- empirical economics research. --- empirical economics. --- error detection. --- explicit error bounds. --- explicit error estimates. --- exponential Lvy processes. --- finance. --- financial reports. --- financial statistics. --- first significant digits. --- first-digit analysis. --- first-digit frequency. --- fixed odds. --- forecasts. --- fraud detection. --- fraud. --- fraudulent data sets. --- functions. --- gambling. --- generic potential applications. --- geometry. --- government deficit. --- information-theoretic methods. --- local boostrap model. --- logarithms. --- lottery. --- macroeconomic data. --- managing risk. --- mathematical theory. --- meaningful numbers. --- medical tests. --- misreporting. --- natural data. --- natural sciences. --- non-uniformity. --- normalized functionals. --- number lottery games. --- numbers games. --- origins. --- parametric distributions. --- probability distributions. --- psychology. --- random processes. --- replication. --- scale invariance. --- scientific data sets. --- scientific misconduct. --- second digits. --- significand. --- significant digits. --- small number. --- social statistics. --- statistical relationship. --- statistics education. --- statistics. --- tampering. --- tax filing. --- tax fraud. --- total variation. --- uniform distribution. --- vote counts. --- voting.

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A practical guide to making good decisions in a world of missing dataIn the era of big data, it is easy to imagine that we have all the information we need to make good decisions. But in fact the data we have are never complete, and may be only the tip of the iceberg. Just as much of the universe is composed of dark matter, invisible to us but nonetheless present, the universe of information is full of dark data that we overlook at our peril. In Dark Data, data expert David Hand takes us on a fascinating and enlightening journey into the world of the data we don't see.Dark Data explores the many ways in which we can be blind to missing data and how that can lead us to conclusions and actions that are mistaken, dangerous, or even disastrous. Examining a wealth of real-life examples, from the Challenger shuttle explosion to complex financial frauds, Hand gives us a practical taxonomy of the types of dark data that exist and the situations in which they can arise, so that we can learn to recognize and control for them. In doing so, he teaches us not only to be alert to the problems presented by the things we don’t know, but also shows how dark data can be used to our advantage, leading to greater understanding and better decisions.Today, we all make decisions using data. Dark Data shows us all how to reduce the risk of making bad ones.

Big data. --- Data sets, Large --- Large data sets --- Data sets --- Missing observations (Statistics). --- Data, Missing (Statistics) --- Missing data (Statistics) --- Missing values (Statistics) --- Observations, Missing (Statistics) --- Values, Missing (Statistics) --- Estimation theory --- Multivariate analysis --- Multiple imputation (Statistics) --- Accuracy and precision. --- Adverse selection. --- Ambiguity. --- Analogy. --- Anonymity. --- Approximation. --- Arithmetic mean. --- Astronomer. --- Autism. --- Average. --- Awareness. --- Bankruptcy. --- Benford's law. --- Blood pressure. --- Calculation. --- Clinical trial. --- Confidentiality. --- Confirmation bias. --- Credit card. --- Credit score. --- Crime statistics. --- Customer. --- Dark data. --- Data science. --- Data set. --- Database. --- Decision-making. --- Detection. --- Disease. --- Economics. --- Effectiveness. --- Estimation. --- Experimental psychology. --- Explanation. --- Extrapolation. --- Financial transaction. --- Floor effect. --- Fraud. --- General Data Protection Regulation. --- Hypothesis. --- Identifier. --- Identity theft. --- Illustration. --- Imputation (statistics). --- Income. --- Indication (medicine). --- Inference. --- Information asymmetry. --- Insider trading. --- Insurance fraud. --- Insurance. --- Investor. --- Lawsuit. --- Measurement. --- Meta-analysis. --- Misinformation. --- Mismatch. --- Missing data. --- Observational error. --- Obstacle. --- Percentage. --- Plagiarism. --- Prediction. --- Probability. --- Proportionality (mathematics). --- Pseudonymization. --- Quantity. --- Randomized controlled trial. --- Randomness. --- Respondent. --- Result. --- Rounding. --- Salary. --- Sample Size. --- Sampling (statistics). --- Science. --- Scientist. --- Significant figures. --- Simulation. --- Skewness. --- Social science. --- Statistic. --- Statistical hypothesis testing. --- Statistician. --- Statistics. --- Suggestion. --- Symptom. --- Synthetic data. --- Tax avoidance. --- Tax. --- Technology. --- Theory. --- Thought. --- Uncertainty. --- Unemployment. --- Variable (mathematics). --- Wealth. --- Website. --- Writing. --- Year.