Bhattacharyya distance
= Bhattacharyya distance
{c}
{title2=$D_B(P,Q)=-\ln B(P,Q)$}
The <Bhattacharyya distance> is the negative <natural logarithm> of the <Bhattacharyya coefficient>, with $-\ln0=\infty$. It is zero for identical <probability distributions> and infinite for disjoint <probability supports>. Despite the name, it need not satisfy the <triangle inequality> required of a <metric>.