DiscreteDistribution-class {distr}R Documentation

Class "DiscreteDistribution"

Description

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 from the Class

Objects can be created by calls of the form new("DiscreteDistribution", r, d, p, q). The result of this call is a discrete distribution.

Slots

img:
Object of class "Reals": the space of the image of this distribution which has dimension 1 and the name "Real Space"
param:
Object of class "Parameter": the parameter of this distribution, having only the slot name "Parameter of a discrete distribution"
r:
Object of class "function": generates random numbers
d:
Object of class "function": density/probability function
p:
Object of class "function": cumulative distribution function
q:
Object of class "function": quantile function
support:
Object of class "numeric": a (sorted) vector containing the support of the discrete density function

Extends

Class "UnivariateDistribution", directly.
Class "Distribution", by class "UnivariateDistribution".

Methods

initialize
signature(.Object = "DiscreteDistribution"): initialize method
Math
signature(x = "DiscreteDistribution"): application of a mathematical function, e.g. sin or exp (does not work with log!), to this discrete distribution
-
signature(e1 = "DiscreteDistribution"): application of `-' to this discrete distribution
*
signature(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.
support
signature(object = "DiscreteDistribution"): returns the support
plot
signature(object = "DiscreteDistribution"): plots density, cumulative distribution and quantile function

Note

Working with a computer, we use a finite interval as support which carries at least mass 1-TruncQuantile.

Author(s)

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@uni-bayreuth.de

See Also

Parameter-class UnivariateDistribution-class Binom-class Dirac-class Geom-class Hyper-class Nbinom-class Pois-class AbscontDistribution-class Reals-class RtoDPQ.d

Examples

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.

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