= Zero claim sizes in a compound Poisson representation
{title2=$\lambda_+=\lambda\mathbb P(X>0)$}
If zero-sized claims are allowed, a <compound Poisson distribution> count parameter need not be unique. <Poisson thinning> of zero claims gives the displayed positive-claim count parameter and the conditional <claim size> <probability distribution> given $X>0$, without changing the aggregate. If no positive claims occur, the aggregate is identically zero. This matters when representing a finite weighted sum of <Poisson distribution> counts whose coefficients include zero.
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