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Math Help - gamma distribution

  1. #1
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    gamma distribution

    you get the gamma function which is an integral in the PDF of the gamma distribution.

    How do you integrate the gamma PDF from x=0 to x=1; when you have the gamma function also in the PDF to integrate

    Please help.
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  2. #2
    Moo
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    The gamma function taken at an integer value is just the factorial : Gamma(n)=(n-1)!

    However, it's not the main problem. If you're looking for a general formula of the integral of this pdf between 0 and 1, you won't find it. It can only be expressed in terms of incomplete gamma function. I suggest you have a look at the wikipedia page about the gamma distribution !
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  3. #3
    MHF Contributor matheagle's Avatar
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    The constants \Gamma(\alpha) and \beta^{\alpha} are in the density so that the density integrates to one.

    f(x)={1\over \Gamma(\alpha)\beta^{\alpha}}x^{\alpha-1}e^{-x/\beta} where x>0.

    Do not confuse the gamma function \Gamma(\alpha) with the gamma density X\sim \Gamma(\alpha,\beta)
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