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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 ...
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Benford's law, which describes the frequency of the first digit of many naturally occurring data. The ideal and robust soliton distributions. Zipf's law or the Zipf distribution. A discrete power-law distribution, the most famous example of which is the description of the frequency of words in the English language.
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.
This is a list of probability topics. It overlaps with the (alphabetical) list of statistical topics. There are also the outline of probability and catalog of articles in probability theory. For distributions, see List of probability distributions. For journals, see list of probability journals.
(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
For example, a ranked list of US metropolitan populations also follow Zipf's law, [8] and even forgetting follows Zipf's law. [9] This act of summarizing several natural data patterns with simple rules is a defining characteristic of these "empirical statistical laws".
Boyle's law, which stipulates the reciprocal relation between the pressure and the volume of a gas, was first noted by Richard Towneley and Henry Power. In France, the law is known as Mariotte's law, after Edme Mariotte, who published his results later than Boyle, but crucially added that the relation holds only when temperature is kept constant.