The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz...
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statistics, a wrapped Cauchy distribution is a wrapped probability distribution that results from the "wrapping" of the Cauchy distribution around the unit...
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log-Cauchy distribution is a probability distribution of a random variable whose logarithm is distributed in accordance with a Cauchy distribution. If...
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Breit–Wigner distribution may refer to: Cauchy distribution, also known as the Lorentz distribution or the (non-relativistic) Breit–Wigner distribution Relativistic...
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Mises distribution The wrapped normal distribution The wrapped exponential distribution The wrapped Lévy distribution The wrapped Cauchy distribution The...
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{\displaystyle \ \nu =1\ } the Student's t distribution t ν {\displaystyle t_{\nu }} becomes the standard Cauchy distribution, which has very "fat" tails; whereas...
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Pi (section Cauchy distribution and potential theory)
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...
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Lorentzian may refer to Cauchy distribution, also known as the Lorentz distribution, Lorentzian function, or Cauchy–Lorentz distribution Lorentz transformation...
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A normal distribution is sometimes informally called a bell curve. However, many other distributions are bell-shaped (such as the Cauchy, Student's...
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normal distribution extreme events are less likely than for fat-tailed distributions. Fat-tailed distributions such as the Cauchy distribution (and all...
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In mathematics, the Cauchy principal value, named after Augustin-Louis Cauchy, is a method for assigning values to certain improper integrals which would...
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condition Cauchy's convergence test Cauchy (crater) Cauchy determinant Cauchy distribution Cauchy's equation Cauchy–Euler equation Cauchy's functional...
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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...
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student t distribution, the skewed Cauchy distribution, the Laplace distribution, the uniform distribution, the normal distribution, and the Cauchy distribution...
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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...
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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...
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} 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...
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distribution, and α = 1 {\displaystyle \alpha =1} to the Cauchy distribution. The distributions have undefined variance for α < 2 {\displaystyle \alpha...
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Residue theorem (redirect from Cauchy residue theorem)
In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions...
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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...
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Cauchy–Davenport theorem Cauchy determinant Cauchy distribution Log-Cauchy distribution Wrapped Cauchy distribution Cauchy elastic material Cauchy's equation...
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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"...
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generalisation of the Laplace distribution to function spaces Cauchy distribution, also called the "Lorentzian distribution", ie the Fourier transform of...
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Benford's law (redirect from Benford distribution)
distributions (the Cauchy distribution) obey Benford's law. Although the half-normal distribution does not obey Benford's law, the ratio distribution...
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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...
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the log-gamma distribution; the Fréchet distribution; the q-Gaussian distribution; the log-Cauchy distribution, sometimes described as having a "super-heavy...
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robustness and higher efficiency for mixed distributions and heavy-tailed distribution (like the Cauchy distribution), at the cost of lower efficiency for...
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In mathematics, Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a...
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Dirac delta function (redirect from Dirac delta distribution)
function (infinitesimal version of Cauchy distribution) explicitly appears in an 1827 text of Augustin-Louis Cauchy. Siméon Denis Poisson considered the...
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Expected value (category Theory of probability distributions)
Such subtleties can be seen concretely if the distribution of X is given by the Cauchy distribution Cauchy(0, π), so that f(x) = (x2 + π2)−1. It is straightforward...
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