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

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

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

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...

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

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

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

{\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...

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

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...

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...

} 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...

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

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

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...

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

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...

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...

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

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"...

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

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

probability distributions Infinite divisibility (probability) Bernoulli distribution Binomial distribution Cauchy distribution Erlang distribution Exponential...

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

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...

{\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...

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