# Cauchy-class

0th

Percentile

##### Class "Cauchy"

The Cauchy distribution with location $l$, by default $=0$, and scale $s$ , by default $=1$,has density $$f(x) = \frac{1}{\pi s} \left( 1 + \left(\frac{x - l}{s}\right)^2 \right)^{-1}$$ for all $x$. C.f. rcauchy

Keywords
distribution
##### Objects from the Class

Objects can be created by calls of the form Cauchy(location, scale). This object is a Cauchy distribution.

##### Extends

Class "AbscontDistribution", directly. Class "UnivariateDistribution", by class "AbscontDistribution". Class "Distribution", by class "AbscontDistribution".

##### Is-Relations

By means of setIs, R knows'' that a distribution object obj of class "Cauchy" with location 0 and scale 1 also is a T distribution with parameters df = 1, ncp = 0.

##### concept

• absolutely continuous distribution
• Cauchy distribution
• T(1) distribution
• S4 distribution class
• generating function

CauchyParameter-class AbscontDistribution-class Reals-class rcauchy

##### Aliases
• Cauchy-class
• Cauchy
• initialize,Cauchy-method
##### Examples
C <- Cauchy(location = 1, scale = 1) # C is a Cauchy distribution with location=1 and scale=1.
r(C)(1) # one random number generated from this distribution, e.g. 4.104603
d(C)(1) # Density of this distribution is 0.3183099 for x=1.
p(C)(1) # Probability that x<1 is 0.5.
q(C)(.1) # Probability that x<-2.077684 is 0.1.
location(C) # location of this distribution is 1.
location(C) <- 2 # location of this distribution is now 2.
is(C,"Td") # no
C0 <- Cauchy() # standard, i.e. location = 0, scale = 1
is(C0,"Td") # yes
as(C0,"Td")
Documentation reproduced from package distr, version 2.2.3, License: LGPL-3

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