Cauchy-class {distr}R Documentation

Class "Cauchy"

Description

The Cauchy distribution with location l, by default =0, and scale s , by default =1,has density

f(x) = 1 / (pi s (1 + ((x-l)/s)^2))

for all x. C.f. rcauchy

Objects from the Class

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

Slots

img:
Object of class "Reals": The domain of this distribution has got dimension 1 and the name "Real Space".
param:
Object of class "CauchyParameter": the parameter of this distribution (location and scale), declared at its instantiation
r:
Object of class "function": generates random numbers (calls function rcauchy)
d:
Object of class "function": density function (calls function dcauchy)
p:
Object of class "function": cumulative function (calls function pcauchy)
q:
Object of class "function": inverse of the cumulative function (calls function qcauchy)

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.

Methods

initialize
signature(.Object = "Cauchy"): initialize method
location
signature(object = "Cauchy"): returns the slot location of the parameter of the distribution
location<-
signature(object = "Cauchy"): modifies the slot location of the parameter of the distribution
scale
signature(object = "Cauchy"): returns the slot scale of the parameter of the distribution
scale<-
signature(object = "Cauchy"): modifies the slot scale of the parameter of the distribution
+
signature(e1 = "Cauchy", e2 = "Cauchy"): For the Cauchy distribution the exact convolution formula is implemented thereby improving the general numerical approximation.
*
signature(e1 = "Cauchy", e2 = "numeric")
+
signature(e1 = "Cauchy", e2 = "numeric"): For the Cauchy location scale family we use its closedness under affine linear transformations.

further arithmetic methods see operators-methods

Author(s)

Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de,
Matthias Kohl Matthias.Kohl@stamats.de

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") 

[Package distr version 2.0.6 Index]