A Three-Parameter Rank-Frequency Relation in Natural Languages

Abstract

We present that, the rank-frequency relation in textual data follows f r^-(r+)^-, where f is the token frequency and r is the rank by frequency, with (, , ) as parameters. The formulation is derived based on the empirical observation that d^2 (x+y)/dx^2 is a typical impulse function, where (x,y)=( r, f). The formulation is the power law when =0 and the Zipf--Mandelbrot law when =0. We illustrate that is related to the analytic features of syntax and + to those of morphology in natural languages from an investigation of multilingual corpora.

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Reproductions