Lévy metric
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.
Definition
Let be two cumulative distribution functions. 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).
gollark: Ah, it does expose this, great.
gollark: Maybe I need to somehow tell the API to only read one frame?
gollark: I made it write to stdout and not the actual output file and it seems like it's actually parsing *multiple* bits somehow.
gollark: I used `tail` to select the start of a zstandard stream in the archive, and then `zstd`ed it.
gollark: On this datoid, I mean.
References
- V.M. Zolotarev (2001) [1994], "Lévy metric", Encyclopedia of Mathematics, EMS Press
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