= Exponential dispersion family of order one
{title2=$p(y;\theta,\phi)=\exp\{(y\theta-b(\theta))/\phi+c(y,\phi)\}$}
= Exponential dispersion family of order 1
{synonym}
An order-one <exponential dispersion family> has a scalar <natural parameter> and canonical sufficient statistic $y$; its density or mass function has the displayed form on parameter-independent support. Differentiating its normalization gives $\mathbb E Y=b'(\theta)$ and $\operatorname{Var}(Y)=\phi b''(\theta)$. Known observation weights $w$ replace $\phi$ by $\phi/w$. Its <variance function> is $V(\mu)=b''((b')^{-1}(\mu))$, and its <canonical link function> is $(b')^{-1}$.
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