Cauchy-class | R Documentation |
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
Objects can be created by calls of the form Cauchy(location, scale)
.
This object is a Cauchy distribution.
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
Symmetry
object of class "DistributionSymmetry"
;
used internally to avoid unnecessary calculations.
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@uni-oldenburg.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.
## in RStudio or Jupyter IRKernel, use q.l(.)(.) instead of q(.)(.)
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")
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