https://en.wikipedia.org/wiki/Zipf%27s_law
Zipf's law (/ z ɪ f /, German:) is an ... However, it may be partly explained by statistical analysis of randomly generated texts. ... Citations and the Zipf-Mandelbrot's law; Zipf's Law examples and modelling (1985) Complex systems: Unzipping Zipf's law (2011) Benford's law, Zipf's law, and the Pareto distribution by Terence Tao.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4176592/
for α ≈1 ( Zipf, 1936, 1949 ). 1 In this equation, r is called the frequency rank of a word, and f ( r) is its frequency in a natural corpus. Since the actual observed frequency will depend on the size of the corpus examined, this law states frequencies proportionally: The most frequent word ( r = 1) has a frequency proportional to 1, the

https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0147073
Introduction. Zipf's law constitutes a striking quantitative regularity in the usage of language [1-4].It states that, for a large enough piece of text, the frequency of use n of any word decreases with its rareness r in the text in an approximately hyperbolic way, i.e., n ∝ 1/r, where the symbol "∝" denotes proportionality.Technically, r is called the rank, and the most common (i

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9971120/
Some have argued that the elegance of simplicity of Zipf's law is in fact an oversimplification because word frequency distributions are more complex and cannot be captured in a mathematically simple formula (Mandelbrot, 1953; Piantadosi, 2014).As a consequence, variations to Zipf's law have been proposed, the most common one being introduced by Mandelbrot to account for the true frequency

https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0181987
Zipf's law is a special type of power law, however, namely one in which the slope of this line in a plot with equal axes is -45°; a defining, but often overlooked characteristic. ... Landauer TK, Harshman R. Indexing by latent semantic analysis. Journal of the American Society for Information Science. 1990;41(6):391-407. View Article

https://dspace.mit.edu/bitstream/handle/1721.1/98434/Williams-2015-Zipf%27s%20law.pdf?sequence=1
partitioning, which opens up a rich frontier of rigorous text analysis via a rank ordering of mixed length phrases. Over the last century, the elements of many disparate systems have been found to approximately follow Zipf's law—that element size is inversely proportional to element size rank1,2 —from city populations2-4,

https://royalsocietypublishing.org/doi/10.1098/rsif.2015.0330
where r is the rank that is assigned to every word in the text. For most texts, regardless of language, time of creation, genre of literature, its purpose, etc. one finds that α ∼ 1, which is referred to as Zipf's law [].In figure 1, the word frequency is shown for Darwin's text, The origin of species.The quest for an understanding of the origin of this statistical regularity has been going

https://link.springer.com/chapter/10.1007/978-3-030-84186-7_16
1.1 Zipf's Law. Zipf's law is an important empirical law describing the statistical properties of many natural phenomena. The law states that the frequency of a word in a given corpus has an inverse proportion with its frequency rank [].Ideally, the word that ranks first will be twice as frequent as the word that ranks second and so forth.

https://link.springer.com/chapter/10.1007/978-981-10-4032-0_5
The word frequency analysis method used in Zipf's law has been increasingly applied to scientific evaluation, and currently, to the management of science and technology. Such trend is notable. For example, using the bibliometric analysis of keywords to show the research trends of a subject is a valuable empirical study.

https://www.degruyter.com/document/doi/10.1515/9783110763560-015/html
Abstract. In a given text, the occurrence of words follows a famously systematic frequency distribution, obeying a power law known as Zipf's law. Its most common form is the doubly logarithmic chart. This research demonstrates that the ignored parameter C in the original Zipf's law displays a unique pattern. Moreover, the parameter C

https://www.nature.com/articles/474164a
Unzipping Zipf's law. Lada Adamic. Nature 474 , 164-165 ( 2011) Cite this article. 2767 Accesses. 34 Citations. 9 Altmetric. Metrics. One mathematical model can account for power-law

https://www.semanticscholar.org/paper/Applications-and-Explanations-of-Zipf%E2%80%99s-Law-Powers/1f7e50d220f41f4fac985a991c8d5187323aab4c
It is demonstrated how Zipf's analysis can be extended to include some of these phenomena, and closer examination uncovers systematic deviations from its normative form. Recently I have been intrigued by the reappearance of an old friend, George Kingsley Zipf, in a number of not entirely expected places. The law named for him is ubiquitous, but Zipf did not actually discover the law so much as

https://link.springer.com/article/10.3758/s13423-014-0585-6
for α ≈ 1 and β ≈ 2.7 (Mandelbrot, 1953, 1962; Zipf, 1936, 1949).This paper will study Eq. 2 as the current incarnation of "Zipf's law," although we will use the term near-Zipfian more broadly to mean frequency distributions where this law at least approximately holds. Such distributions are observed universally in languages, even in extinct and yet-untranslated languages like

