Zipf's law states that the frequency of a token in a text is directly proportional to its rank or position in the sorted list. This law describes how tokens are distributed in languages: some tokens occur very frequently, some occur with intermediate frequency, and some tokens rarely occur.

Let's see the code for obtaining the log-log plot in NLTK that is based on Zipf's law:

>>> import nltk
>>> from nltk.corpus import gutenberg
>>> from nltk.probability import FreqDist
>>> import matplotlib
>>> import matplotlib.pyplot as plt
>>> matplotlib.use('TkAgg')
>>> fd = FreqDist()
>>> for text in gutenberg.fileids():
. . . for word in gutenberg.words(text):
. . . fd.inc(word)
>>> ranks = []
>>> freqs = []
>>> for rank, word in enumerate(fd):
. . . ranks.append(rank+1)
. . . freqs.append(fd[word])
. . .
>>> plt.loglog(ranks, freqs)
>>> plt.xlabel('frequency(f)', fontsize=14, fontweight='bold')
>>> plt.ylabel('rank(r)', fontsize=14, fontweight='bold')
>>> plt.grid(True)
>>> plt.show()

The preceding code will obtain a plot of rank versus the frequency of words in a document. So, we can check whether Zipf's law holds for all the documents or not by seeing the proportionality relationship between rank and the frequency of words.