Class "Cauchy"
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.
imgObject of class "Reals": The domain of this distribution has got dimension 1
and the name "Real Space".
paramObject of class "CauchyParameter": the parameter of this distribution (location and scale),
declared at its instantiation
rObject of class "function": generates random numbers (calls function rcauchy)
dObject of class "function": density function (calls function dcauchy)
pObject of class "function": cumulative function (calls function pcauchy)
qObject of class "function": inverse of the cumulative function (calls function qcauchy)
.withArithlogical: used internally to issue warnings as to interpretation of arithmetics
.withSimlogical: used internally to issue warnings as to accuracy
.logExactlogical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function
.lowerExactlogical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function
Symmetryobject 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
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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