A Crucial Parameter for Rank-Frequency Relation in Natural Languages
Chenchen Ding
$f \propto r^{-\alpha} \cdot (r+\gamma)^{-\beta}$ has been empirically shown
more precise than a na\"ive power law $f\propto r^{-\alpha}$ to model the
rank-frequency ($r$-$f$) relation of words in natural languages. This work
shows that the only crucial parameter in the formulation is $\gamma$, which
depicts the resistance to vocabulary growth on a corpus. A method of parameter
estimation by searching an optimal $\gamma$ is proposed, where a ``zeroth
word'' is introduced technically for the calculation. The formulation and
parameters are further discussed with several case studies.