A gamma approximation to the Bayesian posterior distribution of a   discrete parameter of the Generalized Poisson model
  Let $X$ have a Generalized Poisson distribution with mean $kb$, where $b$ is a known constant in the unit interval and $k$ is a discrete, non-negative parameter. We show that if an uninformative uniform prior for $k$ is assumed, then the posterior distribution of $k$ can be approximated using the gamma distribution when $b$ is small. 
T. F. Khang
stat.ME