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

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...

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

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

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

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

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

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...

} 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...

Lorentzian may refer to Cauchy distribution, also known as the Lorentz distribution, Lorentzian function, or Cauchy–Lorentz distribution Lorentz lineshape (spectroscopy)...

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 application of the residue theorem One method can be used...

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

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

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

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

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

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 witch of Agnesi. As the probability density function of the Cauchy distribution, the witch of Agnesi has applications in probability theory. It also...

In probability theory, the "standard" Cauchy distribution is the probability distribution whose probability density function (pdf) is f ( x ) = 1 π (...

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...

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...

X has a standard Cauchy distribution. Then φX(t) = e−|t|. This is not differentiable at t = 0, showing that the Cauchy distribution has no expectation...

generated from data set drawn from a Cauchy distribution is bimodal. Examples of variables with bimodal distributions include the time between eruptions...

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

probability distribution functions are bell curves. Some bell shaped functions, such as the Gaussian function and the probability distribution of the Cauchy distribution...

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"...