Lévy metric

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 Pierre Lévy.

Definition

Let F, G : mathbb{R} o [0, + infty) be two cumulative distribution functions. Define the Lévy distance between them to be: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} }.

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).

ee also

* Lévy-Prokhorov metric
* Wasserstein metric

References

*


Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • Levy — or Lévy may refer to:*Levy County, Florida * Forced labor; see conscription or national service * An imposition of a tax * A judicial remedy where the property of a judgment debtor is seized for public sale to satisfy a monetary judgment * An… …   Wikipedia

  • Lévy-Prokhorov metric — In mathematics, the Lévy Prokhorov metric (sometimes known just as the Prokhorov metric) is a metric (i.e. a definition of distance) on the collection of probability measures on a given metric space. It is named after the French mathematician… …   Wikipedia

  • Metric Structures for Riemannian and Non-Riemannian Spaces —   Author(s) Misha Gromov …   Wikipedia

  • Metric Hosiery Company — The Metric Hosiery Company was a New York City firm which lost out to a rival business, when E. J. Korvette stores transferred their buying of hosiery to Maro Industries. Gabriel I. Levy, a Yonkers lawyer, filed a $4.6 million damage suit in 1966 …   Wikipedia

  • Wasserstein metric — In mathematics, the Wasserstein (or Vasershtein) metric is a distance function defined between probability distributions on a given metric space M. Intuitively, if each distribution is viewed as a unit amount of dirt piled on M, the metric is the …   Wikipedia

  • Paul Pierre Lévy — For other uses, see Paul Lévy (disambiguation). Paul Lévy Paul Pierre Lévy Born …   Wikipedia

  • List of mathematics articles (L) — NOTOC L L (complexity) L BFGS L² cohomology L function L game L notation L system L theory L Analyse des Infiniment Petits pour l Intelligence des Lignes Courbes L Hôpital s rule L(R) La Géométrie Labeled graph Labelled enumeration theorem Lack… …   Wikipedia

  • Lp space — In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p norm for finite dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford Schwartz 1958, III.3),… …   Wikipedia

  • Carbon tax — Part of a series on Green economics Concepts …   Wikipedia

  • Endgame tablebase — A typical interface for querying a tablebase An endgame tablebase is a computerized database that co …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”