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- Cauchy_distribution abstract "The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution.The simplest Cauchy distribution is called the standard Cauchy distribution. It is the distribution of a random variable that is the ratio of two independent standard normal variables and has the probability density functionIts cumulative distribution function has the shape of an arctangent function arctan(x):The Cauchy distribution is often used in statistics as the canonical example of a "pathological" distribution since both its mean and its variance are undefined. (But see the section Explanation of undefined moments below.) The Cauchy distribution does not have finite moments of order greater than or equal to one; only fractional absolute moments exist. The Cauchy distribution has no moment generating function.Its importance in physics is the result of it being the solution to the differential equation describing forced resonance. In mathematics, it is closely related to the Poisson kernel, which is the fundamental solution for the Laplace equation in the upper half-plane. In spectroscopy, it is the description of the shape of spectral lines which are subject to homogeneous broadening in which all atoms interact in the same way with the frequency range contained in the line shape. Many mechanisms cause homogeneous broadening, most notably collision broadening, and Chantler–Alda radiation. In its standard form, it is the maximum entropy probability distribution for a random variate X for which".
- Cauchy_distribution thumbnail Cauchy_pdf.svg?width=300.
- Cauchy_distribution wikiPageExternalLink c.html.
- Cauchy_distribution wikiPageExternalLink SEC294.
- Cauchy_distribution wikiPageID "7003".
- Cauchy_distribution wikiPageRevisionID "605444267".
- Cauchy_distribution boxWidth "300".
- Cauchy_distribution cdfImage "300".
- Cauchy_distribution hasPhotoCollection Cauchy_distribution.
- Cauchy_distribution id "p/c020850".
- Cauchy_distribution kurtosis Indeterminate_form.
- Cauchy_distribution mean Indeterminate_form.
- Cauchy_distribution mgf "does not exist".
- Cauchy_distribution name "Cauchy".
- Cauchy_distribution parameters Location_parameter.
- Cauchy_distribution parameters "γ > 0 scale".
- Cauchy_distribution pdfImage "(The purple curve is the standard Cauchy distribution)".
- Cauchy_distribution pdfImage "300".
- Cauchy_distribution skewness Indeterminate_form.
- Cauchy_distribution title "Cauchy Distribution".
- Cauchy_distribution title "Cauchy distribution".
- Cauchy_distribution type "density".
- Cauchy_distribution urlname "CauchyDistribution".
- Cauchy_distribution variance Indeterminate_form.
- Cauchy_distribution subject Category:Continuous_distributions.
- Cauchy_distribution subject Category:Power_laws.
- Cauchy_distribution subject Category:Probability_distributions.
- Cauchy_distribution subject Category:Probability_distributions_with_non-finite_variance.
- Cauchy_distribution subject Category:Stable_distributions.
- Cauchy_distribution type Abstraction100002137.
- Cauchy_distribution type Arrangement105726596.
- Cauchy_distribution type Cognition100023271.
- Cauchy_distribution type ContinuousDistributions.
- Cauchy_distribution type Distribution105729036.
- Cauchy_distribution type ProbabilityDistributionsWithNon-finiteVariance.
- Cauchy_distribution type PsychologicalFeature100023100.
- Cauchy_distribution type Structure105726345.
- Cauchy_distribution comment "The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution.The simplest Cauchy distribution is called the standard Cauchy distribution.".
- Cauchy_distribution label "Cauchy distribution".
- Cauchy_distribution label "Cauchy-Verteilung".
- Cauchy_distribution label "Cauchy-verdeling".
- Cauchy_distribution label "Distribución de Cauchy".
- Cauchy_distribution label "Distribuição de Cauchy".
- Cauchy_distribution label "Distribuzione di Cauchy".
- Cauchy_distribution label "Loi de Cauchy (probabilités)".
- Cauchy_distribution label "Rozkład Cauchy'ego".
- Cauchy_distribution label "Распределение Коши".
- Cauchy_distribution label "توزيع كوشي".
- Cauchy_distribution label "コーシー分布".
- Cauchy_distribution label "柯西分布".
- Cauchy_distribution sameAs Cauchyho_rozdělení.
- Cauchy_distribution sameAs Cauchy-Verteilung.
- Cauchy_distribution sameAs Distribución_de_Cauchy.
- Cauchy_distribution sameAs Loi_de_Cauchy_(probabilités).
- Cauchy_distribution sameAs Distribuzione_di_Cauchy.
- Cauchy_distribution sameAs コーシー分布.
- Cauchy_distribution sameAs Cauchy-verdeling.
- Cauchy_distribution sameAs Rozkład_Cauchy'ego.
- Cauchy_distribution sameAs Distribuição_de_Cauchy.
- Cauchy_distribution sameAs m.0207d.
- Cauchy_distribution sameAs Q726441.
- Cauchy_distribution sameAs Q726441.
- Cauchy_distribution sameAs Cauchy_distribution.
- Cauchy_distribution wasDerivedFrom Cauchy_distribution?oldid=605444267.
- Cauchy_distribution depiction Cauchy_pdf.svg.
- Cauchy_distribution isPrimaryTopicOf Cauchy_distribution.