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Math Help - Inverse Gamma Distribution

  1. #1
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    Inverse Gamma Distribution

    For the Inverse Gamma Distribution, show that

    Var(Y) = Beta^2 / {[(alpha-1)^2]*[alpha-2]} , alpha > 2.
    Last edited by mr fantastic; August 27th 2009 at 09:38 PM. Reason: Added the distribution type to main body of post
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  2. #2
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    Quote Originally Posted by ynotidas View Post
    For the Inverse Gamma Distribution, show that

    Var(Y) = Beta^2 / {[(alpha-1)^2]*[alpha-2]} , alpha > 2.
    Where do you get stuck? Please show the working you've done.
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  3. #3
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    I get stuck in the beginning, should I start off with V(Y)=E(Y^2)-Mu^2?
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  4. #4
    MHF Contributor matheagle's Avatar
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    show your work
    I need to see the density you're using.
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    Quote Originally Posted by ynotidas View Post
    I get stuck in the beginning, should I start off with V(Y)=E(Y^2)-Mu^2?
    Start by computing E(Y^2), with a density (or whatever alternative definition your teacher has choosen):

    f(y;\alpha,\beta)=\frac{\beta^{\alpha}}{\Gamma(\al  pha)}(1/y)^{\alpha} exp(-\beta/y)

    You will not need to do the integral, as with a bit of jiggery-pokery you should be able to rearrange the integrand to be a multiple of the density of another Inverse Gamma distribution.

    CB
    Last edited by CaptainBlack; August 28th 2009 at 12:31 AM.
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  6. #6
    MHF Contributor matheagle's Avatar
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    But the beta could be in the denominator instead
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  7. #7
    Grand Panjandrum
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    Quote Originally Posted by matheagle View Post
    But the beta could be in the denominator instead
    It hardly matters, with whatever definition the OP has of the density (or rather of what the parameters are) the basic method will work, and as we are not going to do it for them there is no problem in presenting the method for one version, it will work with the other/s though with a different final answer. It just gives them an additional opportunity to contribute to the solution themselves.

    CB
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