# Cauchy-class

From distr v2.3.1
by Peter Ruckdeschel

##### 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

##### See Also

`CauchyParameter-class`

`AbscontDistribution-class`

`Reals-class`

`rcauchy`

##### 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 2.3.1, License: LGPL-3*

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