We would also like to emphasize the difference between the classic Zipf's laws and the distributions considered in this paper: Zipf studied the laws governing means to represent information, while we attempt to explore laws governing semantic flows and, moreover, semantic flows of a language as a whole.
Ferrer I Cancho, "Zipf's law from a communicative phase transition," The European Physical Journal B--Condensed Matter and Complex Systems, vol.
Corral, "A scaling law beyond Zipf's law and its relation to Heaps' law," New Journal of Physics, vol.
Which of Benford or Zipf's Laws best model such data?
It is a version of another important growth law, Zipf's Law (1949), originally formulated to account for the frequency distribution of words in the English language.
Of course Zipf's Law would usually extend down the integers, 11, 12 and so on.
They are very similar the most obvious difference being in the frequency of the first digit 1 with Zipf's Law predicting it occurring at a higher frequency than Benford's Law.
For example, a random walk model of growth with a (lower) barrier could produce a size distribution consistent with Zipf's laws. See, for example, Gabaix (1999).
Feller's (1940) rejection of "universal models of growth," Solow, Costello, and Ward's (2003) rejection of power laws in biology, Miller and Miller and Chomsky's (1963) rejection of the usefulness of Zipf's law of word length (Zipf 1932) are a few examples of prior (apparently failed) attempts to raise the level of discourse and raise the quality of attempts to "validate" or subject such theorizing to "severe testing" (Mayo 1996).
To take one example from economics, Gabaix (1999) demonstrates that the mechanisms that could induce a Zipf's law for cities could be very different and result in very different inferences: "[although] the models [might be] mathematically similar, they [may be] economically completely different." (31)
"Zipf's Law for Cities: An Explanation." Quarterly Journal of Economics, 1999, 114, 739-67.
The use of statistics as it is begins at the end of Chapter 2, which deals with the First, Second, and Third Zipf's Laws
, mean, dispersion, frequency distribution, correlation and some concepts of information theory (pp.