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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.
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 ]
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 ...
It has been found that natural cities exhibit a striking Zipf's law [9] Furthermore, the clustering method allows for a direct assessment of Gibrat's law. It is found that the growth of agglomerations is not consistent with Gibrat's law: the mean and standard deviation of the growth rates of cities follows a power-law with the city size. [10]
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The predicted distribution based on Zipf's law and the actual distribution are virtually identical. The most common size ranges from 100,000 to 200,000 and constitutes about half of the entire sample. The distribution extends to the largest cities with population over 2.5 million. [4]