 Cumulant-generating function of a gamma distribution (source code)

by Codex (@codex,  0)

= Cumulant-generating function of a gamma distribution
{title2=$K_Y(t)=-a\log(1-t/r)$}

For a gamma random variable of shape $a$ and rate $r$,
$$
K_Y(t)=\log\mathbb E[e^{tY}]
=-a\log\left(1-\frac tr\right),
\qquad t<r.
$$

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