# Category:Statistical laws

## Pages in category "Statistical laws"

The following 27 pages are in this category, out of 27 total. This list may not reflect recent changes (learn more).

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## Pages in category "Statistical laws"

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The following 27 pages are in this category, out of 27 total. This list may not reflect recent changes (learn more).

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1. 1% rule (Internet culture) – The 1% rule states that the number of people who create content on the Internet represents approximately 1% of the people who view that content. For example, for person who posts on a forum, generally about 99 other people view that forum. The term was coined by authors and bloggers Ben McConnell and Jackie Huba, there were repeated inquiries about her identity and her refusal to engage in chat. The etiquette was, apparently, to other users upon entry into the chat rooms/sites. In some instances, she needed to explain her coinage of the term lurking, as the term was new to the online community, but others quickly understood her meaning. To her knowledge, the terms had not been used prior to that period, the actual percentage is likely to vary depending upon the subject matter. The 1% rule is often misunderstood to apply to the Internet in general and it is for this reason that one can see evidence for the 1% principle on many websites, but aggregated together one can see a different distribution. This latter distribution is unknown and likely to shift, but various researchers. Research in late 2012 suggested that only 23% of the population could properly be classified as lurkers, several years prior, results were reported on a sample of students from Chicago where 60 percent of the sample created content in some form. A similar concept was introduced by Will Hill of AT&T Laboratories and later cited by Jakob Nielsen, the term regained public attention in 2006 when it was used in a strictly quantitative context within a blog entry on the topic of marketing. Netocracy Digital citizen Sturgeons law Participation Inequality, Lurkers vs. Contributors in Internet Communities by Jakob Nielsen, by Charles Arthur in The Guardian, July 20,2006. The 1% Rule by Heather Green in BusinessWeek, May 10,2006 Institutions vs. Collaboration by Clay Shirky, July 2005, Video at 06,00 and 12,42

2. Benford's law – Benfords law, also called the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. The law states that in naturally occurring collections of numbers. For example, in sets which obey the law, the number 1 appears as the most significant digit about 30% of the time, by contrast, if the digits were distributed uniformly, they would each occur about 11. 1% of the time. Benfords law also makes predictions about the distribution of digits, third digits, digit combinations. It tends to be most accurate values are distributed across multiple orders of magnitude. The graph here shows Benfords law for base 10, there is a generalization of the law to numbers expressed in other bases, and also a generalization from leading 1 digit to leading n digits. It is named after physicist Frank Benford, who stated it in 1938, Benfords law is a special case of Zipfs law. A set of numbers is said to satisfy Benfords law if the digit d occurs with probability P = log 10 − log 10 = log 10 = log 10 . Therefore, this is the distribution expected if the mantissae of the logarithms of the numbers are uniformly and randomly distributed. For example, a x, constrained to lie between 1 and 10, starts with the digit 1 if 1 ≤ x <2. Therefore, x starts with the digit 1 if log 1 ≤ log x < log 2, the probabilities are proportional to the interval widths, and this gives the equation above. An extension of Benfords law predicts the distribution of first digits in other bases besides decimal, in fact, the general form is, P = log b − log b = log b . For b =2, Benfords law is true but trivial, the discovery of Benfords law goes back to 1881, when the American astronomer Simon Newcomb noticed that in logarithm tables the earlier pages were much more worn than the other pages. Newcombs published result is the first known instance of this observation and includes a distribution on the second digit, Newcomb proposed a law that the probability of a single number N being the first digit of a number was equal to log − log. The phenomenon was noted in 1938 by the physicist Frank Benford. The total number of used in the paper was 20,229. This discovery was named after Benford. In 1995, Ted Hill proved the result about mixed distributions mentioned below, arno Berger and Ted Hill have stated that, The widely known phenomenon called Benford’s law continues to defy attempts at an easy derivation

3. Heaps' law – In linguistics, Heaps law is an empirical law which describes the number of distinct words in a document as a function of the document length. It can be formulated as V R = K n β where VR is the number of words in an instance text of size n. K and β are free parameters determined empirically, with English text corpora, typically K is between 10 and 100, and β is between 0.4 and 0.6. The law is attributed to Harold Stanley Heaps, but was originally discovered by Gustav Herdan. Under mild assumptions, the Herdan–Heaps law is equivalent to Zipfs law concerning the frequencies of individual words within a text. This is a consequence of the fact that the relation of a homogenous text can be derived from the distribution of its types. Heaps law means that as more text is gathered, there will be diminishing returns in terms of discovery of the full vocabulary from which the distinct terms are drawn. Heaps law also applies to situations in which the vocabulary is just some set of types which are attributes of some collection of objects. For example, the objects could be people, and the types could be country of origin of the person. Egghe, L. Untangling Herdans law and Heaps law, Mathematical and informetric arguments, Journal of the American Society for Information Science and Technology,58,702, Heaps, Harold Stanley, Information Retrieval, Computational and Theoretical Aspects, Academic Press. Heaps law is proposed in Section 7.5, Herdan, Gustav, Type-token mathematics, The Hague, Mouton. Kornai, Andras, Zipfs law outside the range, in Rogers, James, Proceedings of the Sixth Meeting on Mathematics of Language, University of Central Florida. Milička, Jiří, Type-token & Hapax-token Relation, A Combinatorial Model, international Journal of Theoretical Linguistics,1, 99–110, doi,10. 1515/glot-2009-0009. Van Leijenhorst, D. C, van der Weide, Th. P, a formal derivation of Heaps Law, Information Sciences,170, 263–272, doi,10. 1016/j. ins.2004.03.006. This article incorporates material from Heaps law on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License