+ Reply to Thread
Results 1 to 8 of 8

Thread: Poisson Distribution

  1. #1
    Points: 1,252, Level: 19
    Level completed: 52%, Points required for next Level: 48

    Posts
    13
    Thanks
    1
    Thanked 0 Times in 0 Posts

    Poisson Distribution




    Hi,

    I am using the Poission distribution to calculate probabillity for x = X.

    Poisson distribution is skewed to the right when lambda is small.

    Problem I have is that distribution for my x is rather skewed to the left when the expectancy.

    Is there any other known distribution I can use to calculate x = X, that is skewed to the left when expectancy for x is small?

    Is it is possible to use the binomial distribution where I use p as "skewness parameter" and n be 'expected value'/prob?

    Really appreciate som help for this.

  2. #2
    TS Contributor
    Points: 12,227, Level: 72
    Level completed: 45%, Points required for next Level: 223
    rogojel's Avatar
    Location
    I work in Europe, live in Hungary
    Posts
    1,470
    Thanks
    160
    Thanked 332 Times in 312 Posts

    Re: Poisson Distribution

    Hi,
    try the beta distribution - it can be nicely left skewed.

    e.g. http://keisan.casio.com/exec/system/1180573226 with parameters 10 and 3

    regards

  3. #3
    Points: 1,252, Level: 19
    Level completed: 52%, Points required for next Level: 48

    Posts
    13
    Thanks
    1
    Thanked 0 Times in 0 Posts

    Re: Poisson Distribution

    Thanks for your reply.

    My variable x is discrete and can only take whole values. Thats why I first thought Poission would be so great.

    Beta distributed variable can only take values between 0-1, unless I miss something here?

    How would you apply beta distribution to calculate probabillity that x >= 4 if expected value for x = 3,1 and x~beta(10, 3)?

  4. #4
    TS Contributor
    Points: 12,227, Level: 72
    Level completed: 45%, Points required for next Level: 223
    rogojel's Avatar
    Location
    I work in Europe, live in Hungary
    Posts
    1,470
    Thanks
    160
    Thanked 332 Times in 312 Posts

    Re: Poisson Distribution

    Well, I could normalize the variable -by dividing all values by the maximum - so instead of x>4 I would look at the probability of x>0.5 if the maximum value is 8, say.

    regards

  5. #5
    Devorador de queso
    Points: 95,705, Level: 100
    Level completed: 0%, Points required for next Level: 0
    Awards:
    Posting AwardCommunity AwardDiscussion EnderFrequent Poster
    Dason's Avatar
    Location
    Tampa, FL
    Posts
    12,931
    Thanks
    307
    Thanked 2,629 Times in 2,245 Posts

    Re: Poisson Distribution

    Can you post a histogram of your data?
    I don't have emotions and sometimes that makes me very sad.

  6. #6
    Points: 1,252, Level: 19
    Level completed: 52%, Points required for next Level: 48

    Posts
    13
    Thanks
    1
    Thanked 0 Times in 0 Posts

    Re: Poisson Distribution

    Hi,

    @rogojel - this still feels wrong since beta distributed variable is continuously and my variable is not. There is also no upper limit on my variable.

    What I am trying to do is to fit a distribution for a basketplayers points.

    Expected points for my player is easy;

    E(Points) = E(x) * 1 + E(y) * 2 + E(z) * 3

    I guess variance of points will be;

    Var(Points) = E(x) * 1^2 + E(y) * 2^2 + E(z) * 3^2

    Points will surely not follow a poisson distribution since Var(points) > E(Points). One way around this would be to do simulations of x, y and z and then simply count number of times points > some value. I would however prefer to calculate that chance analytic.

    Any advice please..

    Edit:
    Histogram of real data seems to be a bit skewed to left, so x, y and z are probably not following a poisson distribution at all.

  7. #7
    Super Moderator
    Points: 13,151, Level: 74
    Level completed: 76%, Points required for next Level: 99
    Dragan's Avatar
    Location
    Illinois, US
    Posts
    2,014
    Thanks
    0
    Thanked 223 Times in 192 Posts

    Re: Poisson Distribution

    In view of the above, I would point out to you that there are several variations of the basic Poisson discrete distribution. From what you are describing it appears to be a "Poisson-Stopped-Sum Distribution."

    That said, there are several variations of the (Poisson) distribution noted above. The general theory gives special forms such as: Hermite, Neyman Type A, Ploya-Aeppli, and the Lagrangian-Poisson distributions.

    For further details see: Johnson, N., Kotz, S, & Kemp, A. W. (1993). Univariate Discrete Distributions (2-nd edition), Wiley & Sons, New York.

  8. The Following 2 Users Say Thank You to Dragan For This Useful Post:

    rogojel (02-10-2017), samot79 (02-20-2017)

  9. #8
    Points: 1,252, Level: 19
    Level completed: 52%, Points required for next Level: 48

    Posts
    13
    Thanks
    1
    Thanked 0 Times in 0 Posts

    Re: Poisson Distribution


    Sorry for my late reply.

    Thanks for your reply Dragan, I have not heard of "Poisson-Stopped-Sum" and will definitly look it up.
    Last edited by samot79; 02-20-2017 at 05:15 AM.

+ Reply to Thread

           




Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts






Advertise on Talk Stats