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    Negativ Binomial distribution




    I am trying to count number of occurrence for variable X. I have considered X as Poisson distributed since this sounds like a Poisson process. But there seems to be overdispersion in the distribution.

    Poisson distribution will give me unrealistic probabilities when x is much higher than E(X).

    If X -Poi(10) than P(X > 14) = 0,083. I did this to compare with NB later.

    I have read that the Negative Binomial distribution (NB) can adjust for overdispearson. But I am not sure if I am doing this correct, and I also have problem to interpret the result I will have. My scenario does not really have a number of tries nor a chance to success.

    As I understand it, the random variable in NB is number of failures and not number of successes.

    Let Y = number of failures. And X, still my variable, number of successes. I have estimated p = 0.2.

    Number of tries has to be 10/0.2 = 50 since I know E(X) = 10 and there E(Y) has to be = 40. 50-10.

    Now I want to search P(X > 14) using NB. Since I wont have a probability distribution for X I have to search for;

    P(Y<=40) where Y -NB(40, 0.2) and X >14 = 0,121.

    Am I doing this right? Would you have the same answer?

    So the interpretation will be;

    Probability that I will have at least 15 successes within 50 tries, when expected number of failures is = 40

    I am doing my calculations in Excel. Formula looks like this;

    NEGBINOM(number of failures; number of success; probability success; cumulative)

    for this case;
    NEGBINOM(40;15;0.2;TRUE)

    I would really appreciate if someone could help me understand, and let me know if I am doing anything wrong.

  2. #2
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    Re: Negativ Binomial distribution

    Hmm, this is not an area I am overly familiar with but I enjoy learning.

    The one spot that catches me is using the 0.2 for probability when it is your actual probability. Then you test your actual data with it. Not sure if that is right, but as I said I am unexperienced in this area.
    Stop cowardice, ban guns!

  3. #3
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    Re: Negativ Binomial distribution


    Also new for me, so learning here as well

    Come this far to understand what im doing is wrong since Excel does not give distribution for my variabel X.

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