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Probability distribution
Zipf's law (/zɪf/) is an empirical law stating that when a set of measured values is sorted in decreasing order, the value of the n-th entry is often approximately
Zipf's_law
Discrete probability distribution
and statistics, the Zipf–Mandelbrot law is a discrete probability distribution. Also known as the Pareto–Zipf law, it is a power-law distribution on ranked
Zipf–Mandelbrot_law
Linguistics law
In linguistics, the brevity law (also called Zipf's law of abbreviation) is a linguistic law that qualitatively states that the more frequently a word
Brevity_law
Functional relationship between two quantities
Power laws. Zipf, Power-laws, and Pareto – a ranking tutorial Archived 2007-10-26 at the Wayback Machine Stream Morphometry and Horton's Laws "How the
Power_law
Statistical distribution
individuals. All are real-world observations that follow power laws, such as Zipf's law, the Yule distribution, or the Pareto distribution. If one ranks
Rank–size_distribution
Application of Zipf's law to publications by field
Lotka's law, named after Alfred J. Lotka, is one of a variety of special applications of Zipf's law. It describes the frequency of publication by authors
Lotka's_law
Surname list
noted for Zipf's law Christoph Zipf (born 1962), professional tennis player from Germany Jonathan Zipf (born 1986), German triathlete Redl-Zipf This page
Zipf
American linguist (1902–1950)
within nations, and many other collections of data. He is the eponym of Zipf's law, which states that while only a few words are used very often, many or
George_Kingsley_Zipf
Observation that in many real-life datasets, the leading digit is likely to be small
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
Benford's_law
Word appearing only once in a text or record
less commonly used. Hapax legomena are quite common, as predicted by Zipf's law, which states that the frequency of any word in a corpus is inversely
Hapax_legomenon
Concept in sociology
Huberman, Bernardo A. (2002). "Zipf's law and the Internet". Glottometrics. 3: 143–150. Adamic, Lada A. "Zipf, Power-law, Pareto - a ranking tutorial"
Popularity
Statement based on repeated empirical observations that describes some natural phenomenon
as laws include the Titius–Bode law of planetary positions, Zipf's law of linguistics, and Moore's law of technological growth. Many of these laws fall
Scientific_law
Study of the quantitative aspects of information
is mostly based on Lotka's law, named after Alfred J. Lotka, Zipf's law, named after George Kingsley Zipf, Bradford's law named after Samuel C. Bradford
Informetrics
Probability distribution
parameter |citeseerx= (help) M. E. J. Newman (2005). "Power laws, Pareto distributions and Zipf's law". Contemporary Physics. 46 (5): 323–51. arXiv:cond-mat/0412004
Pareto_distribution
Economic principle
log-normal, as predicted by Gibrat's law. While the city size distribution is often associated with Zipf's law, this holds only in the upper tail. When
Gibrat's_law
Counterintuitive result in probability
number of combinations at the alphabet level. Zipf's law states that the frequency of words is a power law function of its frequency rank: word frequency
Infinite_monkey_theorem
Heuristic for distinct words in a document
Herdan (1960). Under mild assumptions, the Herdan–Heaps law is asymptotically equivalent to Zipf's law concerning the frequencies of individual words within
Heaps's_law
Pattern of references in science journals
distribution Zipf's law, originally used for word frequencies Zipf–Mandelbrot law PageRank The Long Tail Black, Paul E. (2004-12-12). "Bradford's law, in Dictionary
Bradford's_law
Theorized increase of longevity with age
relation to Zipf’s Law, and to socioeconomic inequality, arguing that "Lindy’s Law, Pareto’s Law and Zipf’s Law are in effect synonymous laws." Doomsday
Lindy_effect
Value of a communication network in terms of its connections
Bitcoin to the Zipf's Law and the theoretical Metcalfe result. The Metcalfe's Law is a critical component of Santostasi's Bitcoin Power Law Theory. In a
Metcalfe's_law
Power law growth of entropy of language or a stochastic process
addition to the term that is linear. It is closely related to Zipf's law and the neural scaling law for large language models. Hilberg's hypothesis was proposed
