Definitions for cauchy distribution
cauchy dis·tri·bu·tion

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1. Cauchy distributionnoun

   A continuous probability distribution such that its probability density function is

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1. Cauchy distribution

   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 Cauchy distribution f ( x ; x 0 , γ ) {\displaystyle f(x;x_{0},\gamma )} is the distribution of the x-intercept of a ray issuing from ( x 0 , γ ) {\displaystyle (x_{0},\gamma )} with a uniformly distributed angle. It is also the distribution of the ratio of two independent normally distributed random variables with mean zero. The Cauchy distribution is often used in statistics as the canonical example of a "pathological" distribution since both its expected value and its variance are undefined (but see § 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. In mathematics, it is closely related to the Poisson kernel, which is the fundamental solution for the Laplace equation in the upper half-plane. It is one of the few distributions that is stable and has a probability density function that can be expressed analytically, the others being the normal distribution and the Lévy distribution.

WikidataRate this definition:0.0 / 0 votes

1. Cauchy distribution

   The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution, Cauchy–Lorentz distribution, Lorentz function, or Breit–Wigner distribution. The simplest Cauchy distribution is called the standard Cauchy distribution. It has the distribution of a random variable that is the ratio of two independent standard normal random variables. This has the probability density function Its 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. Both its mean and its variance are undefined. 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

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Numerology

1. Chaldean Numerology

   The numerical value of cauchy distribution in Chaldean Numerology is: 5

2. Pythagorean Numerology

   The numerical value of cauchy distribution in Pythagorean Numerology is: 5

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Cauchy_Distribution
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Cauchy_Distribution
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=cauchy distribution