A Two Parameters Equation for Word Rank-Frequency Relation

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) = left(fracrtt maxrright)1-s left(fracrtt max+t · rtt expr+t · rtt expright)1+(1+t)s ] where rtt max and rtt 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.