Hilberg's_hypothesis
Adages and sayings named after a person
after George Kingsley Zipf (1902–1950), whose statistical body of research led to the observation. More generally, the term Zipf's law refers to the probability
List of laws named after people
List_of_laws_named_after_people
Statistical behavior found in a wide variety of datasets
ranked list of US metropolitan populations also follow Zipf's law, and even forgetting follows Zipf's law. This act of summarizing several natural data patterns
Empirical_statistical_laws
Subdiscipline of mathematical linguistics
Heaps' law: It describes the number of distinct words in a document (or set of documents) as a function of the document length. Brevity law or Zipf's law of
Quantitative_linguistics
Statistical principle about ratio of effects to causes
(Paris). Volume 1 Volume 2 Newman, MEJ (2005). "Power laws, Pareto Distributions, and Zipf's law" (PDF). Contemporary Physics. 46 (5): 323–351. arXiv:cond-mat/0412004
Pareto_principle
15th-century codex in an unknown script
second-most-common word, and three times as often as the third-most-common, following Zipf's law. The mix of word lengths and the ratio of unique words to total words
Voynich_manuscript
basic concepts for the purpose of historical-comparative linguistics Zipf's law, a theory stating that the frequency of any word is inversely proportional
Most_common_words_in_English
Hypothesis that more people will lurk in a virtual community than will participate
distribution frequency of the 1% rule fit followed Zipf's law, which is a specific type of power law. The "90–9–1" version of this rule states that for
1%_rule
Linguistic law
Menzerath's law, observing that calls are abbreviated when used in longer sequences. Zipf's law Brevity law Heaps' law Bradford's law Benford's law Pareto
Menzerath's_law
Universal principle
empirical observations may be called laws: Say's law in economics, the Titius-Bode law of planetary positions, Zipf's law in linguistics, Thomas Malthus's
Law_(principle)
Rank of cities based on their population
relationship between rank and frequency is expressed with reference to Zipf's law. The law applied to cities states that "if cities are ranked in decreasing
Urban_hierarchy
Austrian brewery
The Zipf Brewery (in German: Brauerei Zipf) is a brewery in the Upper Austrian municipality of Neukirchen an der Vöckla (Vöcklabruck District). It is named
Zipf_Brewery
Probability distribution in mathematics
distribution is a probability distribution by itself, it is not associated with Zipf's law with the same exponent. The zeta distribution is defined for positive
Zeta_distribution
Feature of some statistical distributions
characterizing distributions such as the Gutenberg–Richter law or the words-occurrence Zipf's law, and those highlighted by Anderson and Shirky are of very
Long_tail
Hypothetical language of extraterrestrial beings
language. Laurance Doyle and others have suggested an application of Zipf's law for detection of alien language in the search for extraterrestrial intelligence
Alien_language
frequency table. The law is named after George Kingsley Zipf, an early twentieth century American linguist. Zipf popularized Zipf's law and sought to explain
List of examples of Stigler's law
List_of_examples_of_Stigler's_law
Columbia University in 1989. In 1992 Li published a short paper proving that Zipf's law holds for randomly generated sequences of symbols, when the distribution
Wentian_Li
American astrophysicist
includes proposing a statistical theory of human population which explains Zipf's law and proposing a novel test for panspermia in the galaxy. Lin is currently
Henry_Lin_(astronomer)
Idea that agents prefer to do what's easiest
communicate efficiently with least effort and this theory is known as Zipf's law. Within the context of information seeking, the principle of least effort
Principle_of_least_effort
Whole of an object being mathematically similar to part of itself
analysis Self-similar process Teragon Tessellation Tweedie distributions Zipf's law Fractal Mandelbrot, Benoit B. (1982). The Fractal Geometry of Nature,
Self-similarity
Phenomenon in statistics where highest-ranked data points are outliers
