DiscreteDistribution-class {distr} | R Documentation |
The DiscreteDistribution
-class is the mother-class of the classes Binom
, Dirac
,
Geom
, Hyper
, Nbinom
and Poisson
. Further discrete distributions can be defined either by
declaration of own random number generator, density and cumulative distribution and quantile functions, or as result of a
convolution of two discrete distributions or by application of a mathematical operator to a discrete distribution. An
additional way is, to specify only the random number generator. The function RtoDPQ.d
then approximates the three
remaining slots d
, p
and q
by random sampling.
Objects can be created by calls of the form new("DiscreteDistribution", r, d, p, q)
.
The result of this call is a discrete 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 a discrete distribution" r
:"function"
: generates random numbersd
:"function"
: density/probability functionp
:"function"
: cumulative distribution functionq
:"function"
: quantile functionsupport
:"numeric"
: a (sorted) vector containing the support of the discrete
density function
Class "UnivariateDistribution"
, directly.
Class "Distribution"
, by class "UnivariateDistribution"
.
signature(.Object = "DiscreteDistribution")
: initialize method signature(x = "DiscreteDistribution")
: application of a mathematical function, e.g. sin
or
exp
(does not work with log
!), to this discrete distributionsignature(e1 = "DiscreteDistribution")
: application of `-' to this discrete distributionsignature(e1 = "DiscreteDistribution", e2 = "numeric")
: multiplication of this discrete distribution
by an object of class `numeric'signature(e1 = "DiscreteDistribution", e2 = "numeric")
: division of this discrete distribution
by an object of class `numeric'signature(e1 = "DiscreteDistribution", e2 = "numeric")
: addition of this discrete distribution
to an object of class `numeric'signature(e1 = "DiscreteDistribution", e2 = "numeric")
: subtraction of an object of class `numeric'
from this discrete distribution signature(e1 = "numeric", e2 = "DiscreteDistribution")
: multiplication of this discrete distribution
by an object of class `numeric'signature(e1 = "numeric", e2 = "DiscreteDistribution")
: addition of this discrete distribution
to an object of class `numeric'signature(e1 = "numeric", e2 = "DiscreteDistribution")
: subtraction of this discrete distribution
from an object of class `numeric'signature(e1 = "DiscreteDistribution", e2 = "DiscreteDistribution")
: Convolution of two discrete
distributions. The slots p, d and q are approximated by grids.signature(e1 = "DiscreteDistribution", e2 = "DiscreteDistribution")
: Convolution of two discrete
distributions. The slots p, d and q are approximated by grids.signature(object = "DiscreteDistribution")
: returns the supportsignature(object = "DiscreteDistribution")
: plots density, cumulative distribution and quantile
function Working with a computer, we use a finite interval as support which carries at least mass 1-TruncQuantile.
Thomas Stabla Thomas.Stabla@uni-bayreuth.de,
Florian Camphausen Florian.Camphausen@uni-bayreuth.de,
Peter Ruckdeschel Peter.Ruckdeschel@uni-bayreuth.de,
Matthias Kohl Matthias.Kohl@stamats.de
Parameter-class
UnivariateDistribution-class
Binom-class
Dirac-class
Geom-class
Hyper-class
Nbinom-class
Pois-class
AbscontDistribution-class
Reals-class
RtoDPQ.d
B = Binom(prob=0.1,size=10) # B is a Binomial distribution with prob=0.1 and size=10. P = Pois(lambda=1) # P is a Poisson distribution with lambda=1. D1 = B+1 # a new discrete distributions with exact slots d, p, q D2 = D1*3 # a new discrete distributions with exact slots d, p, q D3 = B+P # a new discrete distributions with approximated slots d, p, q D4 = D1+P # a new discrete distributions with approximated slots d, p, q support(D4) # the (approximated) support of this distribution is 1, 2, ..., 21 r(D4)(1) # one random number generated from this distribution, e.g. 4 d(D4)(1) # The (approximated) density for x=1 is 0.1282716. p(D4)(1) # The (approximated) probability that x<=1 is 0.1282716. q(D4)(.5) # The (approximated) 50 percent quantile is 3.