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This is an accepted version of this page This is the latest accepted revision, reviewed on 17 January 2025. 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 ...
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".
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.
Frank Albert Benford Jr. (July 10, 1883 [1] – December 4, 1948 [2]) was an American electrical engineer and physicist best known for rediscovering and generalizing Benford's Law, an earlier statistical statement by Simon Newcomb, about the occurrence of digits in lists of data.
Its growth rate is similar to , but slower by an exponential factor. One way of approaching this result is by taking the natural logarithm of the factorial, which turns its product formula into a sum, and then estimating the sum by an integral: ln n ! = ∑ x = 1 n ln x ≈ ∫ 1 n ln x d x = n ln n − n + 1. {\displaystyle \ln ...
"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 1881, Newcomb discovered the statistical principle now known as Benford's law. He observed that the earlier pages of logarithm books, used at that time to carry out logarithmic calculations, were far more worn than the later pages. This led him to formulate the principle that, in any list of numbers taken from an arbitrary set of data, more ...
Benford's law describes the occurrence of digits in many data sets, such as heights of buildings. According to Benford's law, the probability that the first decimal-digit of an item in the data sample is d (from 1 to 9) equals log 10 (d + 1) − log 10 (d), regardless of the unit of measurement. [78]