# Mixture of Gamma, Poisson, and Pareto Distribution

1. Sep 30, 2009

### cse63146

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:

$$f(X|\lambda\vartheta) = \frac{(\lambda\vartheta)^{k}e^{-\lambda\vartheta}}{k!}$$

$$g(\theta) = \frac{(h^{-1})^{h}}{\Gamma(h)}\lambda^{h - 1}e^{-(h^{-1})\lambda}$$

$$h(\lambda) = k\frac{\lambda^k}{\lambda^{k+1}}$$

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

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

I'm also not sure what I should bind the pareto distribution to. Any help?

Last edited by a moderator: May 4, 2017