tea.mathoverflow.net - Discussion Feed (What is the probability distribution of "reputation" ?)

Alexander Chervov comments on "What is the probability distribution of "reputation" ?" (19526)

Alexander Chervov — Wed, 11 Jul 2012 04:34:40 -0700

Indeed uniform does not seems to fit, here is reputation of N*35 user (first user on the page http://mathoverflow.net/users?page="put N here").
(For uniform "Differences with previous" should be constant).
Ratios are more stable.

page first user Rep Difference with previous Ratio
1 60
2 15.4 44.6 3.896103896
3 10.7 4.7 1.439252336
4 7.5 3.2 1.426666667
5 6 1.5 1.25
6 4.8 1.2 1.25
7 3.9 0.9 1.230769231
8 3.3 0.6 1.181818182
9 2.8 0.5 1.178571429
10 2.5 0.3 1.12
11 2.2 0.3 1.136363636
12 2 0.2 1.1
13 1.8 0.2 1.111111111
14 1.7 0.1 1.058823529

@Alex qubeat Thank you very much.

Alex 'qubeat' comments on "What is the probability distribution of "reputation" ?" (19522)

Alex 'qubeat' — Mon, 09 Jul 2012 13:23:28 -0700

@Alexander Chervov: zip with plain text with reputations is here http://sdrv.ms/MgYkKX , but I doubt it is uniform, it indeed rather resembles lognormal ... yet I do not have time to apply necessary tests

Alexander Chervov comments on "What is the probability distribution of "reputation" ?" (19520)

Alexander Chervov — Mon, 09 Jul 2012 10:17:44 -0700

@Alex qubeat. May I ask you to share the data file with reputations?

If take users with reputation greater than say 1000, what PDF will we have? My guess is uniform . Is it true?

Alex 'qubeat' comments on "What is the probability distribution of "reputation" ?" (19519)

Alex 'qubeat' — Mon, 09 Jul 2012 04:42:19 -0700

@Qiaochu Yuan: I think, the Erlang distribution with k=3 and small rate parameter may display similar behavior http://en.wikipedia.org/wiki/Erlang_distribution - i.e. user stops doing something (e.g. log out SE) after k=3 rare events of certain kind.

Will Jagy comments on "What is the probability distribution of "reputation" ?" (19500)

Will Jagy — Sat, 07 Jul 2012 11:13:35 -0700

Just about the only thing i remember from "QB VII" is the judge saying "we award the plaintiff one half-penny for his...reputation." The line may have been dubbed by Charles Gray, who was a good guy in You Only Live Twice, a bad guy in Diamonds are Forever, and the narrator in Rocky Horror Picture Show.

http://www.imdb.com/title/tt0071039/

http://www.imdb.com/title/tt0071039/trivia

Alex 'qubeat' comments on "What is the probability distribution of "reputation" ?" (19499)

Alex 'qubeat' — Sat, 07 Jul 2012 10:36:42 -0700

Log-normal distribution is often used in different areas http://en.wikipedia.org/wiki/Log-normal_distribution and may be justified as an approximation for a parameter that may be described as a composition of few different factors.

Qiaochu Yuan comments on "What is the probability distribution of "reputation" ?" (19497)

Qiaochu Yuan — Fri, 06 Jul 2012 23:28:21 -0700

I briefly studied such statistics for other StackExchange sites last summer and the conclusion I came to was that user activity was distributed approximately like a power law with exponent 2. I would expect this to be roughly true for reputation as well, at least for reputation gain per unit time.

Alex 'qubeat' comments on "What is the probability distribution of "reputation" ?" (19496)

Alex 'qubeat' — Fri, 06 Jul 2012 13:50:18 -0700

More than half users have unit reputation, for other users distribution of log(reputation) is here http://sdrv.ms/NJjezV.

WillieWong comments on "What is the probability distribution of "reputation" ?" (19468)

WillieWong — Tue, 03 Jul 2012 03:19:20 -0700

Holy cow! I'm the 1%! Unlike a certain Ken Jennings

Alexander Chervov comments on "What is the probability distribution of "reputation" ?" (19465)

Alexander Chervov — Tue, 03 Jul 2012 01:24:31 -0700

Just curiosity. Is it gaussian ? Or we have "heavy tail" (Joel David Hamkins, David Speyer) ?
(Probably it is worth to cut down users with very small reputation (<12) we will rest with 33% of users,
see http://mathoverflow.net/users?page=169 )
Only 4% of users has reputation more than 1000 - see http://mathoverflow.net/users?page=20 )
1% more than 5000 http://mathoverflow.net/users?page=5 )

Probably Guassian is bad idea, may be uniform is better ?
User reputation depends on 1) entrance time 2) "activity/quality" (roughly speaking reputation earned per day).
Probably 2) distributed by Gaussian, but 1) probably uniform - may be the same amount of new users appear every "month".
If 2) is Gaussian with small sigma, and 1) is uniform, then in total we get uniform distribution