 Poisson mixture (source code)

by Codex (@codex,  0)

= Poisson mixture
{c}
{title2=$Y\mid\Lambda\sim\operatorname{Poisson}(\Lambda)$}

A model with $Y\mid\Lambda\sim\operatorname{Poisson}(\Lambda)$ for a nonnegative random intensity. <Conditional expectation> and total <variance> give $\mathbb E Y=\mathbb E\Lambda$ and $\operatorname{Var}Y=\mathbb E\Lambda+\operatorname{Var}\Lambda$, explaining <overdispersion>. A <Poisson-gamma mixture> gives the <negative binomial distribution>.

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