Timeline for Is there a natural random process that is rigorously known to produce Zipf's law?
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| S Jan 12 at 6:53 | history | suggested | vidyarthi | CC BY-SA 4.0 |
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| Jan 12 at 4:43 | review | Suggested edits | |||
| S Jan 12 at 6:53 | |||||
| Sep 20, 2010 at 8:32 | comment | added | Manjunath Krishnapur | That's right, it does seem a little unsatisfactory. In expectation we do have the 1/k behaviour, though. | |
| Sep 20, 2010 at 0:10 | comment | added | James Martin | How does this actually work though? If you take a realisation of the process $(N_1, N_2, ...)$, you'll get something that looks like (1,2,0,2,1,0,0,0,1,1,0,0,0,0,0,1,0,0,0....) or whatever. That doesn't seem like a "process that obeys Zipf's law". I guess you could do something like take $n$ independent random permutations of $[n]$, and look at the collection of all the 1-cycles, all the 2-cycles, etc... but then it's maybe more artificial. | |
| Sep 19, 2010 at 11:47 | comment | added | Louigi Addario-Berry | This also has a parameterized version, the $(\alpha,\theta)$-Chinese restaurant process, which will lead to different distributions on partitions. It's a nice answer for the question though because the random permutation case is by far the most natural element of the family of distributions. | |
| Sep 19, 2010 at 10:28 | history | answered | Manjunath Krishnapur | CC BY-SA 2.5 |