= Mixed Poisson distribution
{title2=$S\mid\Theta\sim\operatorname{Poisson}(n\Theta)$}
{wiki}
A mixture of <Poisson distributions> over a nonnegative random intensity. With exposure $n>0$ and <prior density> $\pi(\theta)$, its <probability mass function> is $p_n(s)=\int_0^\infty e^{-n\theta}(n\theta)^s\pi(\theta)\,d\theta/s!$. A gamma mixing distribution gives a <negative binomial distribution>. Counts sharing the same latent intensity are <conditionally independent>, but generally dependent after mixing.
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