Zero-truncated claim-count distribution
= Zero-truncated claim-count distribution
{title2=$G_{N\mid N>0}(z)=\frac{G_N(z)-G_N(0)}{1-G_N(0)}$}
For a nonnegative integer claim count $N$ with $p=\mathbb P(N=0)<1$, the conditional law given $N>0$ has masses $\mathbb P(N=n)/(1-p)$ for $n\ge1$. Its <probability generating function> is $(G_N(z)-p)/(1-p)$. Truncation at zero is meaningful only when the positive-count event has positive probability.