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Logarithmic Form of Zipf's Law

The power law relationship of Zipf's law can be expressed in an equivalent logarithmic form, which is useful for visualizing the distribution on a log-log plot. This form is written as logni=αlogi+c\log n_i = -\alpha \log i + c, where nin_i is the frequency of the iextrmthi^{ extrm{th}} most frequent word, α\alpha is the distribution's exponent, and cc is a constant. On a log-log plot, the frequencies of words, excluding a few highly frequent exceptions, roughly form a straight line.

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Updated 2026-05-13

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