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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 ...
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.
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.
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.
Theodore Preston Hill (born December 28, 1943), professor emeritus at the Georgia Institute of Technology, is an American mathematician specializing mainly in probability theory. He is an Elected Member of the International Statistical Institute (1993), and an Elected Fellow of the Institute of Mathematical Statistics (1999).
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Benford's law. Benford's law. This was first stated in 1881 by Simon Newcomb, [1] and rediscovered in 1938 by Frank Benford. [2] The first rigorous formulation and proof seems to be due to Ted Hill in 1988.; [3] see also the contribution by Persi Diaconis. [4] Bertrand's ballot theorem.
(Hasty generalization is the mistaken application of this law to small data sets.) Law of anomalous numbers (also called first-digit law and (Newcomb–)Benford law), an observation about the frequency distribution of leading digits in many real-life sets of numerical data. Pigeonhole principle, the occurrence of mathematical coincidences