The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz...

statistics, a wrapped Cauchy distribution is a wrapped probability distribution that results from the "wrapping" of the Cauchy distribution around the unit...

log-Cauchy distribution is a probability distribution of a random variable whose logarithm is distributed in accordance with a Cauchy distribution. If...

{\displaystyle \ \nu =1\ } the Student's t distribution t ν {\displaystyle t_{\nu }} becomes the standard Cauchy distribution, which has very "fat" tails; whereas...

Breit–Wigner distribution may refer to: Cauchy distribution, also known as the Lorentz distribution or the (non-relativistic) Breit–Wigner distribution Relativistic...

Mises distribution The wrapped normal distribution The wrapped exponential distribution The wrapped Lévy distribution The wrapped Cauchy distribution The...

A normal distribution is sometimes informally called a bell curve. However, many other distributions are bell-shaped (such as the Cauchy, Student's...

dx=\pi .} The Shannon entropy of the Cauchy distribution is equal to ln(4π), which also involves π. The Cauchy distribution plays an important role in potential...

In mathematics, the Cauchy principal value, named after Augustin-Louis Cauchy, is a method for assigning values to certain improper integrals which would...

Lorentzian may refer to Cauchy distribution, also known as the Lorentz distribution, Lorentzian function, or Cauchy–Lorentz distribution Lorentz transformation...

normal distribution extreme events are less likely than for fat-tailed distributions. Fat-tailed distributions such as the Cauchy distribution (and all...

Cauchy–Davenport theorem Cauchy determinant Cauchy distribution Log-Cauchy distribution Wrapped Cauchy distribution Cauchy elastic material Cauchy's equation...

family of distribution as X, in the following cases: Cauchy distribution, F distribution, log logistic distribution. Examples: If X is a Cauchy (μ, σ) random...

John Tukey. Consider the mixture distribution defined by F(x)   =   (1 − 10−10) (standard normal) + 10−10 (standard Cauchy). The mean of i.i.d. observations...

the ratio Z = X/Y is a ratio distribution. An example is the Cauchy distribution (also called the normal ratio distribution), which comes about as the ratio...

complex-valued function along a curve in the complex plane; application of the Cauchy integral formula; and application of the residue theorem. One method can...

student t distribution, the skewed Cauchy distribution, the Laplace distribution, the uniform distribution, the normal distribution, and the Cauchy distribution...

distribution, and α = 1 {\displaystyle \alpha =1} to the Cauchy distribution. The distributions have undefined variance for α < 2 {\displaystyle \alpha...

condition Cauchy's convergence test Cauchy (crater) Cauchy determinant Cauchy distribution Cauchy's equation Cauchy–Euler equation Cauchy's functional...

theory, a Cauchy process is a type of stochastic process. There are symmetric and asymmetric forms of the Cauchy process. The unspecified term "Cauchy process"...

} With k = 1, the distributions of X and 1 / X are identical (X is then Cauchy distributed (0,1)). If k > 1 then the distribution of 1 / X is bimodal...

In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions...

In mathematics, Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a...

generalisation of the Laplace distribution to function spaces Cauchy distribution, also called the "Lorentzian distribution", ie the Fourier transform of...

associated probability distribution is the normal distribution. They also include the Cauchy process. For the symmetric Cauchy process, the associated...

of the distribution of step sizes. He used the term Cauchy flight for the case where the distribution of step sizes is a Cauchy distribution, and Rayleigh...

robustness and higher efficiency for mixed distributions and heavy-tailed distribution (like the Cauchy distribution), at the cost of lower efficiency for...

function (infinitesimal version of Cauchy distribution) explicitly appears in an 1827 text of Augustin-Louis Cauchy. Siméon Denis Poisson considered the...

distributions (the Cauchy distribution) obey Benford's law. Although the half-normal distribution does not obey Benford's law, the ratio distribution...

the log-gamma distribution; the Fréchet distribution; the q-Gaussian distribution; the log-Cauchy distribution, sometimes described as having a "super-heavy...