A metric for convergence in distribution (Q1962182)

Let \(\mathcal P\) denote the set of all probability distributions in \({\mathbb R}^k\). The author shows that \[ \gamma (F,G)=\sqrt {\iint \exp\{-\tfrac 18 \|x-y \|^2\} [dF(x) dF(y)-2 dF(x) dG(y)+dG(x) dG(y)]} \] defines a metric for convergence in distribution in \(\mathcal P\), where \(F,G\) are elements of \(\mathcal P,\) and \(\|x-y\|\) is the Euclidean distance between \(x\) and \(y\). Theoretical properties and computational advantages (with potential applications) of \(\gamma\) are discussed.