Class "LatticeDistribution"

Description

The LatticeDistribution-class is the mother-class of the classes Binom, Dirac, Geom, Hyper, Nbinom and Poisson. It formalizes a distribution on a regular affine linear lattice.

Objects from the Class

The usual way to generate objects of class LatticeDistribution is to call the generating function LatticeDistribution.
Somewhat more flexible, but also proner to inconsistencies is a call to new("LatticeDistribution"), where you may explicitly specify random number generator, (counting) density, cumulative distribution and quantile functions. For conveniance, in this call to new("LatticeDistribution"), an additional possibility is to only specify the random number generator. The function RtoDPQ.d then approximates the three remaining slots d, p and q by random sampling.

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": (counting) 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

lattice

Object of class "Lattice": the lattice generating the support.

.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.

Extends

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

Methods

initialize

signature(.Object = "LatticeDistribution"): initialize method

-

signature(e1 = "LatticeDistribution"): application of ‘-’ to this lattice distribution

*

signature(e1 = "LatticeDistribution", e2 = "numeric"): multiplication of this lattice distribution by an object of class ‘numeric’

/

signature(e1 = "LatticeDistribution", e2 = "numeric"): division of this lattice distribution by an object of class ‘numeric’

+

signature(e1 = "LatticeDistribution", e2 = "numeric"): addition of this lattice distribution to an object of class ‘numeric’

-

signature(e1 = "LatticeDistribution", e2 = "numeric"): subtraction of an object of class ‘numeric’ from this lattice distribution

*

signature(e1 = "numeric", e2 = "LatticeDistribution"): multiplication of this lattice distribution by an object of class ‘numeric’

+

signature(e1 = "numeric", e2 = "LatticeDistribution"): addition of this lattice distribution to an object of class ‘numeric’

-

signature(e1 = "numeric", e2 = "LatticeDistribution"): subtraction of this lattice distribution from an object of class ‘numeric’

+

signature(e1 = "LatticeDistribution", e2 = "LatticeDistribution"): Convolution of two lattice distributions. Slots p, d and q are approximated by grids.

-

signature(e1 = "LatticeDistribution", e2 = "LatticeDistribution"): Convolution of two lattice distributions. The slots p, d and q are approximated by grids.

sqrt

signature(x = "LatticeDistribution"): exact image distribution of sqrt(x).

lattice

accessor method to the corresponding slot.

coerce

signature(from = "LatticeDistribution", to = "DiscreteDistribution"): coerces an object from "LatticeDistribution" to "DiscreteDistribution" thereby cancelling out support points with probability 0.

Internal subclass "AffLinLatticeDistribution"

To enhance accuracy of several functionals on distributions, mainly from package distrEx, there is an internally used (but exported) subclass "AffLinLatticeDistribution" which has extra slots a, b (both of class "numeric"), and X0 (of class "LatticeDistribution"), to capture the fact that the object has the same distribution as a * X0 + b. This is the class of the return value of methods

-

signature(e1 = "LatticeDistribution")

*

signature(e1 = "LatticeDistribution", e2 = "numeric")

/

signature(e1 = "LatticeDistribution", e2 = "numeric")

+

signature(e1 = "LatticeDistribution", e2 = "numeric")

-

signature(e1 = "LatticeDistribution", e2 = "numeric")

*

signature(e1 = "numeric", e2 = "LatticeDistribution")

+

signature(e1 = "numeric", e2 = "LatticeDistribution")

-

signature(e1 = "numeric", e2 = "LatticeDistribution")

-

signature(e1 = "AffLinLatticeDistribution")

*

signature(e1 = "AffLinLatticeDistribution", e2 = "numeric")

/

signature(e1 = "AffLinLatticeDistribution", e2 = "numeric")

+

signature(e1 = "AffLinLatticeDistribution", e2 = "numeric")

-

signature(e1 = "AffLinLatticeDistribution", e2 = "numeric")

*

signature(e1 = "numeric", e2 = "AffLinLatticeDistribution")

+

signature(e1 = "numeric", e2 = "AffLinLatticeDistribution")

-

signature(e1 = "numeric", e2 = "AffLinLatticeDistribution")

There is also an explicit coerce-method from class "AffLinLatticeDistribution" to class "AffLinDiscreteDistribution" which cancels out support points with probability 0.

Note

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

Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

See Also

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

Examples

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B <- Binom(prob = 0.1,size = 10) # B is a Binomial distribution w/ prob=0.1 and size=10.
P <- Pois(lambda = 1) # P is a Poisson distribution with lambda = 1.
D1 <- B+1 # a new Lattice distributions with exact slots d, p, q
D2 <- D1*3 # a new Lattice distributions with exact slots d, p, q
D3 <- B+P # a new Lattice distributions with approximated slots d, p, q
D4 <- D1+P # a new Lattice 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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