A Two Parameters Equation for Word Rank-Frequency Relation

Abstract

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 \[ f (r;s,t) = (r_ maxr )^1-s (r_ max+t r_ expr+t r_ exp )^1+(1+t)s \] 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.

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