Skip to main content
2 of 2
added 760 characters in body; added 2 characters in body
Dick Palais
  • 15.3k
  • 2
  • 73
  • 83

I'm not sure if this is an "answer" to your question, but I recall seeing somewhere that someone had shown that if you create a document by selecting the characters a...z plus a space character with uniform frequency then the "words" of such a document have a frequency distribution that follows Zipf's Law. (A little anecdote: when I was an undergraduate, I took a course on "Inductive Logic" given by Zipf. I recall being rather annoyed because he spent a lot of the time lecturing about "his" law and having us form groups that as part of our class work collected statistics to test it :-)

(Added Remarks) I recalled that when we tested Zipf's Laws for city populations back then (more than 50 years ago !) the results were quite good---i.e., the population of the n-th city was pretty close to $1/n$ times the population of the first for many countries. I decided to see if that was still so. For the US it pretty much is:

http://www.infoplease.com/ipa/A0763098.html#axzz0zuwyduxq

However, for China, it is WAY off---not even close:

http://en.wikipedia.org/wiki/List_of_cities_in_the_People%27s_Republic_of_China_by_population

Of course the population of Chinese cities has been changing rapidly due to migrations into them from the countryside, and perhaps Zipf's Law pertains only to stable situations when things are in equilibrium.

Dick Palais
  • 15.3k
  • 2
  • 73
  • 83