https://colala.berkeley.edu/papers/piantadosi2014zipfs.pdf
a power law known as Zipf's law: the rth most frequent word has a frequency f(r) that scales according to f(r) ∝ 1 rα (1) for α ≈1 (Zipf, 1936, 1949)1. In this equation, r is called the "frequency rank" of a word, and f(r) is its frequency in a natural corpus. Since the actual observed frequency will depend on the size of the

https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.3.013084
Zipf's law, while others present Zipf's law only temporarily and, therefore, spuriously. A truly Zipfian dynamics ... scientific citations [6,7], and many natural sys-tems, such as earthquakes [7,8] and lunar craters [7]. There are ... a result confirmed by empirical analysis. From this body of analysis, it clearly emerges that our

https://www.semanticscholar.org/paper/The-Theoretical-Foundation-of-Zipf%27s-Law-and-Its-to-Fedorowicz/f68ab9248803d45abeba1544c1767aa9caf2e418
To analyze, evaluate and apply Zipf's Law in Computer Science through the content analysis of literature published in ACM journals, 13, 053 unique keywords out of 107,467 total keywords retrieved from 1954 to 2008 from Journals are analyzed.

https://www.researchgate.net/publication/264873465_Zipf's_Law_What_and_Why
The most famous quantitative law of language is Zipf 's law. and it deals with the frequency distribution of words. Before formulating this quan titative la w, one should introduce some

https://arxiv.org/abs/1809.08399
Zipf's law is the main regularity of quantitative linguistics. Despite of many works devoted to foundations of this law, it is still unclear whether it is only a statistical regularity, or it has deeper relations with information-carrying structures of the text. This question relates to that of distinguishing a meaningful text (written in an unknown system) from a meaningless set of symbols

https://journals.sagepub.com/doi/10.2466/pms.1994.79.1.153
Abstract. Zipf's law relates the frequencies of words found in speech samples to the numbers of different words at each frequency. The present study extended this law to very small samples (400 words) of both written and oral speech. A secondary purpose was to investigate whether oral and written samples from the same speakers deviate from Zipf

https://www.semanticscholar.org/paper/Zipf's-Law-for-Cities%3A-An-Explanation-Gabaix/2d9112b0d599b47af6ebc11d67db8650a30ee4d4
Zipf 's law is a very tight constraint on the class of admissible models of local growth. It says that for most countries the size distribution of cities strikingly fits a power law: the number of cities with populations greater than S is proportional to 1/S. Suppose that, at least in the upper tail, all cities follow some proportional growth process (this appears to be verified empirically).

https://academic.oup.com/qje/article/114/3/739/1848099
Abstract. Zipf's law is a very tight constraint on the class of admissible models of local growth. It says that for most countries the size distribution of cities strikingly fits a power law: the number of cities with populations greater than S is proportional to 1/S.Suppose that, at least in the upper tail, all cities follow some proportional growth process (this appears to be verified

https://scholar.harvard.edu/sites/scholar.harvard.edu/files/xgabaix/files/zipfs_law.pdf
Qtly Jrnl Econ 114-3. XAVIER GABAIX. Zipf's law is a very tight constraint on the class of admissible models of local growth. It says that for most countries the size distribution of cities strikingly fits a power law: the number of cities with populations greater than S is proportional to 1/S. Suppose that, at least in the upper tail, all

https://arxiv.org/abs/1006.0814
This paper provides a new geospatial perspective on whether or not Zipf's law holds for all cities or for the largest cities in the United States using a massive dataset and its computing. A major problem around this issue is how to define cities or city boundaries. Most of the investigations of Zipf's law rely on the demarcations of cities imposed by census data, e.g., metropolitan areas and

https://www.tandfonline.com/doi/full/10.1080/09296174.2024.2347055
5. It should be noted that in one of the previous studies (Lin et al., Citation 2014), parameter values of Zipf's law in spoken texts are larger than those in written books. Their research differs from ours in that their parameter values are based on less frequent words (with a rank range of [60,1000], ibid, p.4) instead of the whole

https://www.scotusblog.com/2024/06/supreme-court-strikes-down-bump-stock-ban/
The Supreme Court on Friday struck down a rule that banned bump stocks, issued by the Trump administration after a 2017 mass shooting at a concert in Las Vegas. By a vote of 6-3, the justices rejected the federal government's argument that rifles equipped with bump stocks are machine guns, which are generally prohibited under federal law.