= Natural exponential family
{title2=$f_\theta(y)=h(y)e^{\theta^Ty-\kappa(\theta)}$}
{wiki}
A natural <exponential family> uses its observation vector itself as the canonical <sufficient statistic>. Its <cumulant function> is $\kappa(\theta)=\log\int h(y)e^{\theta^Ty}\,d\nu(y)$ and its <natural parameter space> consists of parameters for which this integral is finite. On the interior, differentiating gives <mean parameter of an exponential family> $\nabla\kappa$ and <covariance matrix> $\nabla^2\kappa$.
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