Cauchy distribution
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- Statistics LibreTexts - The Cauchy Distribution
- Nagoya University - Graduate School of Mathematics - Cauchy Distribution
- National Center for Biotechnology Information - PubMed Central - The Cauchy Distribution in Information Theory
- National Institute of Standards and Technology - Cauchy Distribution
- Stanford University - Cauchy Distribution
- Academia - The generalized Cauchy family of distributions with applications
- Also known as:
- Cauchy-Lorentz distribution
- Related Topics:
- distribution function
- On the Web:
- Nagoya University - Graduate School of Mathematics - Cauchy Distribution (Oct. 11, 2024)
Cauchy distribution, in statistics, continuous distribution function with two parameters, first studied early in the 19th century by French mathematician Augustin-Louis Cauchy. It was later applied by the 19th-century Dutch physicist Hendrik Lorentz to explain forced resonance, or vibrations. At a glance, the Cauchy distribution may look like the normal distribution, but its “tails” do not taper off nearly as quickly as those of the normal distribution.
With location parameter t (the median for the distribution, it does not have a mean) and scale parameter s, the probability density function for the Cauchy distribution is 
The case in which s = 1 and t = 0 is known as the standard Cauchy distribution, which is given by 