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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.
English: illustration of Benford's law, using the population of the countries of the world. The chart depicts the percentage of countries having the corresponding digit as first digit of their population (red bars). For example, 64 countries of 237 (=27%) have 1 as leading digit of the population.
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 ...
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".
However, both types of "law" may be considered instances of a scientific law in the field of statistics. What distinguishes an empirical statistical law from a formal statistical theorem is the way these patterns simply appear in natural distributions , without a prior theoretical reasoning about the data.
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.
Bradford's law is a pattern first described by Samuel C. Bradford in 1934 that estimates the exponentially diminishing returns of searching for references in science journals. One formulation is that if journals in a field are sorted by number of articles into three groups, each with about one-third of all articles, then the number of journals ...