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Zipf, Power-law, Pareto - a ranking tutorial

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Lada A. Adamic


Many man made and naturally occurring phenomena, including city sizes, incomes, word frequencies, and earthquake magnitudes, are distributed according to a power-law distribution. A power-law implies that small occurrences are extremely common, whereas large instances are extremely rare. This regularity or 'law' is sometimes also referred to as Zipf and sometimes Pareto. To add to the confusion, the laws alternately refer to ranked and unranked distributions. Here we show that all three terms, Zipf, power-law, and Pareto, can refer to the same thing, and how to easily move from the ranked to the unranked distributions and relate their exponents.

Last modified 10/4/2000
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Some of the discussion is included in L.A. Adamic and B.A. Huberman, 'Zipf's law and the Internet', Glottometrics 3, 2002, 143-150

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