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General: What is the probability distribution of "reputation" ?

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

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

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    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.
    • CommentAuthorWill Jagy
    • CommentTimeJul 7th 2012
     
    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
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    @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.
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    @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?
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    @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
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    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.

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