= Compound Poisson distribution
{title2=$S=\sum_{i=1}^N X_i,\quad N\sim\operatorname{Poisson}(\lambda)$}
{wiki}
The law of a sum of independent identically distributed claims with an independent <Poisson distribution> count of parameter $\lambda$. If the claim <moment-generating function> is $M_X$, the aggregate transform is $\exp(\lambda(M_X(r)-1))$ wherever finite. It has an atom at zero when the claims are positive. This is the fixed-time law of a <Compound Poisson process>.
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