A Two Parameters Equation for Word Rank-Frequency Relation

05/02/2022

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by   Chenchen Ding, et al.

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Let f (·) be the absolute frequency of words and r be the rank of words in decreasing order of frequency, then the following function can fit the rank-frequency relation f (r;s,t) = (r_ max/r)^1-s(r_ max+t · r_ exp/r+t · r_ exp)^1+(1+t)s where r_ max and r_ exp are the maximum and the expectation of the rank, respectively; s>0 and t>0 are parameters estimated from data. On well-behaved data, there should be s<1 and s · t < 1.