Zipf's Law

What:

• Basically: The most frequent word in a language appears twice as frequent as the second most recent word, three times as the third most frequent word etc.. I.E. The frequency of a word is inversely proportional to it’s rank.

  • Interestingly, every language seems to share this law.

• Mathematically: $f(r)\propto \frac{1}{r^s}$ , where:

  • $f(r)$ is the frequency of a word with rank $r$,
  • $r$ is the rank of the word (1 for the most frequent word, 2 for the second-most frequent, and so on),
  • $s$ is a parameter typically close to 1 (it determines how steep the frequency drop-off is),
  • $\propto$ means “proportional to.”

• Pictorially(?): It looks like the following:

  •