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This is an accepted version of this page This is the latest accepted revision, reviewed on 17 December 2024. Observation that in many real-life datasets, the leading digit is likely to be small For the unrelated adage, see Benford's law of controversy. The distribution of first digits, according to Benford's law. Each bar represents a digit, and the height of the bar is the percentage of ...
Benford's law : In many collections of data, a given data point has roughly a 30% chance of starting with the digit 1. Benford's law of controversy: Passion is inversely proportional to the amount of real information available. Bennett's laws are principles in quantum information theory. Named for Charles H. Bennett.
In fact, fraud can move data in the direction of satisfying that law and thereby occasion wholly erroneous conclusions. [34] Walter R. Mebane Jr., performs a 2nd-digit Benford test on the ballot-box/polling station-level data. He finds that the test shows significant deviations in the vote counts for Karroubi and Rezaei, as well as for Ahmadinejad.
Checking whether votes received for candidates, obey Benford's law. [5] Checking for disproportionate presence of 0s in precinct vote totals, or of rounded numbers in vote shares. Deviation from statistical laws observed in election data. [4] Using machine learning algorithms to detect anomalies. [6]
Fraud can violate civil law (e.g., a fraud victim may sue the fraud perpetrator to avoid the fraud or recover monetary compensation) or criminal law (e.g., a fraud perpetrator may be prosecuted and imprisoned by governmental authorities), or it may cause no loss of money, property, or legal right but still be an element of another civil or ...
Benford's law is an observation that in many real-life sets of numerical data, the leading digit is likely to be small. [21] 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.
Benford's law, also called the First-Digit Law, states that in lists of numbers from many real-life sources of data, the leading digit is 1 almost one third of the time (33% of the time), and larger numbers occur as the leading digit with less and less frequency (as they grow in magnitude), to the point so that 9 is the first digit (of any ...
An Introduction to Benford's Law. Princeton University Press. ISBN 978-0-691-16306-2. Theodore P. Hill (2017). Pushing Limits: From West Point to Berkeley and Beyond. American Mathematical Society and Mathematical Association of America. ISBN 978-1-4704-3584-4. Theodore P. Hill (2018). "Slicing Sandwiches, States, and Solar Systems".