the reasonably distributed portion of the data set.[citation needed] Zipf's law Didier Sornette Laherrère, J.; Sornette, D. (1998). "Stretched exponential
King_effect
British physicist
PMC 1482622. PMID 16723398. Newman, MEJ (2005). "Power laws, Pareto distributions and Zipf's law" (PDF). Contemporary Physics. 46 (5): 323–351. arXiv:cond-mat/0412004
Mark_Newman
Discrete probability distribution
means that the tail of the Yule–Simon distribution is a realization of Zipf's law: f ( k ; ρ ) {\displaystyle f(k;\rho )} can be used to model, for example
Yule–Simon_distribution
investigation of the regularity later known as Zipf's law. M. Petruszewycz, 'L'histoire de la loi d'Estoup-Zipf: documents' Archived 2011-06-05 at the Wayback
Jean-Baptiste_Estoup
Digital collections of natural language data
Language Toolkit Parallel text Speech corpus Translation memory Treebank Zipf's law Yoon, H., & Hirvela, A. (2004). ESL Student Attitudes toward Corpus Use
Text_corpus
Sum of the first n whole number reciprocals; 1/1 + 1/2 + 1/3 + ... + 1/n
distribution of prime numbers. When the value of a large quantity of items has a Zipf's law distribution, the total value of the n most-valuable items is proportional
Harmonic_number
Book by Seth Godin
the next-most popular ice cream, further stating that this is seen in Zipf's law. Godin's central thesis is that in order to be the best in the world,
The_Dip_(book)
British dictionary
categorised in three frequency bands, based on the idea, derived from Zipf's law, that a relatively small number of high-frequency words account for a
Macmillan English Dictionary for Advanced Learners
Macmillan_English_Dictionary_for_Advanced_Learners
Belgian mathematician (1921–1999)
Belevitch had an interest in languages and found a mathematical derivation of Zipf's law. He also published on machine languages. Another field of interest was
Vitold_Belevitch
recent paper by Chao and Shen (2004). The theory is linked to that of Zipf's law. The same approach is used in many other fields. For example, in ethology
Species_discovery_curve
Statistical measure
such distributions are unusual for natural phenomena, as suggested by Zipf's law. T. J. Gaskell and B. J. George propose an enhancement of the Lincoln
Lincoln_index
Indo-Aryan language of India
WordCorp), the y-intercept of Zipf's law is reported as 12.49, and the coefficient is 0.89 and these numbers show that Zipf's law is applicable for Marathi
Marathi_language
2004 non-fiction book by Philip Ball
cycle, random walks, phase transitions, bifurcation theory, traffic flow, Zipf's law, Small world phenomenon, catastrophe theory, the Prisoner's dilemma. The
Critical_Mass_(book)
Discrete probability distribution
determine if they are King Effect members or normal members. By comparison, Zipf's law fits a line through the points (also using the log of the rank and log
Parabolic fractal distribution
Parabolic_fractal_distribution
Taiwanese mathematician alleged to have been murdered by KMT
Retrieved May 4, 2020. Chen, Wen-Chen (1980-01-01). "On the Weak Form of Zipf's Law". Journal of Applied Probability. 17 (3): 611–622. doi:10.2307/3212955
Chen_Wen-chen
Study of the frequency of letters or groups of letters in a ciphertext
significant cryptographically. Index of coincidence Topics in cryptography Zipf's law A Void, a novel by Georges Perec. The original French text is written
Frequency_analysis
Difference between logarithm and harmonic series
summatory function of the Dirichlet hyperbola method. In some formulations of Zipf's law. The answer to the coupon collector's problem.* The mean of the Gumbel
Euler's_constant
Zener Zeno effect – Zeno of Elea Zipf's law – George K. Zipf Zipf–Mandelbrot law (a.k.a. Pareto–Zipf law) – George K. Zipf and Benoît Mandelbrot (or Vilfredo
Scientific phenomena named after people
Scientific_phenomena_named_after_people
British science writer (born 1962)
cycle, random walks, phase transitions, bifurcation theory, traffic flow, Zipf's law, Small world phenomenon, catastrophe theory, the Prisoner's dilemma. The
Philip_Ball
scientific laws named after people (eponymous laws). For other lists of eponyms, see eponym. Eponym Fields of science Glossary of sound laws in the Indo-European
List of scientific laws named after people
List_of_scientific_laws_named_after_people
