I'm trying to compute a maximum likelihood of compound Poisson gamma distribution in R. The distribution is defined by $ \sum_{j=1}^{N} Y_j $ where $Y_n$ is i.i.d sequence independent $\operatorname{gamma}(k,\theta)$ values and $N$ is a Poisson distribution with parameter $\beta$. I'm trying to estimate this parameters $\theta$ and $\beta$ without luck. Thanks in advance.

  • 2
    $\begingroup$ Have you tried EM? This is a latent variable model. $\endgroup$ – Xi'an Nov 13 '18 at 21:50
  • $\begingroup$ I used the optim() function, but that does not work! $\endgroup$ – lina bina Nov 13 '18 at 22:11
  • $\begingroup$ You observed $Y_j$. $\theta$ and $\beta$ are unknown parameters you want to estimate. How about $N$ and $k$? $\endgroup$ – user158565 Nov 13 '18 at 22:25
  • 6
    $\begingroup$ N is observable or not observable? k is known parameter or unknown parameter? $\endgroup$ – user158565 Nov 13 '18 at 22:47
  • 1
    $\begingroup$ Please add a minimal example and explain what is wrong with the results $\endgroup$ – Juho Kokkala Aug 9 '19 at 19:57