= Fixed-size negative binomial generalized linear model
{title2=$\operatorname{Var}(Y)=\mu+\mu^2/\theta$}
For known size $\theta>0$, the <negative binomial distribution> is an <exponential family> with natural parameter $\eta=\log[\mu/(\theta+\mu)]<0$ and cumulant $b_\theta(\eta)=-\theta\log(1-e^\eta)$. A <generalized linear model> can use a <logarithmic link function> for its mean, even though that link is not canonical. Jointly estimating the size changes the family and <variance function>, requiring additional updates beyond a single fixed-family GLM fit; this is what `MASS::glm.nb` does.
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