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Math Help - Estimation

  1. #1
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    Estimation

    suppose that the prior distribution of some parameter theta is a gamma distribution for which the mean is 10 and the variance is 5. determine the prior pdf of theta
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  2. #2
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    Unless there is something I'm missing, there doesn't seem to be a question here. They tell you the distribution of theta. You know the mean and variance of a gamma; solve for the usual parameters.
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  3. #3
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    Consider parameters \displaystyle k, \theta such that \displaystyle \mu = k\theta and \displaystyle \sigma^2 =k\theta^2

    You are told \displaystyle k\theta =10 , k\theta^2 = 5 solve for \displaystyle k, \theta

    The pdf will then be \displaystyle P(x) =\frac{x^{k-1}e^{\frac{-x}{\theta}}}{\Gamma (k)\theta^k}
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  4. #4
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    is that really all there is to it?
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  5. #5
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    That's what I read.

    The whole 'prior' thing made it sounds bigger than what it was. But everything described was prior so it all links together easily.
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