chi-squared divergence

For distributions $P$ and $Q$ with $P\ll Q$, the ${\chi }^2$-distance is

$${\chi }^2(P,Q)={\int }_{q>0}\frac{p^2}{q}(x)\text{d}x-1={\int }_{q>0}\frac{(p(x)-q(x){)}^2}{q(x)}\text{d}x.$$