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)
.withArith:
logical: used internally to issue warnings as to interpretation of arithmetics
.withSim:
logical: used internally to issue warnings as to accuracy
.logExact:
logical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function
.lowerExact:
logical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function

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 2.1.3 Index]