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4.12: 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 ('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


    4.12: Exercises is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Allen B. Downey.

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