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Math Help - Conjugate prior for gamma distribution

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    Question Conjugate prior for gamma distribution

    Conjugate prior for the gamma distribution (with parameters \alpha,\beta) is supposed to be:

    \frac{1}{Z}\frac{p^{\alpha -1}e^{-\beta q}}{{\gamma(\alpha)}^r \beta^{-\alpha s}}

    with the hyperparameters, p, q, r, s when both shape parameter and the scale parameter are known.

    Here I have a gamma distributed variable x, with parameters \alpha and \beta. And I have a conjugate prior with hyperparemeters p,q,r and s. Can anybody help me solving the integration over the parameters \alpha,\beta?

    \int_{a,b} \frac{1}{\gamma(\alpha)\beta^\alpha} x^{\alpha-1} e^{-x/\beta} \frac{1}{Z}\frac{p^{\alpha -1}e^{-\beta q}}{{\gamma(\alpha)}^r \beta^{-\alpha s}} d{a,b}

    It has been a long time since I took a calculus class in the university, so I don't remember much about integration solving. Any assistance will be appreciated!
    Last edited by malaguena; February 14th 2011 at 01:03 AM.
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