In mathematics, the Lévy metric is a metric on the space of cumulative distribution functions of one-dimensional random variables.
It is a special case of the Lévy–Prokhorov metric, and is named after the French mathematician Paul Lévy.
Define the Lévy distance between them to be Intuitively, if between the graphs of F and G one inscribes squares with sides parallel to the coordinate axes (at points of discontinuity of a graph vertical segments are added), then the side-length of the largest such square is equal to L(F, G).
A sequence of cumulative distribution functions
weakly converges to another cumulative distribution function