Cauchy distribution

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In mathematics, the Cauchy-Lorentz distribution (after Augustin-Louis Cauchy and Hendrik Lorentz) is a continuous probability distribution with two parameters: a location parameter and a scale parameter.[1][2] As a probability distribution, it is usually called a Cauchy distribution. Physicists know it as a Lorentz distribution.

When the location parameter is 0 and the scale parameter is 1, the probability density function of the Cauchy distribution reduces to . This is called the standard Cauchy distribution.[2]

The Cauchy distribution is used in spectroscopy to describe the spectral lines found there, and to describe resonance.[3] It is also often used in statistics as the canonical example of a "pathological" distribution, since both its mean and its variance are undefined. The look of a Cauchy distribution is similar to that of a normal distribution, though with longer "tails".[4]

Related pages[change | change source]

References[change | change source]

  1. "List of Probability and Statistics Symbols". Math Vault. 2020-04-26. Retrieved 2020-10-13.
  2. 2.0 2.1 "1.3.6.6.3. Cauchy Distribution". www.itl.nist.gov. Retrieved 2020-10-13.
  3. The Lorentz Oscillator Model
  4. "Cauchy distribution | mathematics". Encyclopedia Britannica. Retrieved 2020-10-13.