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Math Help - Gamma Distribution

  1. #1
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    Gamma Distribution

    Dear all,

    I want to use Gamma distribution. It seems that there must be some constraints on Gamma distribution parameters, because:

    1- the probability values in some cases become greater than one!

    2-if beta is small and alpha is larges => beta^alpha=0 => probability=Inf

    3-if alpah is larges => gamma(alpha)=Inf => probability=NaN

    Dose anybody knows the constraints and what I can do in these situations?

    Thanks
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  2. #2
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    Quote Originally Posted by nhabibi View Post
    Dear all,

    I want to use Gamma distribution. It seems that there must be some constraints on Gamma distribution parameters, because:

    1- the probability values in some cases become greater than one!

    2-if beta is small and alpha is larges => beta^alpha=0 => probability=Inf

    3-if alpah is larges => gamma(alpha)=Inf => probability=NaN

    Dose anybody knows the constraints and what I can do in these situations?

    Thanks
    I would have thought all you need is here: http://en.wikipedia.org/wiki/Gamma_distribution.

    I'm not sure where your trouble is. You'll need to be more specific .... exactly what parameter values are causing you trouble?
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    I would have thought all you need is here: Gamma distribution - Wikipedia, the free encyclopedia.

    I'm not sure where your trouble is. You'll need to be more specific .... exactly what parameter values are causing you trouble?

    Mr. Fantastic,

    -When alpha is large => gamma(alpha)=Inf => probaility=NaN
    for example: (x=1.5385, alpha=213.958, beta=0.0063)
    -If beta is small and alpha is large
    for example: (alpha=159, beta=0.0072).
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  4. #4
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    Quote Originally Posted by nhabibi View Post
    Mr. Fantastic,

    -When alpha is large => gamma(alpha)=Inf => probaility=NaN
    for example: (x=1.5385, alpha=213.958, beta=0.0063)
    -If beta is small and alpha is large
    for example: (alpha=159, beta=0.0072).
    Sorry but I still can't make sense of your problem. What are you trying to do with the gamma distribution?

    There is no theoretical problem if \alpha > 0 and \beta > 0. But if you're using technology to calculate the probabilities, then such values might cause technical problems.
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