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Zipf's law (/ z ɪ f /; German pronunciation:) is an empirical law stating that when a list of measured values is sorted in decreasing order, the value of the n-th entry is often approximately inversely proportional to n. The best known instance of Zipf's law applies to the frequency table of words in a text or corpus of natural language:
All are real-world observations that follow power laws, such as Zipf's law, the Yule distribution, or the Pareto distribution. If one ranks the population size of cities in a given country or in the entire world and calculates the natural logarithm of the rank and of the city population, the resulting graph will show a linear pattern. This is ...
The Brevity law appears universal and has also been observed acoustically when word size is measured in terms of word duration. [5] 2016 evidence suggests it holds in the acoustic communication of other primates. [6] Log per-million word count as a function of wordlength (number of characters) in the Brown Corpus, illustrating Zipf's Brevity Law.
George Kingsley Zipf (/ ˈ z ɪ f / ZIFF; [1] January 7, 1902 – September 25, 1950), was an American linguist and philologist who studied statistical occurrences in different languages. [ 2 ] Zipf earned his bachelors, masters, and doctoral degrees from Harvard University , although he also studied at the University of Bonn and the University ...
Gibrat's law is also applied to cities size and growth rate, [5] where proportionate growth process may give rise to a distribution of city sizes that is 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.
However, what sets Zipf's law as an "empirical statistical law" rather than just a theorem of linguistics is that it applies to phenomena outside of its field, too. For example, a ranked list of US metropolitan populations also follow Zipf's law, [ 8 ] and even forgetting follows Zipf's law. [ 9 ]
From a demographic point of view, Timișoara is defined, according to the Zipf's law, as a second-tier city, along with Iași, Constanța, Cluj-Napoca and Brașov, with extensive macro-territorial functions and having the second largest functional urban area, after Bucharest, of over 5,000 km 2 (1,900 sq mi). [75]
Zipf's law in corpus analysis and population distributions amongst others, where frequency of an item or event is inversely proportional to its frequency rank (i.e. the second most frequent item/event occurs half as often as the most frequent item, the third most frequent item/event occurs one third as often as the most frequent item, and so on).