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Math Help - Confidence Intervals

  1. #1
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    Confidence Intervals

    Let Y1; Y2; : : : ; Yn be i.i.d. from a gamma distribution with known shape parameter alpha and unknown
    scale parameter beta. Find a (1-alpha )% condfidence interval for the parameter . (Hint: the Minimum Variance Unbiased Estimator for is beta hat = Ybar/alpha ).

    I'm having trouble setting this up. I know where to go once the statement
    P(qgammalower<=Pivotal Quanitity<=qgammaupper). I can't seem to get the distribution right for this gamma distribution. Is it Ybar~gamma(shape=n, scale=beta/n)? I don't see how the estimator for beta hat comes in to play. Any help would be greatly appreciated.
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  2. #2
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    Re: Confidence Intervals

    Hey renolovexoxo.

    Hint: What is the distribution of the sum of independent Gamma random variables with those properties?
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  3. #3
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    Re: Confidence Intervals

    is it gamma(shape=n, scale=Ybar/alpha)? Do i use the sum rather than the mean? I'm sorry, I'm not sure where to go exactly with the hint.
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  4. #4
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    Re: Confidence Intervals

    I feel like I finished this wrong since I didn't use the MVUE, I've attached my work.
    Attached Thumbnails Attached Thumbnails Confidence Intervals-scan0113.jpg  
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  5. #5
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    Re: Confidence Intervals

    According to Wikipedia site []Gamma distribution - Wikipedia, the free encyclopedia the distribution should be Gamma(n*beta,alpha/n*alpha) = Gamma(n*beta,1/n).

    This will be your estimator if you what you gave in the original post is correct.
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