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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:
While Zipf's law works well in many cases, it tends to not fit the largest cities in many countries; one type of deviation is known as the King effect. A 2002 study found that Zipf's law was rejected in 53 of 73 countries, far more than would be expected based on random chance. [10]
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 ...
A basic conception within it is that large numbers of people, in a city for example, actually behave as an attractive force for other people to migrate there. It has been related [4] [5] to W. J. Reilly's law of retail gravitation, [6] [7] George Kingsley Zipf's Demographic Energy, [8] and to the theory of trip distribution through gravity models.
However, the long tails 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 different, if not opposite, nature: Anderson and Shirky refer to frequency-rank relations, whereas the Gutenberg–Richter law and the Zipf's law are probability ...
The urban hierarchy ranks each city based on the size of population residing within the nationally defined statistical urban area. Because urban population depends on how governments define their metropolitan areas, urban hierarchies are conventionally ranked at the national level; however, the ranking can be extended globally to include all cities.
Central place theory is an urban geographical theory that seeks to explain the number, size and range of market services in a commercial system or human settlements in a residential system. [1] It was introduced in 1933 to explain the spatial distribution of cities across the landscape. [ 2 ]