Special function in mathematics
dynamical systems. In applied statistics, it occurs in Zipf's law and the Zipf–Mandelbrot law. In particle physics, it occurs in a formula by Julian Schwinger
Hurwitz_zeta_function
2D graphic with logarithmic scales on both axes
parameters from experiment. Semi-log plot (lin–log or log–lin) Power law Zipf's law Log-linear model Log-normal distribution Log-logistic distribution Data
Log–log_plot
Communication lacking coherent meaning
letters, punctuation marks and spaces do not exhibit these regularities. Zipf's law attempts to state this analysis mathematically. By contrast, cryptographers
Nonsense
in the English language. The Zipf–Mandelbrot law is a discrete power law distribution which is a generalization of the Zipf distribution. The beta negative
List of probability distributions
List_of_probability_distributions
Branch of applied mathematics
formulation of language laws and, ultimately, of a general theory of language in the sense of a set of interrelated languages laws. Synergetic linguistics
Mathematical_linguistics
Branch of the Eskaleut language family
in most English corpora of similar size. This makes the application of Zipf's law quite difficult in the Inuit language. Furthermore, the notion of a part
Inuit_languages
Cramér's theorem (second part) Empirical findings Benford's law Pareto principle Zipf's law Boy or Girl paradox Adapted process Basic affine jump diffusion
List_of_probability_topics
Estimate of the importance of a word in a document
own explanation did not propose much theory, aside from a connection to Zipf's law. Attempts have been made to put idf on a probabilistic footing, by estimating
Tf–idf
Large baleen whale species
multiple themes create a song. Humpback whale songs appear to follow Zipf's law, similar to human languages. The function of these songs has been debated
Humpback_whale
speech in children by Greenfield and others (1976).[citation needed] Zipf's law might be able to be used to indicate if a given dataset of animal communication
Animal_consciousness
Data set of American English in 1961
of phenomena by George Kingsley Zipf (for example, see his The Psychobiology of Language), and is known as Zipf's law. Although the Brown Corpus pioneered
Brown_Corpus
harmony - Vowel stems - Weak suppletion - Will (verb) - Word - Word-sense disambiguation - Writing - Writing systems - Wug test X-bar theory Zipf's law
Index_of_linguistics_articles
Middle quantile of a data set or probability distribution
Retrieved 16 March 2015. Newman, M. E. J. (2005). "Power laws, Pareto distributions and Zipf's law". Contemporary Physics. 46 (5): 323–351. arXiv:cond-mat/0412004
Median
Physicist
cities, transportation systems, and the urban population evolution and Zipf's law. The city growth equation reveals that urban population evolution is governed
Marc_Barthelemy
Stochastic process formalizing cumulative advantage
1098/rstb.1925.0002. Newman, M. E. J. (2005). "Power laws, Pareto distributions and Zipf's law". Contemporary Physics. 46 (5): 323–351. arXiv:cond-mat/0412004
Preferential_attachment
Physical process of transition between basic states of matter
S2CID 703231. Schwab, David J; Nemenman, Ilya; Mehta, Pankaj (2014). "Zipf's law and criticality in multivariate data without fine-tuning". Physical Review
Phase_transition
Readability test
or roughly appropriate for a second-year undergraduate. Readability Zipf's law Coleman, Meri; and Liau, T. L. (1975); A computer readability formula
Coleman–Liau_index
French researcher (born 1957)
management) (with Y. Malevergne), Springer, Heidelberg, 2005. Theory of Zipf's law and beyond (with A. Saichev and Y. Malevergne), Lecture Notes in Economics
Didier_Sornette
Grammar of the Inuit languages
in most English corpora of similar size. This makes the application of Zipf's law quite difficult. Furthermore, the notion of a part of speech can be somewhat
Inuit_grammar
One over a whole number
calculations. Unequal probabilities related to unit fractions arise in Zipf's law. This states that, for many observed phenomena involving the selection
Unit_fraction
Symmetry between bosons and fermions
such as earthquakes, neuroavalanches, and solar flares, known as the Zipf's law and the Richter scale. In 2021, supersymmetric quantum mechanics was applied
