+- MKLab (https://mklab.gr)
+-- Forum: [INDEX] (https://mklab.gr/forumdisplay.php?fid=1)
+--- Forum: MATHEMATICS (https://mklab.gr/forumdisplay.php?fid=3)
+---- Forum: ARTICLES (https://mklab.gr/forumdisplay.php?fid=13)
+---- Thread: Zipf's law [wikipedia] (/showthread.php?tid=382)
Zipf's law [wikipedia] - mklabgr - 06-15-2026
Summary
Zipf's law is an empirical observation stating that when values in a dataset are sorted in decreasing order, the frequency of the n-th entry is roughly inversely proportional to n. It is most famously illustrated in language: in a natural language corpus, the most common word appears about twice as often as the second most common, three times as often as the third, and so on — for example, in the Brown Corpus of American English, "the" accounts for nearly 7% of all word occurrences, while "of" accounts for roughly half that at about 3.5%.
Named after American linguist George Kingsley Zipf, the law has since been found to apply well beyond linguistics, appearing in the size distributions of cities and corporations, personal incomes, TV viewership, and even musical notes.
Its mathematical formalization is the Zipfian distribution — a discrete power-law probability distribution — and proposed explanations for why it arises range from Zipf's own "principle of least effort" to preferential attachment processes and statistical artifacts of randomly generated text.
ARTICLE