Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Gamma Poisson Mixture with finite Gamma

  1. Nov 30, 2012 #1
    Dear all

    I am working with a Gamma-Poisson mixture distribution where (and this is not usual) the support of the Gamma distribution (in fact, I am able to restrict to the neg exponential instead of the Gamma...) is finite, e.g. [0,1].
    I would like to derive the mean and a Likelihood function.

    Normally, you end up with a negative binomial distribution for the above mixture, i.e. mean and Likelihood are straightforward.
    But due to the finite support I end up with an incomplete gamma function in my expressions and I am not able to solve the integral "nicely" and give a closed expression for the mean.

    My question: Do you have any experience with such a right truncated gamma poisson mixture? Or any hints where I could find some similar computations that could be helpful?

    Many thanks in advance,

  2. jcsd
  3. Dec 1, 2012 #2
    It begs the question, do you *have* to use a truncated distribution? Other models for the Poisson frequency such as uniform, triangular or beta might be easier to work with.

    Either way you may need numerical methods for integration and/or optimisation, which itself is not a problem, but the complicated normalisation constants in truncated distributions tend to make the calculations all the more unstable.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook