I am curious about corpus linguistics, and especially in this case how corpora is used to prove the Brevity Law, also known as Zip'f law of abbreviation. Simply put, this theorem postulates that the shorter the words are, the more often they occur in language. Of course, visualization will make a great sense of proving the theorem, so I went across this visualization from Wikipedia:

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The x-axis stands for word character length and the y-axis stands for word count, in log per-million count.

My question is, why using log per-million count? Is it for normalization so that the words with lesser counts are well represented in the analysis? Anyone giving an insight to this, as well as some little readings, would greatly appreciated.

Thanks in advance!

1 Answer 1


Per-million count is used to normalize the size of the corpus. If you make your corpus twice as big, you'd expect to get twice as many tokens, but not twice as many types, so normalizing to a particular size (say, a million tokens) means you don't have to worry about any effects from that.

Log per-million count is used because there seems to be a roughly inverse relationship between the two variables (count is proportional to 1 / length); putting it on a log scale will make that inverse relationship appear as a line, and it's a lot easier for the human eye to see whether something is strikingly close to a line than strikingly close to a hyperbola.

  • Its clear! Thanks for the input :)
    – pindakazen
    Commented Jan 2 at 17:54

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