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...

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

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

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

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...

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

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

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

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

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

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

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

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

} 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...

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...

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

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

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

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

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...

Cauchy distribution Log-Cauchy distribution Wrapped Cauchy distribution Cauchy–Euler equation Cauchy's functional equation Cauchy filter Cauchy formula...

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...

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

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...

{\displaystyle q\equiv e^{i\pi \tau }.} The pdf of the wrapped Cauchy distribution (WC) is: W C ( θ ; θ 0 , γ ) = ∑ n = − ∞ ∞ γ π ( γ 2 + ( θ + 2 π...

the Cauchy distribution or some Pareto distributions (α<1) will not converge as n becomes larger; the reason is heavy tails. The Cauchy distribution and...