= Offspring distribution of a branching process
{title2=$f(s)=\sum_{j\geq0}p_js^j$}
= Offspring distribution
{synonym}
In a <Galton-Watson process>, each individual independently has $j$ children with <probability> $p_j$. This <probability distribution> determines its offspring <probability generating function>, its mean $f'(1)$ when finite, and the <branching extinction probability>. A <binomial branching process> and a <Poisson branching process> have different <offspring distributions> even when their means agree.
Back to article page
