Zipf's law


Definition: The probability of occurrence of words or other items starts high and tapers off. Thus, a few occur very often while many others occur rarely.

Formal Definition: Pn ∼ 1/na, where Pn is the frequency of occurrence of the nth ranked item and a is close to 1.

See also Zipfian distribution, Lotka's law, Benford's law, Bradford's law.

Note: In the English language words like "and," "the," "to," and "of" occur often while words like "undeniable" are rare. This law applies to words in human or computer languages, operating system calls, colors in images, etc., and is the basis of many (if not, all!) compression approaches.

Named for George Kingsley Zipf.

Author: PEB

More information

Two graphs illustrating the law.

Go to the Dictionary of Algorithms and Data Structures home page.

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Entry modified 24 August 2009.
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Cite this as:
Paul E. Black, "Zipf's law", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 24 August 2009. (accessed TODAY) Available from: