# 4.12: Exercises

- Page ID
- 17059

Exercise \(\PageIndex{1}\)

*The “rank” of a word is its position in a list of words sorted by frequency: the most common word has rank 1, the second most common has rank 2, etc.*

*Zipf’s law describes a relationship between the ranks and frequencies of words in natural languages (http://en.Wikipedia.org/wiki/Zipf's_law). Specifically, it predicts that the frequency, f, of the word with rank r is:*

\[ f = c r^{-s} \nonumber \]

*where s and c are parameters that depend on the language and the text. If you take the logarithm of both sides of this equation, you get:*

\[ \log{f} = \log{c} - s \log{r} \nonumber \]

*So if you plot log f versus log r, you should get a straight line with slope −s and intercept log c.*

*Write a program that reads a text from a file, counts word frequencies, and prints one line for each word, in descending order of frequency, with log f and log r. Use the graphing program of your choice to plot the results and check whether they form a straight line. Can you estimate the value of s?*

*To make the plots, you might have to install matplotlib (see http://matplotlib.sourceforge.net/).*

**Solution:**