with a Cauchy distribution, then Y = exp(X) has a log-Cauchy distribution; likewise, if Y has a log-Cauchy distribution, then X = log(Y) has a Cauchy distribution...

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

distribution The log-Cauchy distribution The log-Laplace distribution The log-logistic distribution The log-metalog distribution, which is highly shape-flexile...

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

the standardized Student's t-distribution. If ν = 1 {\displaystyle \nu =1} then the distribution is a log-Cauchy distribution. As ν {\displaystyle \nu }...

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...

1 if log 1 ≤ log  x < log 2, or starts with 9 if log 9 ≤ log x < log 10. The interval [log 1, log 2] is much wider than the interval [log 9, log 10] (0...

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...

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

{\text{Beta}}(\alpha ,\beta )} , then Y = log ⁡ X 1 − X {\displaystyle Y=\log {\frac {X}{1-X}}} has a generalized logistic distribution, with density σ ( y ) α σ (...

In mathematics, the Cauchy condensation test, named after Augustin-Louis Cauchy, is a standard convergence test for infinite series. For a non-increasing...

such distribution found is π(N) ~ ⁠N/log(N)⁠, where π(N) is the prime-counting function (the number of primes less than or equal to N) and log(N) is...

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

\beta >0} . This is in contrast with the Cauchy distribution for which the mean and variance do not exist. In the log pdf plots shown here, the type IV tails...

\leq 2} Extreme randomness: all moments are infinite, e.g. the log-Cauchy distribution Wild randomness has applications outside financial markets, e.g...

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

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

or the log_gamma function in Fortran 2008 and later. Some computing languages provide built-in functions to evaluate the Poisson distribution, namely...

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

function to be log-concave. The following distributions are non-log-concave for all parameters: the Student's t-distribution, the Cauchy distribution, the Pareto...

I) Beta prime distribution (type VI) Cauchy distribution (type IV) Chi-squared distribution (type III) Continuous uniform distribution (limit of type...

Local regression Log-Cauchy distribution Log-Laplace distribution Log-normal distribution Log-linear analysis Log-linear model Log-linear modeling –...

method, which uses a log transformation to obtain a test statistic which has a chi-squared distribution under the null, the Cauchy combination test uses...

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

developed as power series. The simple cases are as follows: ν = 1 (Cauchy distribution) Q ( p ) = tan ⁡ ( π ( p − 1 / 2 ) ) {\displaystyle Q(p)=\tan(\pi...

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...

_{k\log(p)}(dx)} Other "power-law" distributions Cauchy distribution Lévy distribution Lévy skew alpha-stable distribution Pareto distribution Zipf's law Zipf–Mandelbrot...

has the Lévy distribution as a limit.) The length of the path followed by a photon in a turbid medium follows the Lévy distribution. A Cauchy process can...

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