Supersymmetry
Algorithm
administratively determined city borders. Naturally natural cities should follow Zipf's law, if they do not, the area is most likely too small, or data has probably
Head/tail_breaks
Event that is both extremely large in effect and of unique origins
power law and lognormal distributions." Internet mathematics 1.2 (2004): 226–251. Newman, Mark EJ. "Power laws, Pareto distributions and Zipf's law." Contemporary
Dragon_king_theory
Graph of wealth or income distribution
index) ROC analysis Social welfare (political science) Economic inequality Zipf's law Pareto distribution Mean deviation Elephant curve Damgaard, Christian;
Lorenz_curve
Vectorizing features using a hash function
immaterial.) Typically, these vectors are extremely sparse—according to Zipf's law. The common approach is to construct, at learning time or prior to that
Feature_hashing
Iron Age culture in central Italy
urbanization utilizing the Rank-Size model, an empirical system premised upon Zipf's Law that examines the connection between the size and the rank of a settlement
Latial_culture
American mathematician (1880–1949)
Lotka–Volterra inter-specific competition equations Lotka's law (a special case of Zipf's law) Lotka's principle Euler–Lotka equation Sharpe–Lotka–McKendrick's
Alfred_J._Lotka
Analytic function in mathematics
zeta function occurs in applied statistics including Zipf's law, Zipf–Mandelbrot law, and Lotka's law. Zeta function regularization is used as one possible
Riemann_zeta_function
Slovak-German linguist and mathematician
Texten (1988) Quantitative Linguistics: An International Handbook (2005) Zipf's law "Gabriel Altmann". Glottopedia. Retrieved 19 June 2023. Köhler, Reinhard;
Gabriel_Altmann
Data visualization
In most cases bibliograms can be described by power laws such as Zipf's law and Bradford's law. In this regard, they have long been studied by mathematicians
Bibliogram
Computer scientist
Phillips, Graham; Shenker, Scott (2012-03-15). On the Implications of Zipf's Law for Web Caching (PDF) (Report). University of Wisconsin-Madison Department
Li_Fan_(engineer)
Factor influencing social behavior
proportional to its rank in size among the urban areas of its economic region (Zipf's law). Kinship – Web of human social relationships Sippe – Kind of a kinship
Size of groups, organizations, and communities
Size_of_groups,_organizations,_and_communities
Comment about usage of information retrieval
reprisal from supervisors. The more common interpretation of Mooers's law is similar to Zipf's principle of least effort. It emphasizes the amount of effort needed
Mooers's_law
Geographical theory of spatial distribution of cities
Demographic gravitation The City (Weber book) Fractal Penrose tiling Zipf's law Boundary problem (in spatial analysis) Unified settlement planning Goodall
Central_place_theory
Ideal gas with no physical scale
ideal gas, changing the thermodynamical variables (N, V, T) by (N, Ω,σw). Zipf's law may emerge in the external limits of the density since it is a special
Scale-free_ideal_gas
believed it was actually a form of incandescence. 1932: Zipf's law, described by George Zipf (1932), was previously discovered by Felix Auerbach (1913)
List_of_multiple_discoveries
Software application for viewing and maintaining databases of chess games
Programs". Retrieved 2015-03-03. Blasius, Bernd; Tönjes, Ralf (2009). "Zipf's law in the popularity distribution of chess openings". Physical Review Letters
Shane's Chess Information Database
Shane's_Chess_Information_Database
Belgian economist and academic
entire urban system, rather than only in the upper tail described by Zipf's law. Kravis Award, University of Pennsylvania, 2002 and 2005 Fellow of the
Jan_Eeckhout
Bare list of a language's words in corpus linguistics
of unique-character words, or as a multi-character word. It seems that Zipf's law holds for frequency lists drawn from longer texts of any natural language
Word_list
Study of language as a complex, dynamic system
model Complex system Quantitative text analysis Zipf's law Brevity law "Word length and frequency - Laws in Quantitative Linguistics". 2015-02-15. Archived
Synergetic_linguistics
travel, tourism, insurance
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travel, tourism, insurance