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| In [[mathematics]], the '''Lévy metric''' is a [[metric (mathematics)|metric]] on the space of [[cumulative distribution function]]s of one-dimensional [[random variable]]s. It is a special case of the [[Lévy–Prokhorov metric]], and is named after the French mathematician [[Paul Lévy (mathematician)|Paul Lévy]].
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| ==Definition==
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| Let <math>F, G : \mathbb{R} \to [0, 1]</math> be two cumulative distribution functions. Define the '''Lévy distance''' between them to be
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| :<math>L(F, G) := \inf \{ \varepsilon > 0 | F(x - \varepsilon) - \varepsilon \leq G(x) \leq F(x + \varepsilon) + \varepsilon \mathrm{\,for\,all\,} x \in \mathbb{R} \}.</math>
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| 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'').
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| ==See also==
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| * [[Càdlàg]]
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| * [[Lévy–Prokhorov metric]]
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| * [[Wasserstein metric]]
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| ==References==
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| * {{springer|author=V.M. Zolotarev|id=l/l058310|title=Lévy metric}}
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| {{DEFAULTSORT:Levy metric}}
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| [[Category:Measure theory]]
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| [[Category:Metric geometry]]
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| [[Category:Probability theory]]
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Latest revision as of 21:31, 18 December 2014
The name of the author is Numbers. What I love performing is doing ceramics but I haven't made a dime with it. Since she was eighteen she's been operating as a meter reader but she's always needed her own business. North Dakota is our beginning place.
Feel free to surf to my weblog; home std test kit