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Mixture of Gamma, Poisson, and Pareto Distribution

  1. Sep 30, 2009 #1
    1. The problem statement, all variables and given/known data

    http://img24.imageshack.us/img24/8093/asss4.jpg [Broken]

    2. Relevant equations



    3. The attempt at a solution

    I know the following:

    [tex]f(X|\lambda\vartheta) = \frac{(\lambda\vartheta)^{k}e^{-\lambda\vartheta}}{k!}[/tex]

    [tex]g(\theta) = \frac{(h^{-1})^{h}}{\Gamma(h)}\lambda^{h - 1}e^{-(h^{-1})\lambda} [/tex]

    [tex]h(\lambda) = k\frac{\lambda^k}{\lambda^{k+1}}[/tex]

    I'm not sure if this is the correct Pareto distribution, since I've never encountered it before.

    [tex]f_X(x) = \int^{\infty}_0\int f(X|\lambda\vartheta) g(\lambda) h(\lambda) d \lambda d\theta[/tex]

    I'm also not sure what I should bind the pareto distribution to. Any help?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
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