Unnormalized Hellinger distance
= Unnormalized Hellinger distance
{title2=$h(P,Q)=\|\sqrt p-\sqrt q\|_{L^2(\nu)}$}
= Unnormalised Hellinger distance
{synonym}
The <Hellinger distance> convention $h^2(P,Q)=\int(\sqrt p-\sqrt q)^2\,d\nu$, with no factor $1/2$, for densities under a common dominating measure. Its range is $[0,\sqrt2]$. This convention makes $\operatorname{TV}(P,Q)\leq h(P,Q)\leq\sqrt{\operatorname{KL}(P,Q)}$ hold with the displayed constants.