Legendre transform of a cumulant-generating function
= Legendre transform of a cumulant-generating function
{title2=$\psi^*$}
The Legendre transform is the convex function
$$
\psi^*(x)=\sup_{\theta\in\mathbb R}\{\theta x-\psi(\theta)\}.
$$
= Legendre transform of a cumulant-generating function
{title2=$\psi^*$}
The Legendre transform is the convex function
$$
\psi^*(x)=\sup_{\theta\in\mathbb R}\{\theta x-\psi(\theta)\}.
$$