Cauchy-class {distr} | R Documentation |
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 can be created by calls of the form Cauchy(location, scale)
.
This object is a Cauchy distribution.
img
:"Reals"
: The domain of this distribution has got dimension 1
and the name "Real Space". param
:"CauchyParameter"
: the parameter of this distribution (location and scale),
declared at its instantiation r
:"function"
: generates random numbers (calls function rcauchy
)d
:"function"
: density function (calls function dcauchy
)p
:"function"
: cumulative function (calls function pcauchy
)q
:"function"
: inverse of the cumulative function (calls function qcauchy
)
Class "AbscontDistribution"
, directly.
Class "UnivariateDistribution"
, by class "AbscontDistribution"
.
Class "Distribution"
, by class "AbscontDistribution"
.
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
.
signature(.Object = "Cauchy")
: initialize method signature(object = "Cauchy")
: returns the slot location
of the parameter of the distribution signature(object = "Cauchy")
: modifies the slot location
of the parameter of the distribution signature(object = "Cauchy")
: returns the slot scale
of the parameter of the distribution 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
Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel Peter.Ruckdeschel@itwm.fraunhofer.de,
Matthias Kohl Matthias.Kohl@stamats.de
CauchyParameter-class
AbscontDistribution-class
Reals-class
rcauchy
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")