AbscontDistribution-class {distr} | R Documentation |
The AbscontDistribution
-class is the mother-class of the classes Beta
, Cauchy
,
Chisq
, Exp
, F
, Gammad
, Lnorm
, Logis
, Norm
, T
, Unif
and
Weibull
. Further absolutely continuous distributions can be defined either by declaration of
own random number generator, density, cumulative distribution and quantile functions, or as result of a
convolution of two absolutely continuous distributions or by application of a mathematical operator to an absolutely
continuous distribution. An additional way is, to specify only the random number generator. The function RtoDPQ
then
approximates the three remaining slots d, p and q by random sampling.
Objects can be created by calls of the form new("AbscontDistribution", r, d, p, q)
.
The result of this call is an absolutely continuous distribution.
img
:"Reals"
: the space of the image of this distribution which has dimension 1
and the name "Real Space" param
:"Parameter"
: the parameter of this distribution, having only
the slot name "Parameter of an absolutely continuous distribution" r
:"function"
: generates random numbersd
:"function"
: density functionp
:"function"
: cumulative distribution functionq
:"function"
: quantile function
Class "UnivariateDistribution"
, directly.
Class "Distribution"
, by class "UnivariateDistribution"
.
signature(.Object = "AbscontDistribution")
: initialize method signature(x = "AbscontDistribution")
: application of a mathematical function, e.g. sin
or
exp
(does not work with log
!), to this absolutely continouos distributionsignature(e1 = "AbscontDistribution")
: application of `-' to this absolutely continuous distributionsignature(e1 = "AbscontDistribution", e2 = "numeric")
: multiplication of this absolutely continuous
distribution by an object of class `numeric'signature(e1 = "AbscontDistribution", e2 = "numeric")
: division of this absolutely continuous
distribution by an object of class `numeric'signature(e1 = "AbscontDistribution", e2 = "numeric")
: addition of this absolutely continuous
distribution to an object of class `numeric'signature(e1 = "AbscontDistribution", e2 = "numeric")
: subtraction of an object of class `numeric' from
this absolutely continuous distribution signature(e1 = "numeric", e2 = "AbscontDistribution")
: multiplication of this absolutely continuous
distribution by an object of class `numeric'signature(e1 = "numeric", e2 = "AbscontDistribution")
: addition of this absolutely continuous
distribution to an object of class `numeric'signature(e1 = "numeric", e2 = "AbscontDistribution")
: subtraction of this absolutely continuous
distribution from an object of class `numeric'signature(e1 = "AbscontDistribution", e2 = "AbscontDistribution")
: Convolution of two absolutely
continuous distributions. The slots p, d and q are approximated by grids.signature(e1 = "AbscontDistribution", e2 = "AbscontDistribution")
: Convolution of two absolutely
continuous distributions. The slots p, d and q are approximated by grids.signature(object = "AbscontDistribution")
: plots density, cumulative distribution and quantile
function
Thomas Stabla statho3@web.de,
Florian Camphausen fcampi@gmx.de,
Peter Ruckdeschel Peter.Ruckdeschel@uni-bayreuth.de,
Matthias Kohl Matthias.Kohl@stamats.de
Parameter-class
UnivariateDistribution-class
Beta-class
Cauchy-class
Chisq-class
Exp-class
Fd-class
Gammad-class
Lnorm-class
Logis-class
Norm-class
Td-class
Unif-class
Weibull-class
DiscreteDistribution-class
Reals-class
RtoDPQ
N = Norm() # N is a normal distribution with mean=0 and sd=1. E = Exp() # E is an exponential distribution with rate=1. A1 = E+1 # a new absolutely continuous distributions with exact slots d, p, q A2 = A1*3 # a new absolutely continuous distributions with exact slots d, p, q A3 = N*0.9 + E*0.1 # a new absolutely continuous distribution with approximated slots d, p, q r(A3)(1) # one random number generated from this distribution, e.g. -0.7150937 d(A3)(0) # The (approximated) density for x=0 is 0.4379882. p(A3)(0) # The (approximated) probability that x <= 0 is 0.4562021. q(A3)(.1) # The (approximated) 10 percent quantile is 0.1.