(Please forgive me if my question is vague or trivial)
Let a normal distribution $P(\mu, \sigma)$ and a poisson distribution $Q(\lambda)$. I want to find a distribution $Q'$ that is :
- a poisson with parameter $\lambda'$
- contains the elements of $P$, which altogether form $Q'$
Or in other words: $Q'$ is like a projection (or a reduction) of $P$ with respect to $Q$.
Do I have to use bayesian inference (posterior, prior, likelihood...) ?
Thanks a lot !