13.12: Exercises

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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 \( s \)?

Solution: http://thinkpython2.com/code/zipf.py. To run my solution, you need the plotting module matplotlib. If you installed Anaconda, you already have matplotlib; otherwise you might have to install it.